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Celestial holography from Chiral strings: In this paper, we studied the relationship between celestial holography and
chiral strings. Chiral strings differ from the usual string theory by a change
of boundary conditions on the string propagators. It is shown that chiral
strings would reproduce graviton amplitudes and could serve as an alternative
description of Einstein's gravity. Celestial holography is a proposed duality
between gravity in asymptotically flat space-time and a CFT living on its
conformal boundary. Since both are CFT descriptions of gravity, we investigate
the potential connection between these two formalisms. In this paper, we find
that both the energetic as well as conformal soft theorems could be derived
from the OPEs of vertex operators of chiral strings. All operators in the CCFT
can be described by Mellin transforming the vertex operators in the chiral
string theories, and the OPE coefficients of CCFT can also be obtained from the
world-sheet description.
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Distinguishing Random and Black Hole Microstates: This is an expanded version of the short report [Phys. Rev. Lett. 126, 171603
(2021)], where the relative entropy was used to distinguish random states drawn
from the Wishart ensemble as well as black hole microstates. In this work, we
expand these ideas by computing many generalizations including the Petz R\'enyi
relative entropy, sandwiched R\'enyi relative entropy, fidelities, and trace
distances. These generalized quantities are able to teach us about new
structures in the space of random states and black hole microstates where the
von Neumann and relative entropies were insufficient. We further generalize to
generic random tensor networks where new phenomena arise due to the locality in
the networks. These phenomena sharpen the relationship between holographic
states and random tensor networks. We discuss the implications of our results
on the black hole information problem using replica wormholes, specifically the
state dependence (hair) in Hawking radiation. Understanding the differences
between Hawking radiation of distinct evaporating black holes is an important
piece of the information problem that was not addressed by entropy calculations
using the island formula. We interpret our results in the language of quantum
hypothesis testing and the subsystem eigenstate thermalization hypothesis
(ETH), deriving that chaotic (including holographic) systems obey subsystem ETH
for all subsystems less than half the total system size.
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U(n) Vector Bundles on Calabi-Yau Threefolds for String Theory
Compactifications: An explicit description of the spectral data of stable U(n) vector bundles on
elliptically fibered Calabi-Yau threefolds is given, extending previous work of
Friedman, Morgan and Witten. The characteristic classes are computed and it is
shown that part of the bundle cohomology vanishes. The stability and the
dimension of the moduli space of the U(n) bundles are discussed. As an
application, it is shown that the U(n) bundles are capable to solve the basic
topological constraints imposed by heterotic string theory. Various explicit
solutions of the Donaldson-Uhlenbeck-Yau equation are given. The heterotic
anomaly cancellation condition is analyzed; as a result an integral change in
the number of fiber wrapping five-branes is found. This gives a definite
prediction for the number of three-branes in a dual F-theory model. The
net-generation number is evaluated, showing more flexibility compared with the
SU(n) case.
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Modelling quantum black hole: Novel bound states are obtained for manifolds with singular potentials. These
singular potentials require proper boundary conditions across boundaries. The
number of bound states match nicely with what we would expect for black holes.
Also they serve to model membrane mechanism for the black hole horizons in
simpler contexts. The singular potentials can also mimic expanding boundaries
elegantly, there by obtaining appropriately tuned radiation rates.
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Canonical quantization of the WZW model with defects and Chern-Simons
theory: We perform canonical quantization of the WZW model with defects and
permutation branes. We establish symplectomorphism between phase space of WZW
model with $N$ defects on cylinder and phase space of Chern-Simons theory on
annulus times $R$ with $N$ Wilson lines, and between phase space of WZW model
with $N$ defects on strip and Chern-Simons theory on disc times $R$ with $N+2$
Wilson lines. We obtained also symplectomorphism between phase space of the
$N$-fold product of the WZW model with boundary conditions specified by
permutation branes, and phase space of Chern-Simons theory on sphere with $N$
holes and two Wilson lines.
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Confinement and Flux Attachment: Flux-attached theories are a novel class of lattice gauge theories whose
gauge constraints involve both electric and magnetic operators. Like ordinary
gauge theories, they possess confining phases. Unlike ordinary gauge theories,
their confinement does not imply a trivial gapped vacuum. This paper will offer
three lessons about the confining phases of flux-attached $\mathbb Z_K$
theories in two spatial dimensions. First, on an arbitrary orientable lattice,
flux attachment that satisfies a simple, explicitly derived criterion leads to
a confining theory whose low-energy behavior is captured by an action of a
general Chern-Simons form. Second, on a square lattice, this criterion can be
solved, and all theories that satisfy it can be enumerated. The simplest such
theory has an action given by a difference of two Chern-Simons terms, and it
features a kind of subsystem symmetry that causes its topological entanglement
entropy to behave pathologically. Third, the simplest flux-attached theory on a
square lattice that does not satisfy the above criterion is exactly solvable
when the gauge group is $\mathbb Z_2$. On a torus, its confined phase possesses
a twofold topological degeneracy that stems from a sum over spin structures in
a dual fermionic theory. This makes this flux-attached $\mathbb Z_2$ theory an
appealing candidate for a microscopic description of a $\mathrm U(1)_2$
Chern-Simons theory.
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Duality Symmetric Quantization of Superstring: A general covariant quantization of superparticle, Green-Schwarz superstring
and a supermembrane with manifest supersymmetry and duality symmetry is
proposed. This quantization provides a natural quantum mechanical description
of curved BPS-type backgrounds related to the ultra-short supersymmetry
multiplets. Half-size commuting and anticommuting Killing spinors admitted by
such backgrounds in quantum theory become truncated $\kappa$-symmetry ghosts.
The symmetry of Killing spinors under dualities transfers to the symmetry of
the spectrum of states.
GS superstring in the generalized semi-light-cone gauge can be quantized
consistently in the background of ten-dimensional supersymmetric gravitational
waves. Upon compactification they become supersymmetric electrically charged
black holes, either massive or massless. However, the generalized light-cone
gauge breaks S-duality. We propose a new family of gauges, which we call black
hole gauges. These gauges are suitable for quantization both in flat Minkowski
space and in the black hole background, and they are duality symmetric. As an
example, a manifestly S-duality symmetric black hole gauge is constructed in
terms of the axion-dilaton-electric-magnetic black hole hair. We also suggest
the U-duality covariant class of gauges for type II superstrings.
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Finding $G_2$ Higgs branch of 4D rank 1 SCFTs: The Schur index of the Higgs branch of four-dimensional $\mathcal{N}=2$ SCFTs
is related to the spectrum of non-unitary two-dimensional CFTs. The rank one
case has been shown to lead to the non-unitary CFTs with Deligne-Cvitanovic
(DC) exceptional sequence of Lie groups. We show that a subsequence $(A_0,
A_{\frac{1}{2}}, A_1, A_2, D_4)$ within the non-unitary sequence is related to
a subsequence in the Mathur-Mukhi-Sen (MMS) sequence of unitary theories. We
show that 2D non-unitary $G_2$ theory is related to unitary $E_6$ theory, and
using this result along with the Galois conjugation, we propose that the $G_2$
Higgs branch is a sub-branch of the $E_6$ Higgs branch.
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Exact equilibrium distributions in statistical quantum field theory with
rotation and acceleration: scalar field: We derive a general exact form of the phase space distribution function and
the thermal expectation values of local operators for the free quantum scalar
field at equilibrium with rotation and acceleration in flat space-time without
solving field equations in curvilinear coordinates. After factorizing the
density operator with group theoretical methods, we obtain the exact form of
the phase space distribution function as a formal series in thermal vorticity
through an iterative method and we calculate thermal expectation values by
means of analytic continuation techniques. We separately discuss the cases of
pure rotation and pure acceleration and derive analytic results for the
stress-energy tensor of the massless field. The expressions found agree with
the exact analytic solutions obtained by solving the field equation in suitable
curvilinear coordinates for the two cases at stake and already - or implicitly
- known in literature. In order to extract finite values for the pure
acceleration case we introduce the concept of analytic distillation of a
complex function. For the massless field, the obtained expressions of the
currents are polynomials in the acceleration/temperature ratios which vanish at
$2\pi$, in full accordance with the Unruh effect.
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Exorcizing Ghosts from the Vacuum Spectra in String-inspired Nonlocal
Tachyon Condensation: Tachyon condensation in quantum field theory (QFT) plays a central role in
models of fundamental interactions and cosmology. Inspired by tower truncation
in string field theory, ultraviolet completions were proposed with
infinite-derivative form factors that preclude the appearance of pathological
ghosts in the particle spectrum, contrary to other local higher-derivative
QFT's. However, if the infinite-derivative QFT exhibits other vacua, each of
them has its own spectrum, which is generally not ghost-free: an infinite tower
of ghost-like resonances pops up above the nonlocal scale at tree-level, whose
consistency is unclear. In this article, a new weakly nonlocal deformation of a
generic local QFT is introduced via a Lorentz and gauge covariant star-product
of fields, which is commutative but nonassociative in general. This framework
realizes tachyon condensation without ghosts at the perturbative level, with
applications for spontaneous symmetry breaking.
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Glueballs Mass Spectrum in an Inflationary Braneworld Scenario: We address the issue of glueball masses in a holographic dual field theory on
the boundary of an AdS space deformed by a four-dimensional cosmological
constant. These glueballs are related to scalar and tensorial fluctuations of
the bulk fields on this space. In the Euclidean AdS4 case the allowed masses
are discretized and are related to distinct inflaton masses on a 3-brane with
several states of inflation. We then obtain the e-folds number in terms of the
glueball masses. In the last part we focus on the Lorentzian dS4 case to focus
on the QCD equation of state in dual field theory.
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Spinning strings in AdS_5 x S^5: A worldsheet perspective: We examine the leading Regge string states relevant for semi-classical
spinning string solutions. Using elementary RNS techniques, quadratic terms in
an effective lagrangian are constructed which describe massive NSNS strings in
a space-time with five-form flux. We then examine the specific case of AdS_5 x
S^5, finding the dependence of AdS "energy" (E_0) on spin in AdS (S), spin on
the sphere (J), and orbital angular momentum on the sphere (\nabla_a \nabla^a).
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Collective coordinate quantization of $CP^1$ model coupled to Hopf term
revisited: We show that the system where $CP^1$ model coupled to Hopf term can reveal
fractional spin in a collective coordinate quantization scheme, provided one
makes a transition to physically inequivalent sector within a same solitonic
sector characterized by a nonvanishing topological number
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Supersymmetry breaking, heterotic strings and fluxes: In this paper we consider compactifications of heterotic strings in the
presence of background flux. The background metric is a T^2 fibration over a K3
base times four-dimensional Minkowski space. Depending on the choice of
three-form flux different amounts of supersymmetry are preserved (N=2,1,0). For
supersymmetric solutions unbroken space-time supersymmetry determines all
background fields except one scalar function which is related to the dilaton.
The heterotic Bianchi identity gives rise to a differential equation for the
dilaton which we discuss in detail for solutions preserving an N=2
supersymmetry. In this case the differential equation is of Laplace type and as
a result the solvability is guaranteed.
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T-Branes, String Junctions, and 6D SCFTs: Recent work on 6D superconformal field theories (SCFTs) has established an
intricate correspondence between certain Higgs branch deformations and
nilpotent orbits of flavor symmetry algebras associated with T-branes. In this
paper, we return to the stringy origin of these theories and show that many
aspects of these deformations can be understood in terms of simple
combinatorial data associated with multi-pronged strings stretched between
stacks of intersecting 7-branes in F-theory. This data lets us determine the
full structure of the nilpotent cone for each semi-simple flavor symmetry
algebra, and it further allows us to characterize symmetry breaking patterns in
quiver-like theories with classical gauge groups. An especially helpful feature
of this analysis is that it extends to "short quivers" in which the breaking
patterns from different flavor symmetry factors are correlated.
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On zero modes of the eleven dimensional superstring: It is shown that recently pointed out by Berkovits on-shell degrees of
freedom of the D=11 superstring do not make contributions into the quantum
states spectrum of the theory. As a consequence, the spectrum coincides with
that of the D=10 type IIA superstring.
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Non-commutative mechanics and Exotic Galilean symmetry: In order to derive a large set of Hamiltonian dynamical systems, but with
only first order Lagrangian, we resort to the formulation in terms of
Lagrange-Souriau 2-form formalism. A wide class of systems derived in different
phenomenological contexts are covered. The non-commutativity of the particle
position coordinates are a natural consequence. Some explicit examples are
considered.
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Integrated correlators with a Wilson line in $\mathcal{N}=4$ SYM: In the context of integrated correlators in $\mathcal{N}=4$ SYM, we study the
2-point functions of local operators with a superconformal line defect.
Starting from the mass-deformed $\mathcal{N}=2^*$ theory in presence of a
$\frac{1}{2}$-BPS Wilson line, we exploit the residual superconformal symmetry
after the defect insertion, and show that the massive deformation corresponds
to integrated insertions of the superconformal primaries belonging to the
stress tensor multiplet with a specific integration measure which is explicitly
derived after enforcing the superconformal Ward identities. Finally, we show
how the Wilson line integrated correlator can be computed by the
$\mathcal{N}=2^*$ Wilson loop vacuum expectation value on a 4-sphere in terms
of a matrix model using supersymmetric localization. In particular, we
reformulate previous matrix model computations by making use of recursion
relations and Bessel kernels, providing a direct link with more general
localization computations in $\mathcal{N}=2$ theories.
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The transfer matrix method in four-dimensional causal dynamical
triangulations: The Causal Dynamical Triangulation model of quantum gravity (CDT) is a
proposition to evaluate the path integral over space-time geometries using a
lattice regularization with a discrete proper time and geometries realized as
simplicial manifolds. The model admits a Wick rotation to imaginary time for
each space-time configuration. Using computer simulations we determined the
phase structure of the model and discovered that it predicts a de Sitter phase
with a four-dimensional spherical semi-classical background geometry. The model
has a transfer matrix, relating spatial geometries at adjacent (discrete
lattice) times. The transfer matrix uniquely determines the theory. We show
that the measurements of the scale factor of the (CDT) universe are well
described by an effective transfer matrix where the matrix elements are
labelled only by the scale factor. Using computer simulations we determine the
effective transfer matrix elements and show how they relate to an effective
minisuperspace action at all scales.
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On Domain Walls of N=1 Supersymmetric Yang-Mills in Four Dimensions: We study the BPS domain walls of supersymmetric Yang-Mills for arbitrary
gauge group. We describe the degeneracies of domain walls interpolating between
arbitrary pairs of vacua. A recently proposed large N duality sheds light on
various aspects of such domain walls. In particular, for the case of G = SU(N)
the domain walls correspond to wrapped D-branes giving rise to a 2+1
dimensional U(k) gauge theory on the domain wall with a Chern-Simons term of
level N. This leads to a counting of BPS degeneracies of domain walls in
agreement with expected results.
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Strongly Topological Interactions of Tensionless Strings: The tensionless limit of classical string theory may be formulated as a
topological theory on the world-sheet. A vector density carries geometrical
information in place of an internal metric. It is found that path-integral
quantization allows for the definition of several, possibly inequivalent
quantum theories. String amplitudes are constructed from vector densities with
zeroes for each in- or out-going string. It is shown that independence of a
metric in quantum mechanical amplitudes implies that the dependence on such
vector density zeroes is purely topological. For example, there is no need for
integration over their world-sheet positions.
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A Logarithmic Conformal Field Theory Solution For Two Dimensional
Magnetohydrodynamics In Presence of The Alf'ven Effect: When Alf`ven effect is peresent in magnetohydrodynamics one is naturally lead
to consider conformal field theories, which have logarithmic terms in their
correlation functions. We discuss the implications of such logarithmic terms
and find a unique conformal field theory with centeral charge
$c=-\frac{209}{7}$, within the border of the minimal series, which satisfies
all the constraints. The energy espectrum is found to be \newline $E(k)\sim
k^{-\frac{13}{7}} \log{k}$.
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Interacción `Oscilador' de Partículas Relativistas: This is a brief introduction on the graduate level to mechanics of various
spin relativistic particles with oscillatorlike interaction. This mathematical
model proposed by M. Moshinsky could have considerable physical applications
for describing processes mediated by tensor fields and in bound state theory.
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Entanglement Entropy of Topological Orders with Boundaries: In this paper we explore how non trivial boundary conditions could influence
the entanglement entropy in a topological order in 2+1 dimensions. Specifically
we consider the special class of topological orders describable by the quantum
double. We will find very interesting dependence of the entanglement entropy on
the boundary conditions particularly when the system is non-Abelian. Along the
way, we demonstrate a streamlined procedure to compute the entanglement
entropy, which is particularly efficient when dealing with systems with
boundaries. We also show how this method efficiently reproduces all the known
results in the presence of anyonic excitations.
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VOA[M4]: We take a peek at a general program that associates vertex (or, chiral)
algebras to smooth 4-manifolds in such a way that operations on algebras mirror
gluing operations on 4-manifolds and, furthermore, equivalent constructions of
4-manifolds give rise to equivalences (dualities) of the corresponding
algebras.
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DUALITY SYMMETRY GROUP OF TWO DIMENSIONAL HETEROTIC STRING THEORY: The equations of motion of the massless sector of the two dimensional string
theory, obtained by compactifying the heterotic string theory on an eight
dimensional torus, is known to have an affine o(8,24) symmetry algebra
generating an O(8,24) loop group. In this paper we study how various known
discrete S- and T- duality symmetries of the theory are embedded in this loop
group. This allows us to identify the generators of the discrete duality
symmetry group of the two dimensional string theory.
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The Large N 't Hooft Limit of Kazama-Suzuki Model: We consider N=2 Kazama-Suzuki model on CP^N=SU(N+1)/SU(N)xU(1). It is known
that the N=2 current algebra for the supersymmetric WZW model, at level k, is a
nonlinear algebra. The N=2 W_3 algebra corresponding to N=2 was recovered from
the generalized GKO coset construction previously. For N=4, we construct one of
the higher spin currents, in N=2 W_5 algebra, with spins (2, 5/2, 5/2, 3). The
self-coupling constant in the operator product expansion of this current and
itself depends on N as well as k explicitly. We also observe a new higher spin
primary current of spins (3, 7/2, 7/2, 4). From the behaviors of N=2, 4 cases,
we expect the operator product expansion of the lowest higher spin current and
itself in N=2 W_{N+1} algebra. By taking the large (N, k) limit on the various
operator product expansions in components, we reproduce, at the linear order,
the corresponding operator product expansions in N=2 classical
W_{\infty}^{cl}[\lambda] algebra which is the asymptotic symmetry of the higher
spin AdS_3 supergravity found recently.
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Multipolar Expansions for Closed and Open Systems of Relativistic
Particles: Dixon's multipoles for a system of N relativistic positive-energy scalar
particles are evaluated in the rest-frame instant form of dynamics. The Wigner
hyper-planes (intrinsic rest frame of the isolated system) turn out to be the
natural framework for describing multipole kinematics. Classical concepts like
the {\it barycentric tensor of inertia} turn out to be extensible to special
relativity only by means of the quadrupole moments of the isolated system. Two
new applications of the multipole technique are worked out for systems of
interacting particles and fields. In the rest-frame of the isolated system of
either free or interacting positive energy particles it is possible to define a
unique world-line which embodies the properties of the most relevant centroids
introduced in the literature as candidates for the collective motion of the
system. This is no longer true, however, in the case of open subsystems of the
isolated system. While effective mass, 3-momentum and angular momentum in the
rest frame can be calculated from the definition of the {\it subsystem
energy-momentum tensor}, the definitions of effective center of motion and
effective intrinsic spin of the subsystem are not unique. Actually, each of the
previously considered centroids corresponds to a different world-line in the
case of open systems. The pole-dipole description of open subsystems is
compared to their description as effective extended objects. Hopefully, the
technique developed here could be instrumental for the relativistic treatment
of binary star systems in metric gravity.
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Spontaneous symmetry breaking and optimization of functional
renormalization group: The requirement for the absence of spontaneous symmetry breaking in the d=1
dimension has been used to optimize the regulator dependence of functional
renormalization group equations in the framework of the sine-Gordon scalar
field theory. Results obtained by the optimization of this kind were compared
to those of the Litim-Pawlowski and the principle of minimal sensitivity
optimization scenarios. The optimal parameters of the compactly supported
smooth (CSS) regulator, which recovers all major types of regulators in
appropriate limits, have been determined beyond the local potential
approximation, and the Litim limit of the CSS was found to be the optimal
choice.
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Nonperturbative 2D Gravity, Punctured Spheres and $Θ$-Vacua in
String Theories: We consider a model of 2D gravity with the coefficient of the
Einstein-Hilbert action having an imaginary part $\pi/2$. This is equivalent to
introduce a $\Theta$-vacuum structure in the genus expansion whose effect is to
convert the expansion into a series of alternating signs, presumably Borel
summable. We show that the specific heat of the model has a physical behaviour.
It can be represented nonperturbatively as a series in terms of integrals over
moduli spaces of punctured spheres and the sum of the series can be rewritten
as a unique integral over a suitable moduli space of infinitely punctured
spheres. This is an explicit realization \`a la Friedan-Shenker of 2D quantum
gravity. We conjecture that the expansion in terms of punctures and the genus
expansion can be derived using the Duistermaat-Heckman theorem. We briefly
analyze expansions in terms of punctured spheres also for multicritical models.
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New Forms of BRST Symmetry on a Prototypical First-Class System: We scrutinize the many known forms of BRST symmetries, as well as some new
ones, realized within a prototypical first-class system. Similarities and
differences among ordinary BRST, anti-BRST, dual-BRST and anti-dual-BRST
symmetries are highlighted and discussed. We identify a precise
$\mathbb{Z}_4\times\mathbb{Z}_2$ discrete group of symmetries of the ghost
sector, responsible for connecting the various forms of BRST transformations.
Considering a Hamiltonian approach, those symmetries can be interrelated by
canonical transformations among ghost variables. However, the distinguished
characteristic role of the dual BRST symmetries can be fully appreciated within
a gauge-fixed Lagrangian viewpoint. New forms of BRST symmetries are given, a
set generalizing particular ones previously reported in the literature as well
as a brand new unprecedented set. The featured gauge invariant prototypical
first-class system encompasses an extensive class of physical models and sheds
light on previous controversies in the current quantum field theory literature.
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A note on the holography of Chern-Simons matter theories with flavour: We study a three-dimensional N=3 U(N)_k x U(N)_{-k} Chern-Simons matter
theory with flavour, corresponding to the N=6
Aharony-Bergman-Jafferis-Maldacena CSM theory coupled to 2N_f fundamental
fields. The dual holographic description is given by the near-horizon geometry
of N M2-branes at a particular hypertoric geometry M_8. We explicitly construct
the space M_8 and match its isometries to the global symmetries of the field
theory. We also discuss the model in the quenched approximation by embedding
probe D6-branes in AdS_4 x CP^3.
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Review of AdS/CFT Integrability, Chapter II.1: Classical AdS5xS5 string
solutions: We review basic examples of classical string solutions in AdS5xS5. We
concentrate on simplest rigid closed string solutions of circular or folded
type described by integrable 1-d Neumann system but mention also various
generalizations and related open-string solutions.
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The Majid-Ruegg model and the Planck scales: A novel differential calculus with central inner product is introduced for
kappa-Minkowski space. The `bad' behaviour of this differential calculus is
discussed with reference to symplectic quantisation and A-infinity algebras.
Using this calculus in the Schrodinger equation gives two values which can be
compared with the Planck mass and length. This comparison gives an approximate
numerical value for the deformation parameter in kappa-Minkowski space. We
present numerical evidence that there is a potentially observable variation of
propagation speed in the Klein-Gordon equation. The modified equations of
electrodynamics (without a spinor field) are derived from noncommutative
covariant derivatives. We note that these equations suggest that the speed of
light is independent of frequency, in contrast to the KG results (with the
caveat that zero current is not the same as in vacuum). We end with some
philosophical comments on measurement related to quantum theory and gravity
(not necessarily quantum gravity) and noncommutative geometry.
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The Primordial Gravitational Wave Background in String Cosmology: We find the spectrum P(w)dw of the gravitational wave background produced in
the early universe in string theory. We work in the framework of String Driven
Cosmology, whose scale factors are computed with the low-energy effective
string equations as well as selfconsistent solutions of General Relativity with
a gas of strings as source. The scale factor evolution is described by an early
string driven inflationary stage with an instantaneous transition to a
radiation dominated stage and successive matter dominated stage. This is an
expanding string cosmology always running on positive proper cosmic time. A
careful treatment of the scale factor evolution and involved transitions is
made. A full prediction on the power spectrum of gravitational waves without
any free-parameters is given. We study and show explicitly the effect of the
dilaton field, characteristic to this kind of cosmologies. We compute the
spectrum for the same evolution description with three differents approachs.
Some features of gravitational wave spectra, as peaks and asymptotic
behaviours, are found direct consequences of the dilaton involved and not only
of the scale factor evolution. A comparative analysis of different treatments,
solutions and compatibility with observational bounds or detection perspectives
is made.
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Matrix factorisations and permutation branes: The description of B-type D-branes on a tensor product of two N=2 minimal
models in terms of matrix factorisations is related to the boundary state
description in conformal field theory. As an application we show that the D0-
and D2-brane for a number of Gepner models are described by permutation
boundary states. In some cases (including the quintic) the images of the
D2-brane under the Gepner monodromy generate the full charge lattice.
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Defect two-point functions in 6d (2,0) theories: We consider correlation functions in 6d $(2,0)$ theories of two
$\frac{1}{2}$-BPS operators inserted away from a $\frac{1}{2}$-BPS surface
defect. In the large central charge limit the leading connected contribution
corresponds to sums of tree-level Witten diagram in AdS$_7\times$S$^4$ in the
presence of an AdS$_3$ defect. We show that these correlators can be uniquely
determined by imposing only superconformal symmetry and consistency conditions,
eschewing the details of the complicated effective Lagrangian. We explicitly
compute all such two-point functions. The result exhibits remarkable hidden
simplicity.
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Brane-induced Skyrmion on S^3: baryonic matter in holographic QCD: We study baryonic matter in holographic QCD with D4/D8/\bar{D8} multi-D brane
system in type IIA superstring theory. The baryon is described as the
"brane-induced Skyrmion", which is a topologically non-trivial chiral soliton
in the four-dimensional meson effective action induced by holographic QCD. We
employ the "truncated-resonance model" approach for the baryon analysis,
including pion and \rho meson fields below the ultraviolet cutoff scale M_KK
\sim 1GeV, to keep the holographic duality with QCD. We describe the baryonic
matter in large N_c as single brane-induced Skyrmion on the three-dimensional
closed manifold S^3 with finite radius R. The interactions between baryons are
simulated by the curvature of the closed manifold S^3, and the decrease of the
size of S^3 represents the increase of the total baryon-number density in the
medium in this modeling. We investigate the energy density, the field
configuration, the mass and the root-mean-square radius of single baryon on S^3
as the function of its radius R. We find a new picture of "pion dominance" near
the critical density in the baryonic matter, where all the (axial) vector meson
fields disappear and only the pion field survive. We also find the "swelling"
phenomena of the baryons as the precursor of the deconfinement, and propose the
mechanism of the swelling in general context of QCD. The properties of the
deconfinement and the chiral symmetry restoration in the baryonic matter are
examined by taking the proper order parameters. We also compare our
truncated-resonance model with another "instanton" description of the baryon in
holographic QCD, considering the role of cutoff scale M_KK.
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Duality Invariance of Cosmological Solutions with Torsion: We show that for a string moving in a background consisting of maximally
symmetric gravity, dilaton field and second rank antisymmetric tensor field,
the $O(d) \otimes O(d)$ transformation on the vacuum solutions gives
inequivalent solutions that are not maximally symmetric. We then show that the
usual physical meaning of maximal symmetry can be made to remain unaltered even
if torsion is present and illustrate this through two toy models by determining
the torsion fields, the metric and Killing vectors. Finally we show that under
the $O(d) \otimes O(d)$ transformation this generalised maximal symmetry can be
preserved under certain conditions. This is interesting in the context of
string related cosmological backgrounds.
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Bosonic Higher Spin Gravity in any Dimension with Dynamical Two-Form: We first propose an alternative to Vasiliev's bosonic higher spin gravities
in any dimension by factoring out a modified sp(2) gauge algebra. We evidence
perturbative equivalence of the two models, which have the same spectrum of
Fronsdal fields at the linearized level. We then embed the new model into a
flat Quillen superconnection containing two extra master fields in form degrees
one and two; more generally, the superconnection contains additional degrees of
freedom associated to various deformations of the underlying non-commutative
geometry. Finally, we propose that by introducing first-quantized sp(2) ghosts
and duality extending the field content, the Quillen flatness condition can be
unified with the sp(2) gauge conditions into a single flatness condition that
is variational with a Frobenius-Chern-Simons action functional.
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Expanding the Black Hole Interior: Partially Entangled Thermal States in
SYK: We introduce a family of partially entangled thermal states in the SYK model
that interpolates between the thermo-field double state and a pure (product)
state. The states are prepared by a euclidean path integral describing the
evolution over two euclidean time segments separated by a local scaling
operator $\mathcal{O}$. We argue that the holographic dual of this class of
states consists of two black holes with their interior regions connected via a
domain wall, described by the worldline of a massive particle. We compute the
size of the interior region and the entanglement entropy as a function of the
scale dimension of $\mathcal{O}$ and the temperature of each black hole. We
argue that the one-sided bulk reconstruction can access the interior region of
the black hole.
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Uniqueness of supersymmetric AdS$_5$ black holes with $SU(2)$ symmetry: We prove that any supersymmetric solution to five-dimensional minimal gauged
supergravity with $SU(2)$ symmetry, that is timelike outside an analytic
horizon, is a Gutowski-Reall black hole or its near-horizon geometry. The proof
combines a delicate near-horizon analysis with the general form for a K\"ahler
metric with cohomogeneity-1 $SU(2)$ symmetry. We also prove that any timelike
supersymmetric soliton solution to this theory, with $SU(2)$ symmetry and a nut
or a complex bolt, has a K\"ahler base with enhanced $U(1)\times SU(2)$
symmetry, and we exhibit a family of asymptotically AdS$_5/\mathbb{Z}_p$
solitons for $p \geq 3$ with a bolt in this class.
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Non-minimal Maxwell-Modified Gauss-Bonnet Cosmologies: Inflation and
Dark Energy: In this paper we show that power-law inflation can be realized in non-minimal
gravitational coupling of electromagnetic field with a general function of
Gauss-Bonnet invariant. Such a non-minimal coupling may appear due to quantum
corrections. We also consider modified Maxwell-$F(G)$ gravity in which
non-minimal coupling between electromagnetic field and $f(G)$ occur in the
framework of modified Gauss-Bonnet gravity. It is shown that inflationary
cosmology and late-time accelerated expansion of the universe are possible in
such a theory.
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Quantum Lattice Solitons: The number state method is used to study soliton bands for three anharmonic
quantum lattices: i) The discrete nonlinear Schr\"{o}dinger equation, ii) The
Ablowitz-Ladik system, and iii) A fermionic polaron model. Each of these
systems is assumed to have $f$-fold translational symmetry in one spatial
dimension, where $f$ is the number of freedoms (lattice points). At the second
quantum level $(n=2)$ we calculate exact eigenfunctions and energies of pure
quantum states, from which we determine binding energy $(E_{\rm b})$, effective
mass $(m^{*})$ and maximum group velocity $(V_{\rm m})$ of the soliton bands as
functions of the anharmonicity in the limit $f \to \infty$. For arbitrary
values of $n$ we have asymptotic expressions for $E_{\rm b}$, $m^{*}$, and
$V_{\rm m}$ as functions of the anharmonicity in the limits of large and small
anharmonicity. Using these expressions we discuss and describe wave packets of
pure eigenstates that correspond to classical solitons.
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Hamiltonian approach to QCD at finite temperature: A novel approach to the Hamiltonian formulation of quantum field theory at
finite temperature is presented. The temperature is introduced by
compactification of a spatial dimension. The whole finite-temperature theory is
encoded in the ground state on the spatial manifold $S^1 (L) \times
\mathbb{R}^2$ where $L$ is the length of the compactified dimension which
defines the inverse temperature. The approach which is then applied to the
Hamiltonian formulation of QCD in Coulomb gauge to study the chiral phase
transition at finite temperatures.
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Note on Shape Moduli Stabilization, String Gas Cosmology and the
Swampland Criteria: In String Gas Cosmology, the simplest shape modulus fields are naturally
stabilized by taking into account the presence of string winding and momentum
modes. We determine the resulting effective potential for these fields and show
that it obeys the de Sitter conjecture, one of the swampland criteria for
effective field theories to be consistent with superstring theory.
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Gauge theory solitons on noncommutative cylinder: We generalize to noncommutative cylinder the solution generation technique,
originally suggested for gauge theories on noncommutative plane. For this
purpose we construct partial isometry operators and complete set of orthogonal
projectors in the algebra of the cylinder, and an isomorphism between the free
module and its direct sum with the Fock module on the cylinder. We construct
explicitly the gauge theory soliton and evaluate the spectrum of perturbations
about this soliton.
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A Cardy Formula for Three-Point Coefficients: How the Black Hole Got its
Spots: Modular covariance of torus one-point functions constrains the three point
function coefficients of a two dimensional CFT. This leads to an asymptotic
formula for the average value of light-heavy-heavy three point coefficients,
generalizing Cardy's formula for the high energy density of states. The
derivation uses certain asymptotic properties of one-point conformal blocks on
the torus. Our asymptotic formula matches a dual AdS_3 computation of one point
functions in a black hole background. This is evidence that the BTZ black hole
geometry emerges upon course-graining over a suitable family of heavy
microstates.
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Transitions of Orbifold Vacua: We study the global structure of vacua of heterotic strings compactified on
orbifolds $T^4/Z_N$ (N=2,3) in the presence of heterotic 5-branes. Gauge
symmetry breaking associated with orbifold is described by instantons in the
field theory. Phase transition between small instantons and heterotic 5-branes
provides top-down, stringy account to the spectrum and modular invariance
condition. Also it takes us from one vacuum to another by emitting and
absorbing instantons. This means that many vacua with different gauge theory
are in fact connected and are inherited from perturbative vacua. It follows
that there are also transitions among twisted fields, heterotic 5-branes and
instantons.
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Geometrical hierarchies in classical supergravity: We introduce a $N=1$ supergravity model with a very simple hidden sector
coupled to the electroweak gauge and Higgs sectors of the MSSM. At the
classical level, supersymmetry and $SU(2)\times U(1)$ are both spontaneously
broken, with vanishing vacuum energy. Two real flat directions control the two
symmetry-breaking scales $m_{3/2}$ and $m_Z$. The two massless scalars are a
gauge singlet and the standard Higgs boson. All other unobserved particles have
masses of order $m_{3/2}$. This may be a new starting point for studying the
compatibility of naturalness with the observed mass hierarchies.
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Lectures on on Black Holes, Topological Strings and Quantum Attractors
(2.0): In these lecture notes, we review some recent developments on the relation
between the macroscopic entropy of four-dimensional BPS black holes and the
microscopic counting of states, beyond the thermodynamical, large charge limit.
After a brief overview of charged black holes in supergravity and string
theory, we give an extensive introduction to special and very special geometry,
attractor flows and topological string theory, including holomorphic anomalies.
We then expose the Ooguri-Strominger-Vafa (OSV) conjecture which relates
microscopic degeneracies to the topological string amplitude, and review
precision tests of this formula on ``small'' black holes. Finally, motivated by
a holographic interpretation of the OSV conjecture, we give a systematic
approach to the radial quantization of BPS black holes (i.e. quantum
attractors). This suggests the existence of a one-parameter generalization of
the topological string amplitude, and provides a general framework for
constructing automorphic partition functions for black hole degeneracies in
theories with sufficient degree of symmetry.
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Towards the uniqueness of Lifshitz black holes and solitons in New
Massive Gravity: We prove that the z=1 and z=3 Lifshitz black hole solutions of New Massive
Gravity in three dimensions are the only static axisymmetric solutions that can
be cast in a Kerr-Schild form with a seed metric given by the Lifshitz
spacetime. Correspondingly, we study the issue of uniqueness of Lifshitz
solitons when considering an ansatz involving a single metric function. We show
this problem can be mapped to the previous one and that the z=1 and z=1/3
Lifshitz soliton solutions are the only ones within this class. Finally, our
approach suggests for the first time an explanation as to what is special about
those particular values of the dynamical critical exponent z at finite
temperature.
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Quantum gravity in terms of topological observables: We recast the action principle of four dimensional General Relativity so that
it becomes amenable for perturbation theory which doesn't break general
covariance. The coupling constant becomes dimensionless (G_{Newton} \Lambda)
and extremely small 10^{-120}. We give an expression for the generating
functional of perturbation theory. We show that the partition function of
quantum General Relativity can be expressed as an expectation value of a
certain topologically invariant observable. This sets up a framework in which
quantum gravity can be studied perturbatively using the techniques of
topological quantum field theory.
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Thermodynamic implications of some unusual quantum theories: Various deformations of the position-momentum algebras operators have been
proposed. Their implications for single systems like the hydrogen atom or the
harmonic oscillator have been addressed. In this paper we investigate the
consequences of some of these algebras for macroscopic systems. The key point
of our analysis lies in the fact that the modification of the Heisenberg
uncertainty relations present in these theories changes the volume of the
elementary cell in the hamiltonian phase space and so the measure needed to
compute partition functions.
The thermodynamics of a non interacting gas are studied for two members of
the Kempf-Mangano-Mann (K.M.M.) deformations. It is shown that the theory which
exhibits a minimal uncertainty in length predicts a new behavior at high
temperature while the one with a minimal uncertainty in momentum displays
unusual features for huge volumes. In the second model negative pressures are
obtained and mixing two different gases does not necessarily increase the
entropy . This suggests a possible violation of the second law of
thermodynamics. Potential consequences of these models in the evolution of the
early universe are briefly discussed.
Constructing the Einstein model of a solid for the q deformed oscillator, we
find that the subset of eigenstates whose energies are bounded from above leads
to a divergent partition function.
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Dynamical Flavor Symmetry Breaking by a Magnetic Field in $2+1$
Dimensions: It is shown that in $2+1$ dimensions, a constant magnetic field is a strong
catalyst of dynamical flavor symmetry breaking, leading to generating a fermion
dynamical mass even at the weakest attractive interaction between fermions. The
essence of this effect is that in a magnetic field, in $2+1$ dimensions, the
dynamics of fermion pairing is essentially one-dimensional. The effect is
illustrated in the Nambu-Jona-Lasinio model in a magnetic field. The low-energy
effective action in this model is derived and the thermodynamic properties of
the model are considered. The relevance of this effect for planar condensed
matter systems and for $3+1$ dimensional theories at high temperature is
pointed out.
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A Consistent Effective Theory of Long-Wavelength Cosmological
Perturbations: Effective field theory provides a perturbative framework to study the
evolution of cosmological large-scale structure. We investigate the
underpinnings of this approach, and suggest new ways to compute correlation
functions of cosmological observables. We find that, in contrast with quantum
field theory, the appropriate effective theory of classical cosmological
perturbations involves interactions that are nonlocal in time. We describe an
alternative to the usual approach of smoothing the perturbations, based on a
path-integral formulation of the renormalization group equations. This
technique allows for improved handling of short-distance modes that are
perturbatively generated by long-distance interactions.
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Poisson Structure and Moyal Quantisation of the Liouville Theory: The symplectic and Poisson structures of the Liouville theory are derived
from the symplectic form of the SL(2,R) WZNW theory by gauge invariant
Hamiltonian reduction. Causal non-equal time Poisson brackets for a Liouville
field are presented. Using the symmetries of the Liouville theory, symbols of
chiral fields are constructed and their *-products calculated. Quantum
deformations consistent with the canonical quantisation result, and a non-equal
time commutator is given.
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2+1 Dimensional Quantum Gravity as a Gaussian Fermionic System and the
3D-Ising Model: We show that 2+1-dimensional Euclidean quantum gravity is equivalent, under
some mild topological assumptions, to a Gaussian fermionic system. In
particular, for manifolds topologically equivalent to $\Sigma_g\times\RrR$ with
$\Sigma_g$ a closed and oriented Riemann surface of genus $g$, the
corresponding 2+1-dimensional Euclidean quantum gravity may be related to the
3D-lattice Ising model before its thermodynamic limit.
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New Couplings of Six-Dimensional Supergravity: We describe the couplings of six-dimensional supergravity, which contain a
self-dual tensor multiplet, to $n_T$ anti-self-dual tensor matter multiplets,
$n_V$ vector multiplets and $n_H$ hypermultiplets. The scalar fields of the
tensor multiplets form a coset $SO(n_T,1)/SO(n_T)$, while the scalars in the
hypermultiplets form quaternionic K\"ahler symmetric spaces, the generic
example being $Sp(n_H,1)/Sp(n_H)\otimes Sp(1)$. The gauging of the compact
subgroup $Sp(n_H) \times Sp(1)$ is also described. These results generalize
previous ones in the literature on matter couplings of $N=1$ supergravity in
six dimensions.
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Recent mathematical developments in the Skyrme model: In this review we present a pedagogical introduction to recent, more
mathematical developments in the Skyrme model. Our aim is to render these
advances accessible to mainstream nuclear and particle physicists. We start
with the static sector and elaborate on geometrical aspects of the definition
of the model. Then we review the instanton method which yields an analytical
approximation to the minimum energy configuration in any sector of fixed baryon
number, as well as an approximation to the surfaces which join together all the
low energy critical points. We present some explicit results for B=2. We then
describe the work done on the multibaryon minima using rational maps, on the
topology of the configuration space and the possible implications of Morse
theory. Next we turn to recent work on the dynamics of Skyrmions. We focus
exclusively on the low energy interaction, specifically the gradient flow
method put forward by Manton. We illustrate the method with some expository toy
models. We end this review with a presentation of our own work on the
semi-classical quantization of nucleon states and low energy nucleon-nucleon
scattering.
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Renormalization Group Flow of Four-fermi with Chern-Simons Interaction: We introduce Chern-Simons interaction into the three dimensional four-fermi
theory, ad suggest a possible line of non-Gaussian infrared stable fixed points
of the four-fermi operator, this line is characterized by the Chern-Simons
coupling.
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A Field Theory Model With a New Lorentz-Invariant Energy Scale: A framework is proposed that allows to write down field theories with a new
energy scale while explicitly preserving Lorentz invariance and without
spoiling the features of standard quantum field theory which allow quick
calculations of scattering amplitudes. If the invariant energy is set to the
Planck scale, these deformed field theories could serve to model quantum
gravity phenomenology. The proposal is based on the idea, appearing for example
in Deformed Special Relativity, that momentum space could be curved rather than
flat. This idea is implemented by introducing a fifth dimension and imposing an
extra constraint on physical field configurations in addition to the mass shell
constraint. It is shown that a deformed interacting scalar field theory is
unitary. Also, a deformed version of QED is argued to give scattering
amplitudes that reproduce the usual ones in the leading order. Possibilities
for experimental signatures are discussed, but more work on the framework's
consistency and interpretation is necessary to make concrete predictions.
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Lectures on Generalized Symmetries: These are a set of lecture notes on generalized global symmetries in quantum
field theory. The focus is on invertible symmetries with a few comments
regarding non-invertible symmetries. The main topics covered are the basics of
higher-form symmetries and their properties including 't Hooft anomalies,
gauging and spontaneous symmetry breaking. We also introduce the useful notion
of symmetry topological field theories (SymTFTs). Furthermore, an introduction
to higher-group symmetries describing mixings of higher-form symmetries is
provided. Some advanced topics covered include the encoding of higher-form
symmetries in holography and geometric engineering constructions in string
theory. Throughout the text, all concepts are consistently illustrated using
gauge theories as examples.
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Generalized Jack polynomials and the AGT relations for the $SU(3)$ group: We find generalized Jack polynomials for the group $SU(3)$ and verify that
their Selberg averages for several first levels are given by Nekrasov
functions. To compute the averages we derive recurrence relations for the
$sl_3$ Selberg integrals.
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Supersymmetric Spectral Form Factor and Euclidean Black Holes: The late-time behavior of spectral form factor (SFF) encodes the inherent
discreteness of a quantum system, which should be generically non-vanishing. We
study an index analog of the microcanonical spectrum form factor in
four-dimensional $\mathcal{N}=4$ super Yang-Mills theory. In the large $N$
limit and at large enough energy, the most dominant saddle corresponds to the
black hole in the AdS bulk. This gives rise to the slope that decreases
exponentially for a small imaginary chemical potential, which is a natural
analog of an early time. We find that the `late-time' behavior is governed by
the multi-cut saddles that arise in the index matrix model, which are
non-perturbatively sub-dominant at early times. These saddles become dominant
at late times, preventing the SFF from decaying. These multi-cut saddles
correspond to the orbifolded Euclidean black holes in the AdS bulk, therefore
giving the geometrical interpretation of the `ramp.' Our analysis is done in
the standard AdS/CFT setting without ensemble average or wormholes.
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Relaxed super self-duality and effective action: A closed-form expression is obtained for a holomorphic sector of the two-loop
Euler-Heisenberg type effective action for N = 2 supersymmetric QED derived in
hep-th/0308136. In the framework of the background-field method, this sector is
singled out by computing the effective action for a background N = 2 vector
multiplet satisfying a relaxed super self-duality condition. The approach
advocated in this letter can be applied, in particular, to the study of the N =
4 super Yang-Mills theory on its Coulomb branch.
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String Primer: This is the written version of a set of introductory lectures on string
theory.
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Inclusive probability of particle creation on classical backgrounds: The quantum theories of boson and fermion fields with quadratic nonstationary
Hamiltoanians are rigorously constructed. The representation of the algebra of
observables is given by the Hamiltonian diagonalization procedure. The
sufficient conditions for the existence of unitary dynamics at finite times are
formulated and the explicit formula for the matrix elements of the evolution
operator is derived. In particular, this gives the well-defined expression for
the one-loop effective action. The ultraviolet and infrared divergencies are
regularized by the energy cutoff in the Hamiltonian of the theory. The possible
infinite particle production is regulated by the corresponding counterdiabatic
terms. The explicit formulas for the average number of particles $N_D$ recorded
by the detector and for the probability $w(D)$ to record a particle by the
detector are derived. It is proved that these quantities allow for the
regularization removal limit and, in this limit, $N_D$ is finite and
$w(D)\in[0,1)$. As an example, the theory of a neutral boson field with
stationary quadratic part of the Hamiltonian and nonstationary source is
considered. The average number of particles produced by this source from the
vacuum during a finite time evolution and the inclusive probability to record a
created particle are obtained. The infrared and ultraviolet asymptotics of the
average density of created particles are derived. As a particular case, quantum
electrodynamics with a classical current is considered. The ultraviolet and
infrared asymptotics of the average number of photons are derived. The
asymptotics of the average number of photons produced by the adiabatically
driven current is found.
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Universal Drinfeld-Sokolov Reduction and Matrices of Complex Size: We construct affinization of the algebra $gl_{\lambda}$ of ``complex size''
matrices, that contains the algebras $\hat{gl_n}$ for integral values of the
parameter. The Drinfeld--Sokolov Hamiltonian reduction of the algebra
$\hat{gl_{\lambda}}$ results in the quadratic Gelfand--Dickey structure on the
Poisson--Lie group of all pseudodifferential operators of fractional order.
This construction is extended to the simultaneous deformation of orthogonal and
simplectic algebras that produces self-adjoint operators, and it has a
counterpart for the Toda lattices with fractional number of particles.
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Observables, gravitational dressing, and obstructions to locality and
subsystems: Quantum field theory - our basic framework for describing all
non-gravitational physics - conflicts with general relativity: the latter
precludes the standard definition of the former's essential principle of
locality, in terms of commuting local observables. We examine this conflict
more carefully, by investigating implications of gauge (diffeomorphism)
invariance for observables in gravity. We prove a dressing theorem, showing
that any operator with nonzero Poincare charges, and in particular any
compactly-supported operator, in flat-spacetime quantum field theory must be
gravitationally dressed once coupled to gravity, i.e. it must depend on the
metric at arbitrarily long distances, and we put lower bounds on this nonlocal
dependence. This departure from standard locality occurs in the most severe way
possible: in perturbation theory about flat spacetime, at leading order in
Newton's constant. The physical observables in a gravitational theory therefore
do not organize themselves into local commuting subalgebras: the principle of
locality must apparently be reformulated or abandoned, and in fact we lack a
clear definition of the coarser and more basic notion of a quantum subsystem of
the Universe. We discuss relational approaches to locality based on
diffeomorphism-invariant nonlocal operators, and reinforce arguments that any
such locality is state-dependent and approximate. We also find limitations to
the utility of bilocal diffeomorphism-invariant operators that are considered
in cosmological contexts. An appendix provides a concise review of the
canonical covariant formalism for gravity, instrumental in the discussion of
Poincare charges and their associated long-range fields.
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A Systematic Study on Matrix Models for Chern-Simons-matter Theories: We investigate the planar solution of matrix models derived from various
Chern-Simons-matter theories compatible with the planar limit. The saddle-point
equations for most of such theories can be solved in a systematic way. A
relation to Fuchsian systems play an important role in obtaining the planar
resolvents. For those theories, the eigenvalue distribution is found to be
confined in a bounded region even when the 't Hooft couplings become large. As
a result, the vevs of Wilson loops are bounded in the large 't Hooft coupling
limit. This implies that many of Chern-Simons-matter theories have quite
different properties from ABJM theory. If the gauge group is of the form ${\rm
U}(N_1)_{k_1}\times{\rm U}(N_2)_{k_2}$, then the resolvents can be obtained in
a more explicit form than in the general cases.
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A mild source for the Wu-Yang magnetic monopole: We establish that the Wu-Yang monopole needs the introduction of a magnetic
point source at the origin in order for it to be a solution of the differential
and integral equations for the Yang-Mills theory. That result is corroborated
by the analysis through distribution theory, of the two types of magnetic
fields relevant for the local and global properties of the Wu-Yang solution.
The subtlety lies on the fact that with the non-vanishing magnetic point source
required by the Yang-Mills integral equations, the Wu-Yang monopole
configuration does not violate, in the sense of distribution theory, the
differential Bianchi identity.
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Two Centered Black Holes and N=4 Dyon Spectrum: The exact spectrum of dyons in a class of N=4 supersymmetric string theories
is known to change discontinuously across walls of marginal stability. We show
that the change in the degeneracy across the walls of marginal stability can be
accounted for precisely by the entropy of two centered small black holes which
disappear as we cross the walls of marginal stability.
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The non-retarded dispersive force between an electrically polarizable
atom and a magnetically polarizable one: Using perturbative QED we show that, while the retarded dispersive force
between an electrically polarizable atom and a magnetically polarizable one is
proportional to $1/r^{8}$, where $r$ is the distance between the atoms, the
non-retarded force is proportiaonal to $1/r^{5}$. This is a rather surprising
result that should be compared with the dispersive van der Waals force between
two electrically polarizable atoms, where the retarded force is also
proportional to $1/r^{8}$, but the non-retarded force is proportional to
$1/r^{7}$.
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Apparently superluminal superfluids: We consider the superfluid phase of a specific renormalizable relativistic
quantum field theory. We prove that, within the regime of validity of
perturbation theory and of the superfluid effective theory, there are
consistent and regular vortex solutions where the superfluid's velocity field
as traditionally defined smoothly interpolates between zero and arbitrarily
large superluminal values. We show that this solution is free of instabilities
and of superluminal excitations. We show that, in contrast, a generic vortex
solution for an ordinary fluid does develop an instability if the velocity
field becomes superluminal. All this questions the characterization of a
superfluid velocity field as the actual velocity of ``something".
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Brane-like States in Superstring Theory and the Dynamics of non-Abelian
Gauge Theories: We propose a string-theoretic ansatz describing the dynamics of SU(N)
Yang-Mills theories in the limit of large N in D=4. The construction uses in a
crucial way open-string vertex operators that describe non-perturbative brane
dynamics. According to our proposal, various gauge theories are described by
string theories with the same action, but with different measures in the
functional integral. The choice of measure defines the gauge group, as well as
the effective space-time dimension of the resulting gauge theory.
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The Hausdorff dimension in polymerized quantum gravity: We calculate the Hausdorff dimension, $d_H$, and the correlation function
exponent, $\eta$, for polymerized two dimensional quantum gravity models. If
the non-polymerized model has correlation function exponent $\eta_0 >3$ then
$d_H=\gamma^{-1}$ where $\gamma$ is the susceptibility exponent. This suggests
that these models may be in the same universality class as certain non-generic
branched polymer models.
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Species Entropy and Thermodynamics: We analyse particle species and the species scale in quantum gravity from a
thermodynamic perspective. In close analogy to black hole thermodynamics, we
propose that particle species own an entropy and a temperature, which is
determined by the species scale. This is identical to the Bekenstein-Hawking
entropy of a corresponding minimal black hole and agrees with the number of
species in a given tower of states. Through the species entropy, we find that
certain entropy bounds are connected to recent swampland constraints. Moreover,
the concept of species entropy and temperature allow us to formulate the laws
of species thermodynamics, which are argued to govern the variations of moduli
in string theory. They can be viewed as general rules that imply certain
swampland conjectures, and vice versa.
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From ALE-instanton Moduli to Super Yang-Mills Theories via Branes: A large class of equivalence relations between the moduli spaces of
instantons on ALE spaces and the Higgs branches of supersymmetric Yang-Mills
theories, are found by means of a certain kind of duality transformation
between brane configurations in superstring theories. 4d, N=2 and 5d, N=1
supersymmetric gauge theories with product gauge groups turn out to correspond
to the ALE-instanton moduli of type II B and type II A superstring theories,
respectively.
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On the Complementarity of F-theory, Orientifolds, and Heterotic Strings: We study F-theory duals of six dimensional heterotic vacua in extreme regions
of moduli space where the heterotic string is very strongly coupled. We
demonstrate how to use orientifold limits of these F-theory duals to regain a
perturbative string description. As an example, we reproduce the spectrum of a
$T^4/\ZZ_{4}$ orientifold as an F-theory vacuum with a singular $K3$ fibration.
We relate this vacuum to previously studied heterotic $E_8\times E_8$
compactifications on $K3$.
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Delicacies of the Mass Perturbation in the Schwinger Model on a Circle: The Hilbert bundle for the massless fermions of the Schwinger model on a
circle, over the space of gauge field configurations, is topologically
non-trivial (twisted). The corresponding bundle for massive fermions is
topologically trivial (periodic). Since the structure of the fermionic Hilbert
bundle changes discontinuously the possibility of perturbing in the mass is
thrown into doubt. In this article, we show that a direct application of the
anti-adiabatic theorem of Low, allows the structure of the massless theory to
be dynamically preserved in the strong coupling limit, ${e\over m}>>1$. This
justifies the use of perturbation theory in the bosonized version of the model,
in this limit.
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Coulomb scattering for scalar field in Scr\" odinger picture: The scattering of a charged scalar field on Coulomb potential on de Sitter
space-time is studied using the solution of the free Klein-Gordon equation. We
find that the scattering amplitude is independent of the choice of the picture
and in addition the total energy is conserved in the scattering process.
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Notes on holographic Schwinger effect: We use the method of evaluating the decay rate in terms of the imaginary part
of a probe brane action to study the holographic Schwinger effect. In the
confining D3-branes case, we find that the Schwinger effect occurs at energy
scales higher than the Kaluza-Klein mass, indicating the absence of such effect
when the dual gauge field theory can be regarded as an 2+1 dimensional theory.
This property is independent of the configuration of the probe brane. In the
case of D3-branes with a B field dual to a noncommutative super Yang-Mills
theory, we study how the decay rate is affected by the noncommutative effect.
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Lorentz Invariance Violation and Symmetry in Randers--Finsler Spaces: Lorentz Invariance violation is a common feature of new physics beyond the
standard model. We show that the symmetry of Randers spaces deduces a modified
dispersion relation with characteristics of Lorentz Invariance violation. The
counterparts of the Lorentz transformation in the Einstein's Special Relativity
are presented explicitly. The coordinate transformations are unitary and form a
group. Generators and algebra satisfied by them are different from usual
Lorentz ones. The Randersian line element as well as speed of light is
invariant under the transformations. In particular, there is another invariant
speed which may be related with Planck scale and the mass of moving particle.
Thus, the Randers spaces is a suitable framework to discuss the Lorentz
Invariance violation.
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On some developments in the Nonsymmetric Kaluza-Klein Theory: We consider a condition for a charge confinement and gravito-electromagnetic
wave solutions in the Nonsymmetric Kaluza-Klein Theory.We consider also an
influence of a cosmological constant on a static,spherically symmetric
solution.We remind to the reader some fudamentals of the Nonsymmetric
Kaluza-Klein Theory and a geometrcal background behind the
theory.Simultaneously we give some remarks concerning misunderstanding
connected to several notions of the Nonsymmetric Kaluza-Klein Theory,Einstein
Unified Field Theory,geometrization and unification of physical interactions
.We reconsider Dirac field in the Nonsymmetric Kaluza-Klein Theory.
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Graviton n-point functions for UV-complete theories in Anti-de Sitter
space: We calculate graviton n-point functions in an anti-de Sitter black brane
background for effective gravity theories whose linearized equations of motion
have at most two time derivatives. We compare the n-point functions in Einstein
gravity to those in theories whose leading correction is quadratic in the
Riemann tensor. The comparison is made for any number of gravitons and for all
physical graviton modes in a kinematic region for which the leading correction
can significantly modify the Einstein result. We find that the n-point
functions of Einstein gravity depend on at most a single angle, whereas those
of the corrected theories may depend on two angles. For the four-point
functions, Einstein gravity exhibits linear dependence on the Mandelstam
variable s versus a quadratic dependence on s for the corrected theory.
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Exact O(d,d) Transformations in WZW Models: Using the algebraic Hamiltonian approach, we derive the exact to all orders
O(d,d) transformations of the metric and the dilaton field in WZW and WZW coset
models for both compact and non-compact groups. It is shown that under the
exact $O(d)\times O(d)$ transformation only the leading order of the inverse
metric $G^{-1}$ is transformed. The quantity $\sqrt{G}\exp(\Phi)$ is the same
in all the dual models and in particular is independent of k. We also show that
the exact metric and dilaton field that correspond to G/U(1)^d WZW can be
obtained by applying the exact O(d,d) transformations on the (ungauged) WZW, a
result that was known to one loop order only. As an example we give the O(2,2)
transformations in the $SL(2,R)$ WZW that transform to its dual exact models.
These include also the exact 3D black string and the exact 2D black hole with
an extra $U(1)$ free field.
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Black Holes as P-Branes: We review briefly the thermodynamical interpretation of black hole physics
and discuss the problems and inconsistencies in this approach. We provide an
alternative interpretation of black holes as quantum objects and investigate
the statistical mechanics of a gas of such objects in the microcanonical
ensemble. We argue that the theory of black holes has the conformal properties
of duality and satisfaction of the statistical bootstrap condition. We show in
the context of mean field theory that the thermal vacuum is the false vacuum
for a black hole and define a microcanonical vacuum which leads to a number
density characteristic of pure states for the Hawking radiation.
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Space-Time Diffeomorphisms in Noncommutative Gauge Theories: In previous work [Rosenbaum M. et al., J. Phys. A: Math. Theor. 40 (2007),
10367-10382, hep-th/0611160] we have shown how for canonical parametrized field
theories, where space-time is placed on the same footing as the other fields in
the theory, the representation of space-time diffeomorphisms provides a very
convenient scheme for analyzing the induced twisted deformation of these
diffeomorphisms, as a result of the space-time noncommutativity. However, for
gauge field theories (and of course also for canonical geometrodynamics) where
the Poisson brackets of the constraints explicitely depend on the embedding
variables, this Poisson algebra cannot be connected directly with a
representation of the complete Lie algebra of space-time diffeomorphisms,
because not all the field variables turn out to have a dynamical character
[Isham C.J., Kuchar K.V., Ann. Physics 164 (1985), 288-315, 316-333].
Nonetheless, such an homomorphic mapping can be recuperated by first modifying
the original action and then adding additional constraints in the formalism in
order to retrieve the original theory, as shown by Kuchar and Stone for the
case of the parametrized Maxwell field in [Kuchar K.V., Stone S.L., Classical
Quantum Gravity 4 (1987), 319-328]. Making use of a combination of all of these
ideas, we are therefore able to apply our canonical reparametrization approach
in order to derive the deformed Lie algebra of the noncommutative space-time
diffeomorphisms as well as to consider how gauge transformations act on the
twisted algebras of gauge and particle fields. Thus, hopefully, adding
clarification on some outstanding issues in the literature concerning the
symmetries for gauge theories in noncommutative space-times.
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A Hierarchy of Superstrings: We construct a hierarchy of supersymmetric string theories by showing that
the general N-extended superstrings may be viewed as a special class of the
(N+1)-extended superstrings. As a side result, we find a twisted (N+2)
superconformal algebra realized in the N-extended string.
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$Z_N$-balls: Solitons from $Z_N$-symmetric scalar field theory: We discuss the conditions under which static, finite-energy, configurations
of a complex scalar field $\phi$ with constant phase and spherically symmetric
norm exist in a potential of the form $V(\phi^*\phi, \phi^N+\phi^{*N})$ with
$N\in\mathbb{N}$ and $N\geq2$, i.e. a potential with a $Z_N$-symmetry. Such
configurations are called $Z_N$-balls. We build explicit solutions in
$(3+1)$-dimensions from a model mimicking effective field theories based on the
Polyakov loop in finite-temperature SU($N$) Yang-Mills theory. We find
$Z_N$-balls for $N=$3, 4, 6, 8, 10 and show that only static solutions with
zero radial node exist for $N$ odd, while solutions with radial nodes may exist
for $N$ even.
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A $T\bar T$-like deformation of the Skyrme model and the Heisenberg
model of nucleon-nucleon scattering: The Skyrme model, though it admits correctly a wide range of static
properties of the nucleon, does not seem to reproduce properly the scattering
behavior of nucleons at high energies. In this paper we present a $T\bar
T$-like deformation of it, inspired by a 1+1 dimensional model, in which
boosted nucleons behave like shock waves. The scattering of the latter
saturates the Froissart bound. We start by showing that 1+1 dimensional $T\bar
T$ deformations of the free abelian pion action are in fact generalizations of
the old Heisenberg model for nucleon-nucleon scattering, yielding the same
saturation of the Froissart bound. We then deform the strong coupling limit of
the bosonized action of multi-flavor QCD in two dimensions using the $T\bar T$
deformation of the WZW action with a mass term. We derive the classical soliton
solution that corresponds to the nucleon, determine its mass and discuss its
transformation into a shock-wave upon boosting. We uplift this action into a
3+1 dimensional $T\bar T$-like deformation of the Skyrme action. We compare
this deformed action to that of chiral perturbation theory.
A possible holographic gravity dual interpretation is explored.
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Continuous Phase Transition of the higher-dimensional topological
de-Sitter Spacetime with the Non-linear Source: For the higher-dimensional dS spacetime embedded with black holes with
non-linear charges, there are two horizons with different radiation
temperatures. By introducing the interplay between two horizons this system can
be regarded as an ordinary thermodynamic system in the thermodynamic
equilibrium described by the thermodynamic quantities
($T_{eff},~P_{eff},~V,~S,~\Phi_{eff}$). In this work, our focus is on the
thermodynamic properties of phase transition for the four-dimensional dS
spacetime with different values of the charge correction $\bar\phi$. We find
that with the increasing of the non-linear charge correction the two horizons
get closer and closer, and the correction entropy is negative which indicates
the interaction between the two horizons stronger and stronger. Furthermore,
the heat capacity at constant pressure, isobaric expansion coefficient, and the
isothermal compression coefficient have the schottky peak at the critical
point. However, the heat capacity as constant volume for the dS spacetime is
nonzero. Finally, the dynamical properties of phase transition for this system
have investigated based on Gibbs free energy, where exists the different
behavior with that for AdS black holes.
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The Euler anomaly and scale factors in Liouville/Toda CFTs: The role played by the Euler anomaly in the dictionary relating sphere
partition functions of four dimensional theories of class $\mathcal{S}$ and two
dimensional nonrational CFTs is clarified. On the two dimensional side, this
involves a careful treatment of scale factors in Liouville/Toda correlators.
Using ideas from tinkertoy constructions for Gaiotto duality, a framework is
proposed for evaluating these scale factors. The representation theory of Weyl
groups plays a critical role in this framework.
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Metastable supergravity vacua with F and D supersymmetry breaking: We study the conditions under which a generic supergravity model involving
chiral and vector multiplets can admit viable metastable vacua with
spontaneously broken supersymmetry and realistic cosmological constant. To do
so, we impose that on the vacuum the scalar potential and all its first
derivatives vanish, and derive a necessary condition for the matrix of its
second derivatives to be positive definite. We study then the constraints set
by the combination of the flatness condition needed for the tuning of the
cosmological constant and the stability condition that is necessary to avoid
unstable modes. We find that the existence of such a viable vacuum implies a
condition involving the curvature tensor for the scalar geometry and the charge
and mass matrices for the vector fields. Moreover, for given curvature, charges
and masses satisfying this constraint, the vector of F and D auxiliary fields
defining the Goldstino direction is constrained to lie within a certain domain.
The effect of vector multiplets relative to chiral multiplets is maximal when
the masses of the vector fields are comparable to the gravitino mass. When the
masses are instead much larger or much smaller than the gravitino mass, the
effect becomes small and translates into a correction to the effective
curvature. We finally apply our results to some simple classes of examples, to
illustrate their relevance.
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$\widehat{sl(2)}$ decomposition of denominator formulae of some BKM Lie
superalgebras -- II: The square-root of Siegel modular forms of CHL Z_N orbifolds of type II
compactifications are denominator formulae for some Borcherds-Kac-Moody Lie
superalgebras for N=1,2,3,4. We study the decomposition of these Siegel modular
forms in terms of characters of two sub-algebras: one is a $\widehat{sl(2)}$
and the second is a Borcherds extension of the $\widehat{sl(2)}$. This is a
continuation of our previous work where we studied the case of Siegel modular
forms appearing in the context of Umbral moonshine. This situation is more
intricate and provides us with a new example (for N=5) that did not appear in
that case. We restrict our analysis to the first N terms in the expansion as a
first attempt at deconstructing the Siegel modular forms and unravelling the
structure of potentially new Lie algebras that occur for N=5,6.
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Extended Superconformal Algebras from Classical and Quantum Hamiltonian
Reduction: We consider the extended superconformal algebras of the Knizhnik-Bershadsky
type with $W$-algebra like composite operators occurring in the commutation
relations, but with generators of conformal dimension 1,$\frac{3}{2}$ and 2,
only. These have recently been neatly classified by several groups, and we
emphasize the classification based on hamiltonian reduction of affine Lie
superalgebras with even subalgebras $G\oplus sl(2)$. We reveiw the situation
and improve on previous formulations by presenting generic and very compact
expressions valid for all algebras, classical and quantum. Similarly generic
and compact free field realizations are presented as are corresponding
screening charges. Based on these a discussion of singular vectors is
presented. (Based on talk by J.L. Petersen at the Int. Workshop on "String
Theory, Quantum Gravity and the Unification of the Fundamental Interactions",
Rome Sep. 21-26, 1992)
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Fermion masses in noncommutative geometry: Recent indications of neutrino oscillations raise the question of the
possibility of incorporating massive neutrinos in the formulation of the
Standard Model (SM) within noncommutative geometry (NCG). We find that the NCG
requirement of Poincare duality constrains the numbers of massless quarks and
neutrinos to be unequal unless new fermions are introduced. Possible scenarios
in which this constraint is satisfied are discussed.
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On the Fedosov Deformation Quantization beyond the Regular Poisson
Manifolds: A simple iterative procedure is suggested for the deformation quantization of
(irregular) Poisson brackets associated to the classical Yang-Baxter equation.
The construction is shown to admit a pure algebraic reformulation giving the
Universal Deformation Formula (UDF) for any triangular Lie bialgebra. A simple
proof of classification theorem for inequivalent UDF's is given. As an example
the explicit quantization formula is presented for the quasi-homogeneous
Poisson brackets on two-plane.
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SQCD: A Geometric Apercu: We take new algebraic and geometric perspectives on the old subject of SQCD.
We count chiral gauge invariant operators using generating functions, or
Hilbert series, derived from the plethystic programme and the Molien-Weyl
formula. Using the character expansion technique, we also see how the global
symmetries are encoded in the generating functions. Equipped with these methods
and techniques of algorithmic algebraic geometry, we obtain the character
expansions for theories with arbitrary numbers of colours and flavours.
Moreover, computational algebraic geometry allows us to systematically study
the classical vacuum moduli space of SQCD and investigate such structures as
its irreducible components, degree and syzygies. We find the vacuum manifolds
of SQCD to be affine Calabi-Yau cones over weighted projective varieties.
|
Null Vectors in Logarithmic Conformal Field Theory: The representation theory of the Virasoro algebra in the case of a
logarithmic conformal field theory is considered. Here, indecomposable
representations have to be taken into account, which has many interesting
consequences. We study the generalization of null vectors towards the case of
indecomposable representation modules and, in particular, how such logarithmic
null vectors can be used to derive differential equations for correlation
functions. We show that differential equations for correlation functions with
logarithmic fields become inhomogeneous.
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Monopoles, Duality and Chiral Symmetry Breaking in N=2 Supersymmetric
QCD: We study four dimensional $N=2$ supersymmetric gauge theories with matter
multiplets. For all such models for which the gauge group is $SU(2)$, we derive
the exact metric on the moduli space of quantum vacua and the exact spectrum of
the stable massive states. A number of new physical phenomena occur, such as
chiral symmetry breaking that is driven by the condensation of magnetic
monopoles that carry global quantum numbers. For those cases in which conformal
invariance is broken only by mass terms, the formalism automatically gives
results that are invariant under electric-magnetic duality. In one instance,
this duality is mixed in an interesting way with $SO(8)$ triality.
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Evolution of Gravitational Perturbations in Non-Commutative Inflation: We consider the non-commutative inflation model of [3] in which it is the
unconventional dispersion relation for regular radiation which drives the
accelerated expansion of space. In this model, we study the evolution of linear
cosmological perturbations through the transition between the phase of
accelerated expansion and the regular radiation-dominated phase of Standard
Cosmology, the transition which is analogous to the reheating period in scalar
field-driven models of inflation. If matter consists of only a single
non-commutative radiation fluid, then the curvature perturbations are constant
on super-Hubble scales. On the other hand, if we include additional matter
fields which oscillate during the transition period, e.g. scalar moduli fields,
then there can be parametric amplification of the amplitude of the curvature
perturbations. We demonstrate this explicitly by numerically solving the full
system of perturbation equations in the case where matter consists of both the
non-commutative radiation field and a light scalar field which undergoes
oscillations. Our model is an example where the parametric resonance of the
curvature fluctuations is driven by the oscillations not of the inflaton field,
but of the entropy mode
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Entanglement Entropy in Internal Spaces and Ryu-Takayanagi Surfaces: We study minimum area surfaces associated with a region, $R$, of an internal
space. For example, for a warped product involving an asymptotically $AdS$
space and an internal space $K$, the region $R$ lies in $K$ and the surface
ends on $\partial R$. We find that the result of Graham and Karch can be
avoided in the presence of warping, and such surfaces can sometimes exist for a
general region $R$. When such a warped product geometry arises in the IR from a
higher dimensional asymptotic AdS, we argue that the area of the surface can be
related to the entropy arising from entanglement of internal degrees of freedom
of the boundary theory. We study several examples, including warped or direct
products involving $AdS_2$, or higher dimensional $AdS$ spaces, with the
internal space, $K=R^m, S^m$; $Dp$ brane geometries and their near horizon
limits; and several geometries with a UV cut-off. We find that such RT surfaces
often exist and can be useful probes of the system, revealing information about
finite length correlations, thermodynamics and entanglement. We also make some
preliminary observations about the role such surfaces can play in bulk
reconstruction, and their relation to subalgebras of observables in the
boundary theory.
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The VECRO hypothesis: We consider three fundamental issues in quantum gravity: (a) the black hole
information paradox (b) the unboundedness of entropy that can be stored inside
a black hole horizon (c) the relation between the black hole horizon and the
cosmological horizon. With help from the small corrections theorem, we convert
each of these issues into a sharp conflict. We then argue that all three
conflicts can be resolved by the following hypothesis: {\it the vacuum
wavefunctional of quantum gravity contains a `vecro' component made of virtual
fluctuations of configurations of the same type that arise in the fuzzball
structure of black hole microstates}. Further, if we assume that causality
holds to leading order in gently curved spacetime, then we {\it must} have such
a vecro component in order to resolve the above conflicts. The term vecro
stands for `Virtual Extended Compression-Resistant Objects', and characterizes
the nature of the vacuum fluctuations that resolve the puzzles. It is
interesting that puzzle (c) may relate the role of quantum gravity in black
holes to observations in the sky.
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Entanglement entropy in de Sitter: no pure states for conformal matter: In this paper, we consider the entanglement entropy of conformal matter for
finite and semi-infinite entangling regions, as well as the formation of
entanglement islands in four-dimensional de Sitter spacetime partially reduced
to two dimensions. We analyze complementarity and pure state condition of
entanglement entropy of pure states as a consistency test of the CFT formulas
in this geometrical setup, which has been previously used in the literature to
study the information paradox in higher-dimensional de Sitter in the context of
the island proposal. We consider two different types of Cauchy surfaces in the
extended static patch and flat coordinates, correspondingly. For former, we
found that entanglement entropy of a pure state is always bounded from below by
a constant and never becomes zero, as required by quantum mechanics. In turn,
the difference between the entropies for some region and its complement, which
should be zero for a pure state, in direct calculations essentially depends on
how the boundaries of these regions evolve with time. Regarding the flat
coordinates, it is impossible to regularize spacelike infinity in a way that
would be compatible with complementarity and pure state condition, as opposed,
for instance, to two-sided Schwarzschild black hole. Finally, we discuss the
information paradox in de Sitter and show that the island formula does not
resolve it, at least in this setup. Namely, we give examples of a region with a
time-limited growth of entanglement entropy, for which there is no island
solution, and the region, for which entanglement entropy does not grow, but the
island solution exists.
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Holography as a Gauge Phenomenon in Higher Spin Duality: Employing the world line spinning particle picture we discuss the appearance
of several different `gauges' which we use to gain a deeper explanation of the
Collective/Gravity identification. We discuss transformations and algebraic
equivalences between them. For a bulk identification we develop a `gauge
independent' representation where all gauge constraints are eliminated. This
`gauge reduction' of Higher Spin Gravity demonstrates that the physical content
of 4D AdS HS theory is represented by the dynamics of an unconstrained scalar
field in 6d. It is in this gauge reduced form that HS Theory can be seen to be
equivalent to a 3+3 dimensional bi-local collective representation of CFT3.
|
Non-Abelian Gauge Theory on q-Quantum Spaces: Gauge theories on q-deformed spaces are constructed using covariant
derivatives. For this purpose a ``vielbein'' is introduced, which transforms
under gauge transformations. The non-Abelian case is treated by establishing a
connection to gauge theories on commutative spaces, i.e. by a Seiberg-Witten
map. As an example we consider the Manin plane. Remarks are made concerning the
relation between covariant coordinates and covariant derivatives.
|
Cosmological evolutions of $F(R)$ nonlinear massive gravity: Recently a new extended nonlinear massive gravity model has been proposed
which includes the $F(R)$ modifications to dRGT model.We follow the $F(R)$
nonlinear massive gravity and study its implications on cosmological
evolutions. We derive the critical points of the cosmic system and study the
corresponding kinetics by performing the phase-plane analysis.
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A Kaluza-Klein inspired action for chiral p-forms and their anomalies: The dynamics of chiral p-forms can be captured by a lower-dimensional
parity-violating action motivated by a Kaluza-Klein reduction on a circle. The
massless modes are (p-1)-forms with standard kinetic terms and Chern-Simons
couplings to the Kaluza-Klein vector of the background metric. The massive
modes are p-forms charged under the Kaluza-Klein vector and admit parity-odd
first-order kinetic terms. Gauge invariance is implemented by a
Stueckelberg-like mechanism using (p-1)-forms. A Chern-Simons term for the
Kaluza-Klein vector is generated at one loop by massive p-form modes. These
findings are shown to be consistent with anomalies and supersymmetry for
six-dimensional supergravity theories with chiral tensor multiplets.
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The Riemann-Hilbert problem associated with the quantum Nonlinear
Schrodinger equation: We consider the dynamical correlation functions of the quantum Nonlinear
Schrodinger equation. In a previous paper we found that the dynamical
correlation functions can be described by the vacuum expectation value of an
operator-valued Fredholm determinant. In this paper we show that a
Riemann-Hilbert problem can be associated with this Fredholm determinant. This
Riemann-Hilbert problem formulation permits us to write down completely
integrable equations for the Fredholm determinant and to perform an asymptotic
analysis for the correlation function.
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Viscosity and dissipative hydrodynamics from effective field theory: With the goal of deriving dissipative hydrodynamics from an action, we study
classical actions for open systems, which follow from the generic structure of
effective actions in the Schwinger-Keldysh Closed-Time-Path formalism with two
time axes and a doubling of degrees of freedom. The central structural feature
of such effective actions is the coupling between degrees of freedom on the two
time axes. This reflects the fact that from an effective field theory point of
view, dissipation is the loss of energy of the low-energy hydrodynamical
degrees of freedom to the integrated-out, UV degrees of freedom of the
environment. The dynamics of only the hydrodynamical modes may therefore not
posses a conserved stress-energy tensor. After a general discussion of the CTP
effective actions, we use the variational principle to derive the
energy-momentum balance equation for a dissipative fluid from an effective
Goldstone action of the long-range hydrodynamical modes. Despite the absence of
conserved energy and momentum, we show that we can construct the first-order
dissipative stress-energy tensor and derive the Navier-Stokes equations near
hydrodynamical equilibrium. The shear viscosity is shown to vanish in the
classical theory under consideration, while the bulk viscosity is determined by
the form of the effective action. We also discuss the thermodynamics of the
system and analyse the entropy production.
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Superconformal Gravity And The Topology Of Diffeomorphism Groups: Twisted four-dimensional supersymmetric Yang-Mills theory famously gives a
useful point of view on the Donaldson and Seiberg-Witten invariants of
four-manifolds. In this paper we generalize the construction to include a path
integral formulation of generalizations of Donaldson invariants for smooth
families of four-manifolds. Mathematically these are equivariant cohomology
classes for the action of the oriented diffeomorphism group on the space of
metrics on the manifold. In principle these cohomology classes should contain
nontrivial information about the topology of the diffeomorphism group of the
four-manifold. We show that the invariants may be interpreted as the standard
topologically twisted path integral of four-dimensional $\mathcal{N}=2$
supersymmetric Yang-Mills coupled to topologically twisted background fields of
conformal supergravity.
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Tunneling, Page Curve and Black Hole Information: In a recent paper [1], we proposed that the quantum states of black hole
responsible for the Bekenstein-Hawking entropy are given by Bell states of
Fermi quanta in the interior of black hole. In this paper, we include the
effect of tunneling on these entangled states and show that partial tunneling
of these Bell states of Fermi quanta give rises to the Page curve of Hawking
radiation. We also show that the entirety of information initially stored in
the black hole is returned to the outside via the Hawking radiation.
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Quasi-instantons in QCD with chiral symmetry restoration: We show, without using semiclassical approximations, that, in
high-temperature QCD with chiral symmetry restoration and U(1) axial symmetry
breaking, the partition function for sufficiently light quarks can be expressed
as an ensemble of noninteracting objects with topological charge that obey the
Poisson statistics. We argue that the topological objects are
"quasi-instantons" (rather than bare instantons) taking into account quantum
effects. Our result is valid even close to the (pseudo)critical temperature of
the chiral phase transition.
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Moduli Backreaction on Inflationary Attractors: We investigate the interplay between moduli dynamics and inflation, focusing
on the KKLT-scenario and cosmological $\alpha$-attractors. General couplings
between these sectors can induce a significant backreaction and potentially
destroy the inflationary regime; however, we demonstrate that this generically
does not happen for $\alpha$-attractors. Depending on the details of the
superpotential, the volume modulus can either be stable during the entire
inflationary trajectory, or become tachyonic at some point and act as a
waterfall field, resulting in a sudden end of inflation. In the latter case
there is a universal supersymmetric minimum where the scalars end up,
preventing the decompactification scenario. The gravitino mass is independent
from the inflationary scale with no fine-tuning of the parameters. The
observational predictions conform to the universal value of attractors, fully
compatible with the Planck data, with possibly a capped number of e-folds due
to the interplay with moduli.
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MHV Techniques for QED Processes: Significant progress has been made in the past year in developing new `MHV'
techniques for calculating multiparticle scattering amplitudes in Yang-Mills
gauge theories. Most of the work so far has focussed on applications to Quantum
Chromodynamics, both at tree and one-loop level. We show how such techniques
can also be applied to abelian theories such as QED, by studying the simplest
tree-level multiparticle process, e^+e^- to n \gamma. We compare explicit
results for up to n=5 photons using both the Cachazo, Svrcek and Witten `MHV
rules' and the related Britto-Cachazo-Feng `recursion relation' approaches with
those using traditional spinor techniques.
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Multicritical tensor models and hard dimers on spherical random lattices: Random tensor models which display multicritical behaviors in a remarkably
simple fashion are presented. They come with entropy exponents \gamma =
(m-1)/m, similarly to multicritical random branched polymers. Moreover, they
are interpreted as models of hard dimers on a set of random lattices for the
sphere in dimension three and higher. Dimers with their exclusion rules are
generated by the different interactions between tensors, whose coupling
constants are dimer activities. As an illustration, we describe one
multicritical point, which is interpreted as a transition between the dilute
phase and a crystallized phase, though with negative activities.
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Higgs Field as Weak Boson in five Dimensions: We propose a five-dimensional standard model which regards the Higgs field as
a weak boson associated with the fifth dimension. The kinetic term of the Higgs
field is obtained from the fifth components of field strengths defined in five
dimension. The coupling constant of the fermion fields and the Higgs field is
only the weak coupling constant. However, since the vacuum expectation value
depends on the fifth coordinate, we can explain the various mass spectrum of
elementary particles.
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Functional Evolution of Free Quantum Fields: We consider the problem of evolving a quantum field between any two (in
general, curved) Cauchy surfaces. Classically, this dynamical evolution is
represented by a canonical transformation on the phase space for the field
theory. We show that this canonical transformation cannot, in general, be
unitarily implemented on the Fock space for free quantum fields on flat
spacetimes of dimension greater than 2. We do this by considering time
evolution of a free Klein-Gordon field on a flat spacetime (with toroidal
Cauchy surfaces) starting from a flat initial surface and ending on a generic
final surface. The associated Bogolubov transformation is computed; it does not
correspond to a unitary transformation on the Fock space. This means that
functional evolution of the quantum state as originally envisioned by Tomonaga,
Schwinger, and Dirac is not a viable concept. Nevertheless, we demonstrate that
functional evolution of the quantum state can be satisfactorily described using
the formalism of algebraic quantum field theory. We discuss possible
implications of our results for canonical quantum gravity.
|
Ginzburg-Landau effective action for a fluctuating holographic
superconductor: Under holographic prescription for Schwinger-Keldysh closed time contour for
non-equilibrium system, we consider fluctuation effect of the order parameter
in a holographic superconductor model. Near the critical point, we derive the
time-dependent Ginzburg-Landau effective action governing dynamics of the
fluctuating order parameter. In a semi-analytical approach, the time-dependent
Ginzburg-Landau action is computed up to quartic order of the fluctuating order
parameter, and first order in time derivative.
|
Black hole entropy and moduli-dependent species scale: We provide a moduli-dependent definition of species scale in quantum gravity
based on black hole arguments. Concretely, it is derived from of a lower bound
on the entropy of extremal black holes with higher curvature corrections, which
ensures that the black hole can be reliably described within the effective
theory. By demanding that our definition coincides with a recent proposal for a
moduli-dependent species scale motivated from the topological string, we
conclude that the conjecture $\mathcal{Z}_{BH} = |\mathcal{Z}_{\rm top}|^2$
relating the black hole to the topological string partition functions should
hold, at least within the regime of validity of our analysis.
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On the Perturbative Quantization of Einstein-Hilbert Gravity Embedded in
a Higher Derivative Model: In a perturbative approach Einstein-Hilbert gravity is quantized about a flat
background. In order to render the model power counting renormalizable, higher
order curvature terms are added to the action. They serve as Pauli-Villars type
regulators and require an expansion in the number of fields in addition to the
standard expansion in the number of loops. Renormalization is then performed
within the BPHZL scheme, which provides the action principle to construct the
Slavnov-Taylor identity and invariant differential operators. The final
physical state space of the Einstein-Hilbert theory is realized via the quartet
mechanism of Kugo and Ojima. Renormalization group and Callan-Symanzik equation
are derived for the Green functions and, formally, also for the $S$-matrix.
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Structure constants of operators on the Wilson loop from integrability: We study structure constants of local operators inserted on the Wilson loop
in ${\cal N}=4$ super Yang-Mills theory. We compute the structure constants in
the SU(2) sector at tree level using the correspondence between operators on
the Wilson loop and the open spin chain. The results are interpreted as the
summation over all possible ways of changing the signs of magnon momenta in the
hexagon form factors. This is consistent with a holographic description of the
correlator as the cubic open string vertex, which consists of one hexagonal
patch and three boundaries. We then conjecture that a similar expression should
hold also at finite coupling.
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Bootstrapping 2d $φ^4$ Theory with Hamiltonian Truncation Data: We combine the methods of Hamiltonian Truncation and the recently proposed
generalisation of the S-matrix bootstrap that includes local operators to
determine the two-particle scattering amplitude and the two-particle form
factor of the stress tensor at $s>0$ in the 2d $\phi^4$ theory. We use the form
factor of the stress tensor at $s\le 0$ and its spectral density computed using
Lightcone Conformal Truncation (LCT), and inject them into the generalized
S-matrix bootstrap set-up. The obtained results for the scattering amplitude
and the form factor are fully reliable only in the elastic regime. We
independently construct the "pure" S-matrix bootstrap bounds (bootstrap without
including matrix elements of local operators), and find that the sinh-Gordon
model and its analytic continuation the "staircase model" saturate these
bounds. Surprisingly, the $\phi^4$ two-particle scattering amplitude also very
nearly saturates these bounds, and moreover is extremely close to that of the
sinh-Gordon/staircase model.
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String Theory Versus Black Hole Complementarity: It is argued that string theory on the Euclidean version of the Schwarzschild
black hole -- the cigar geometry -- admits a zero mode that is localized at the
tip of the cigar. The presence of this mode implies that in string theory,
unlike in general relativity, the tip of the cigar is a special region. This is
in tension with the Euclidean version of the black hole complementarity
principle. We provide some qualitative arguments that link between this zero
mode and the origin of the black hole entropy and firewall at the horizon.
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Correspondences among CFTs with different W-algebra symmetry: W-algebras are constructed via quantum Hamiltonian reduction associated with
a Lie algebra $\mathfrak{g}$ and an $\mathfrak{sl}(2)$-embedding into
$\mathfrak{g}$. We derive correspondences among correlation functions of
theories having different W-algebras as symmetry algebras. These W-algebras are
associated to the same $\mathfrak{g}$ but distinct
$\mathfrak{sl}(2)$-embeddings.
For this purpose, we first explore different free field realizations of
W-algebras and then generalize previous works on the path integral derivation
of correspondences of correlation functions. For
$\mathfrak{g}=\mathfrak{sl}(3)$, there is only one non-standard (non-regular)
W-algebra known as the Bershadsky-Polyakov algebra. We examine its free field
realizations and derive correlator correspondences involving the WZNW theory of
$\mathfrak{sl}(3)$, the Bershadsky-Polyakov algebra and the principal
$W_3$-algebra. There are three non-regular W-algebras associated to
$\mathfrak{g}=\mathfrak{sl}(4)$. We show that the methods developed for
$\mathfrak{g}=\mathfrak{sl}(3)$ can be applied straightforwardly. We briefly
comment on extensions of our techniques to general $\mathfrak{g}$.
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Surface defects, the superconformal index and q-deformed Yang-Mills: Recently a prescription to compute the four-dimensional N = 2 superconformal
index in the presence of certain BPS surface defects has been given. These
surface defects are labelled by symmetric representations of SU(N). In the
present paper we give a prescription to compute the superconformal index in the
presence of surface defects labelled by arbitrary representations of SU(N).
Furthermore, we extend the dictionary between the N = 2 superconformal
Schur-index and correlators of q-deformed Yang-Mills to incorporate such
surface defects.
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Elliptic quantum groups: This note for the Proceedings of the International Congress of Mathematical
Physics gives an account of a construction of an ``elliptic quantum group''
associated with each simple classical Lie algebra. It is closely related to
elliptic face models of statistical mechanics, and, in its semiclassical limit,
to the Wess-Zumino-Witten model of conformal field theory on tori.
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Branes from a non-Abelian (2,0) tensor multiplet with 3-algebra: In this paper, we study the equations of motion for non-Abelian N=(2,0)
tensor multiplets in six dimensions, which were recently proposed by Lambert
and Papageorgakis. Some equations are regarded as constraint equations. We
employ a loop extension of the Lorentzian three-algebra (3-algebra) and examine
the equations of motion around various solutions of the constraint equations.
The resultant equations take forms that allow Lagrangian descriptions. We find
various (5+d)-dimensional Lagrangians and investigate the relation between them
from the viewpoint of M-theory duality.
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Fermionic Correlators from Integrability: We study three-point functions of single-trace operators in the su(1|1)
sector of planar N = 4 SYM borrowing several tools based on Integrability. In
the most general configuration of operators in this sector, we have found a
determinant expression for the tree-level structure constants. We then compare
the predictions of the recently proposed hexagon program against all available
data. We have obtained a match once additional sign factors are included when
the two hexagon form-factors are assembled together to form the structure
constants. In the particular case of one BPS and two non-BPS operators we
managed to identify the relevant form-factors with a domain wall partition
function of a certain six-vertex model. This partition function can be
explicitly evaluated and factorizes at all loops. In addition, we use this
result to compute the structure constants and show that at strong coupling in
the so-called BMN regime, its leading order contribution has a determinant
expression.
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Non-Abelian Brane Worlds: The Heterotic String Story: We discuss chiral supersymmetric compactifications of the SO(32) heterotic
string on Calabi-Yau manifolds equipped with direct sums of stable bundles with
structure group U(n). In addition we allow for non-perturbative heterotic
five-branes. These models are S-dual to Type I compactifications with D9- and
D5-branes, which by themselves are mirror symmetric to general intersecting
D6-brane models. For the construction of concrete examples we consider
elliptically fibered Calabi-Yau manifolds with SU(n) bundles given by the
spectral cover construction. The U(n) bundles are obtained via twisting by line
bundles. We present a four-generation Pati-Salam and a three-generation
Standard-like model.
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Kaehler Corrections for the Volume Modulus of Flux Compactifications: No-scale models arise in many compactifications of string theory and
supergravity, the most prominent recent example being type IIB flux
compactifications. Focussing on the case where the no-scale field is a single
unstabilized volume modulus (radion), we analyse the general form of
supergravity loop corrections that affect the no-scale structure of the Kaehler
potential. These corrections contribute to the 4d scalar potential of the
radion in a way that is similar to the Casimir effect. We discuss the interplay
of this loop effect with string-theoretic alpha' corrections and its possible
role in the stabilization of the radion.
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PT-Symmetric Quantum Electrodynamics: The Hamiltonian for quantum electrodynamics becomes non-Hermitian if the
unrenormalized electric charge $e$ is taken to be imaginary. However, if one
also specifies that the potential $A^\mu$ in such a theory transforms as a
pseudovector rather than a vector, then the Hamiltonian becomes PT symmetric.
The resulting non-Hermitian theory of electrodynamics is the analog of a
spinless quantum field theory in which a pseudoscalar field $\phi$ has a cubic
self-interaction of the form $i\phi^3$. The Hamiltonian for this cubic scalar
field theory has a positive spectrum, and it has recently been demonstrated
that the time evolution of this theory is unitary. The proof of unitarity
requires the construction of a new operator called C, which is then used to
define an inner product with respect to which the Hamiltonian is self-adjoint.
In this paper the corresponding C operator for non-Hermitian quantum
electrodynamics is constructed perturbatively. This construction demonstrates
the unitarity of the theory. Non-Hermitian quantum electrodynamics is a
particularly interesting quantum field theory model because it is
asymptotically free.
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About the S^3 Group-manifold Reduction of Einstein Gravity: We exhibit a new consistent group-manifold reduction of pure Einstein gravity
in the vielbein formulation when the compactification group manifold is S^3.
The novel feature in the reduction is to exploit the two 3-dimensional Lie
algebras that S^3 admits. The first algebra is introduced into the
group-manifold reduction in the standard way through the Maurer-Cartan 1-forms
associated to the symmetry of the general coordinate transformations. The
second algebra is associated to the linear adjoint group and it is introduced
into the group-manifold reduction through a local transformation in the
internal tangent space. We discuss the characteristics of the resulting
lower-dimensional theory and we emphasize the novel results generated by the
new group-manifold reduction. As an application of the reduction we show that
the lower-dimensional theory admits a domain wall solution which upon uplifting
to the higher-dimension results to be the self-dual (in the non-vanishing
components of both curvature and spin connection) Kaluza-Klein monopole. This
discussion may be relevant in the dimensional reductions of M-theory, string
theory and also in the Bianchi cosmologies in four dimensions.
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An extended standard model and its Higgs geometry from the matrix model: We find a simple brane configuration in the IKKT matrix model which resembles
the standard model at low energies, with a second Higgs doublet and
right-handed neutrinos. The electroweak sector is realized geometrically in
terms of two minimal fuzzy ellipsoids, which can be interpreted in terms of
four point-branes in the extra dimensions. The electroweak Higgs connects these
branes and is an indispensable part of the geometry. Fermionic would-be zero
modes arise at the intersections with two larger branes, leading precisely to
the correct chiral matter fields at low energy, along with right-handed
neutrinos which can acquire a Majorana mass due to a Higgs singlet. The larger
branes give rise to $SU(3)_c$, extended by $U(1)_B$ and another $U(1)$ which
are anomalous at low energies and expected to disappear. At higher energies,
mirror fermions and additional fields arise, completing the full ${\cal N}=4$
supersymmetry. The brane configuration is a solution of the model, assuming a
suitable effective potential and a non-linear stabilization of the singlet
Higgs. The basic results can be carried over to ${\cal N}=4$ $SU(N)$
super-Yang-Mills on ordinary Minkowski space with sufficiently large $N$.
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Non-abelian plane waves and stochastic regimes for (2+1)-dimensional
gauge field models with Chern-Simons term: An exact time-dependent solution of field equations for the 3-d gauge field
model with a Chern-Simons (CS) topological mass is found. Limiting cases of
constant solution and solution with vanishing topological mass are considered.
After Lorentz boost, the found solution describes a massive nonlinear
non-abelian plane wave. For the more complicate case of gauge fields with CS
mass interacting with a Higgs field, the stochastic character of motion is
demonstrated.
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Search for new physics in light of interparticle potentials and a very
heavy dark matter candidate: It is generally well known that the Standard Model of particle physics is not
the ultimate theory of fundamental interactions as it has inumerous unsolved
problems, so it must be extended. Deciphering the nature of dark matter remains
one of the great challenges of contemporary physics. Supersymmetry is probably
the most attractive extension of the SM. In the first part of this thesis we
study the interparticle potentials generated by the interactions between
spin-1/2 sources that are mediated by spin-1 particles in the limit of low
momentum transfer. We investigate different representations of spin-1 particle
to see how it modifies the profiles of the interparticle potentials and we also
include in our analysis all types of couplings between fermionic currents and
the mediator boson. The spin- and velocity-dependent interparticle potentials
that we obtain can be used to explain effects possibly associated to new
macroscopic forces such as modifications of the inverse-square law and possible
spin-gravity coupling effects. The second part of this thesis is based on the
dark matter phenomenology of well-motivated $U(1)'$ extensions of the Minimal
Supersymmetric Standard Model. In these models the right-handed sneutrino is a
good DM candidate whose dark matter properties are in agreement with the
present relic density and current experimental limits on the DM-nucleon
scattering cross section. In order to see how heavy can the RH sneutrino be as
a viable thermal dark matter candidate we explore its DM properties in the
parameter region that minimize its relic density via resonance effects and thus
allows it to be a heavier DM particle. We found that the RH sneutrino can
behave as a good DM particle within minimal cosmology even with masses of the
order of tens of TeV, which is much above the masses that viable thermal DM
candidates usually have in most of dark matter particle models.
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Coulomb Branch and The Moduli Space of Instantons: The moduli space of instantons on C^2 for any simple gauge group is studied
using the Coulomb branch of N=4 gauge theories in three dimensions. For a given
simple group G, the Hilbert series of such an instanton moduli space is
computed from the Coulomb branch of the quiver given by the over-extended
Dynkin diagram of G. The computation includes the cases of non-simply-laced
gauge groups G, complementing the ADHM constructions which are not available
for exceptional gauge groups. Even though the Lagrangian description for
non-simply laced Dynkin diagrams is not currently known, the prescription for
computing the Coulomb branch Hilbert series of such diagrams is very simple.
For instanton numbers one and two, the results are in agreement with previous
works. New results and general features for the moduli spaces of three and
higher instanton numbers are reported and discussed in detail.
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Projectors, Shadows, and Conformal Blocks: We introduce a method for computing conformal blocks of operators in
arbitrary Lorentz representations in any spacetime dimension, making it
possible to apply bootstrap techniques to operators with spin. The key idea is
to implement the "shadow formalism" of Ferrara, Gatto, Grillo, and Parisi in a
setting where conformal invariance is manifest. Conformal blocks in
$d$-dimensions can be expressed as integrals over the projective null-cone in
the "embedding space" $\mathbb{R}^{d+1,1}$. Taking care with their analytic
structure, these integrals can be evaluated in great generality, reducing the
computation of conformal blocks to a bookkeeping exercise. To facilitate
calculations in four-dimensional CFTs, we introduce techniques for writing down
conformally-invariant correlators using auxiliary twistor variables, and
demonstrate their use in some simple examples.
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Free BMN Correlators With More Stringy Modes: In the type IIB maximally supersymmetric pp-wave background, stringy excited
modes are described by BMN (Berenstein-Madalcena-Nastase) operators in the dual
$\mathcal{N}=4$ super-Yang-Mills theory. In this paper, we continue the studies
of higher genus free BMN correlators with more stringy modes, mostly focusing
on the case of genus one and four stringy modes in different transverse
directions. Surprisingly, we find that the non negativity of torus two-point
functions, which is a consequence of a previously proposed probability
interpretation and has been verified in the cases with two and three stringy
modes, is no longer true for the case of four or more stringy modes.
Nevertheless, the factorization formula, which is also a proposed holographic
dictionary relating the torus two-point function to a string diagram
calculation, is still valid. We also check the correspondence of planar
three-point functions with Green-Schwarz string vertex with many string modes.
We discuss some issues in the case of multiple stringy modes in the same
transverse direction. Our calculations provide some new perspectives on pp-wave
holography.
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A discussion on a possibility to interpret quantum mechanics in terms of
general relativity: It is shown that, with some reasonable assumptions, the theory of general
relativity can be made compatible with quantum mechanics by using the field
equations of general relativity to construct a Robertson-Walker metric for a
quantum particle so that the line element of the particle can be transformed
entirely to that of the Minkowski spacetime, which is assumed by a quantum
observer, and the spacetime dynamics of the particle described by a Minkowski
observer takes the form of quantum mechanics. Spacetime structure of a quantum
particle may have either positive or negative curvature. However, in order to
be describable using the familiar framework of quantum mechanics, the spacetime
structure of a quantum particle must be "quantised" by an introduction of the
imaginary number $i$. If a particle has a positive curvature then the
quantisation is equivalent to turning the pseudo-Riemannian spacetime of the
particle into a Riemannian spacetime. This means that it is assumed the
particle is capable of measuring its temporal distance like its spatial
distances. On the other hand, when a particle has a negative curvature and a
negative energy density then quantising the spacetime structure of the particle
is equivalent to viewing the particle as if it had a positive curvature and a
positive energy density.
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Higher Form Symmetries and M-theory: We discuss the geometric origin of discrete higher form symmetries of quantum
field theories in terms of defect groups from geometric engineering in
M-theory. The flux non-commutativity in M-theory gives rise to (mixed) 't Hooft
anomalies for the defect group which constrains the corresponding global
structures of the associated quantum fields. We analyze the example of 4d
$\mathcal{N}=1$ SYM gauge theory in four dimensions, and we reproduce the
well-known classification of global structures from reading between its lines.
We extend this analysis to the case of 7d $\mathcal{N}=1$ SYM theory, where we
recover it from a mixed 't Hooft anomaly among the electric 1-form center
symmetry and the magnetic 4-form center symmetry in the defect group. The case
of five-dimensional SCFTs from M-theory on toric singularities is discussed in
detail. In that context we determine the corresponding 1-form and 2-form defect
groups and we explain how to determine the corresponding mixed 't Hooft
anomalies from flux non-commutativity. Several predictions for non-conventional
5d SCFTs are obtained. The matching of discrete higher-form symmetries and
their anomalies provides an interesting consistency check for 5d dualities.
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N=2 Supersymmetric Yang-Mills and the Quantum Hall Effect: It is argued that there are strong similarities between the infra-red physics
of N=2 supersymmetric Yang-Mills and that of the quantum Hall effect, both
systems exhibit a hierarchy of vacua with a sub-group of the modular group
mapping between them. The scaling flow for pure SU(2) N=2 supersymmetric
Yang-Mills in 4-dimensions is re-examined and an earlier suggestion in the
literature, that was singular at strong coupling, is modified to a form that is
well behaved at both weak and strong coupling and describes the crossover in an
analytic fashion. Similarities between the phase diagram and the flow of SUSY
Yang-Mills and that of the quantum Hall effect are then described, with the
Hall conductivity in the latter playing the role of the theta-parameter in the
former. Hall plateaux, with odd denominator filling fractions, are analogous to
fixed points at strong coupling in N=2 SUSY Yang-Mills, where the massless
degrees of freedom carry an odd monopole charge.
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Casimir effect for a dilute dielectric ball at finite temperature: The Casimir effect at finite temperature is investigated for a dilute
dielectric ball; i.e., the relevant internal and free energies are calculated.
The starting point in this study is a rigorous general expression for the
internal energy of a system of noninteracting oscillators in terms of the sum
over the Matsubara frequencies. Summation over the angular momentum values is
accomplished in a closed form by making use of the addition theorem for the
relevant Bessel functions. For removing the divergences the renormalization
procedure is applied that has been developed in the calculation of the
corresponding Casimir energy at zero temperature. The behavior of the
thermodynamic characteristics in the low and high temperature limits is
investigated.
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Running Newton Constant, Improved Gravitational Actions, and Galaxy
Rotation Curves: A renormalization group (RG) improvement of the Einstein-Hilbert action is
performed which promotes Newton's constant and the cosmological constant to
scalar functions on spacetime. They arise from solutions of an exact RG
equation by means of a ``cutoff identification'' which associates RG scales to
the points of spacetime. The resulting modified Einstein equations for
spherically symmetric, static spacetimes are derived and analyzed in detail.
The modifications of the Newtonian limit due to the RG evolution are obtained
for the general case. As an application, the viability of a scenario is
investigated where strong quantum effects in the infrared cause Newton's
constant to grow at large (astrophysical) distances. For two specific RG
trajectories exact vacuum spacetimes modifying the Schwarzschild metric are
obtained by means of a solution-generating Weyl transformation. Their possible
relevance to the problem of the observed approximately flat galaxy rotation
curves is discussed. It is found that a power law running of Newton's constant
with a small exponent of the order $10^{-6}$ would account for their
non-Keplerian behavior without having to postulate the presence of any dark
matter in the galactic halo.
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Generating Quantum Matrix Geometry from Gauged Quantum Mechanics: Quantum matrix geometry is the underlying geometry of M(atrix) theory.
Expanding upon the idea of level projection, we propose a quantum-oriented
non-commutative scheme for generating the matrix geometry of the coset space
$G/H$. We employ this novel scheme to unveil unexplored matrix geometries by
utilizing gauged quantum mechanics on higher dimensional spheres. The resultant
matrix geometries manifest as $\it{pure}$ quantum Nambu geometries: Their
non-commutative structures elude capture through the conventional commutator
formalism of Lie algebra, necessitating the introduction of the quantum Nambu
algebra. This matrix geometry embodies a one-dimension-lower quantum internal
geometry featuring nested fuzzy structures. While the continuum limit of this
quantum geometry is represented by overlapping classical manifolds, their
fuzzification cannot reproduce the original quantum geometry. We demonstrate
how these quantum Nambu geometries give rise to novel solutions in Yang-Mills
matrix models, exhibiting distinct physical properties from the known fuzzy
sphere solutions.
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A Localization Computation in Confining Phase: In this note we show that the gaugino condensation of 4d N=1 supersymmetric
gauge theories in the confining phase can be computed by the localization
technique with an appropriate choice of a supersymmetry generator.
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${\mathscr {M}}$cTEQ (${\mathscr {M}}$ ${\bf c}$hiral perturbation
theory-compatible deconfinement ${\bf T}$emperature and ${\bf E}$ntanglement
Entropy up to terms ${\bf Q}$uartic in curvature) and FM (${\bf F}$lavor
${\bf M}$emory): A holographic computation of $T_c$ at ${\it intermediate\ coupling}$ from
M-theory dual of thermal QCD-like theories, has been missing in the literature.
Filling this gap, we demonstrate a novel UV-IR mixing, (conjecture and provide
evidence for) a non-renormalization beyond 1 loop of ${\bf M}-{\bf c}$hiral
perturbation theory arXiv:2011.04660[hep-th]-compatible deconfinement ${\bf
T}$emperature, and show equivalence with an ${\bf E}$ntanglement (as well as
Wald) entropy arXiv:0709.2140[hep-th] computation, up to terms ${\bf Q}$uartic
in curvature. We demonstrate a ${\bf F}$lavor-${\bf M}$emory (FM) effect in the
M-theory uplifts of the gravity duals, wherein the no-braner M-theory uplift
retains the "memory" of the flavor D7-branes of the parent type IIB dual in the
sense that a specific combination of the aforementioned quartic corrections to
the metric components precisely along the compact part of the non-compact
four-cycle "wrapped" by the flavor D7-branes, is what determines, e.g., the
Einstein-Hilbert action at O$(R^4)$. The same linear combination of O$(R^4)$
metric corrections, upon matching the phenomenological value of the coupling
constant of one of the SU(3) NLO ChPT Lagrangian, is required to have a
definite sign. Interestingly, in the decompactification limit of the spatial
circle, we ${\it derive}$ this, and obtain the values of the relevant O$(R^4)$
metric corrections. Further, equivalence with Wald entropy for the black hole
at ${\cal O}(R^4)$ imposes a linear constraint on the same linear combination
of metric corrections. Remarkably, when evaluating $T_c$ from an entanglement
entropy computation in the thermal gravity dual, due to a delicate cancelation
between the ${\cal O}(R^4)$ corrections from a subset of the abovementioned
metric components, one sees that there are no corrections to $T_c$ at quartic
order supporting the conjecture referred to above.
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Confinement and the Short Type I' Flux Tube: We show that the recent world-sheet analysis of the quantum fluctuations of a
short flux tube in type II string theory leads to a simple and precise
description of a pair of stuck D0branes in an orientifold compactification of
the type I' string theory. The existence of a stable type I' flux tube of
sub-string-scale length is a consequence of the confinement of quantized flux
associated with the scalar dualized ten-form background field strength *F_{10},
evidence for a -2brane in the BPS spectrum of M theory. Using heterotic-type I
duality, we infer the existence of an M2brane of finite width O(\sqrt{\alpha'})
in M-theory, the strong coupling resolution of a spacetime singularity in the
D=9 twisted and toroidally compactified E_8 x E_8 heterotic string. This
phenomenon has a bosonic string analog in the existence of a stable short
electric flux tube arising from the confinement of photons due to tachyon field
dynamics. The appendix clarifies the appearance of nonperturbative states and
enhanced gauge symmetry in toroidal compactifications of the type I' string. We
account for all of the known disconnected components of the moduli space of
theories with sixteen supercharges, in striking confirmation of heterotic-type
I duality.
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Reply to the comment by D. Kreimer and E. Mielke: We respond to the comment by Kreimer et. al. about the torsional contribution
to the chiral anomaly in curved spacetimes. We discuss their claims and refute
its main conclusion.
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Rotating black holes at future colliders: Greybody factors for brane
fields: We study theoretical aspects of the rotating black hole production and
evaporation in the extra dimension scenarios with TeV scale gravity, within the
mass range in which the higher dimensional Kerr solution provides good
description. We evaluate the production cross section of black holes taking
their angular momenta into account. We find that it becomes larger than the
Schwarzschild radius squared, which is conventionally utilized in literature,
and our result nicely agrees with the recent numerical study by Yoshino and
Nambu within a few percent error for higher dimensional case. In the same
approximation to obtain the above result, we find that the production cross
section becomes larger for the black hole with larger angular momentum. Second,
we derive the generalized Teukolsky equation for spin 0, 1/2 and 1 brane fields
in the higher dimensional Kerr geometry and explicitly show that it is
separable in any dimensions. For five-dimensional (Randall-Sundrum) black hole,
we obtain analytic formulae for the greybody factors in low frequency expansion
and we present the power spectra of the Hawking radiation as well as their
angular dependence. Phenomenological implications of our result are briefly
sketched.
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Blowup Equations for Refined Topological Strings: G\"{o}ttsche-Nakajima-Yoshioka K-theoretic blowup equations characterize the
Nekrasov partition function of five dimensional $\mathcal{N}=1$ supersymmetric
gauge theories compactified on a circle, which via geometric engineering
correspond to the refined topological string theory on $SU(N)$ geometries. In
this paper, we study the K-theoretic blowup equations for general local
Calabi-Yau threefolds. We find that both vanishing and unity blowup equations
exist for the partition function of refined topological string, and the crucial
ingredients are the $\bf r$ fields introduced in our previous paper. These
blowup equations are in fact the functional equations for the partition
function and each of them results in infinite identities among the refined free
energies. Evidences show that they can be used to determine the full refined
BPS invariants of local Calabi-Yau threefolds. This serves an independent and
sometimes more powerful way to compute the partition function other than the
refined topological vertex in the A-model and the refined holomorphic anomaly
equations in the B-model. We study the modular properties of the blowup
equations and provide a procedure to determine all the vanishing and unity $\bf
r$ fields from the polynomial part of refined topological string at large
radius point. We also find that certain form of blowup equations exist at
generic loci of the moduli space.
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The $\imath ε$ prescription in the SYK model: We introduce an $\imath \epsilon$ prescription for the SYK model both at
finite and at zero temperature. This prescription regularizes all the naive
ultraviolet divergences of the model. As expected the prescription breaks the
conformal invariance, but the latter is restored in the $\epsilon \to 0$ limit.
We prove rigorously that the Schwinger Dyson equation of the resummed two point
function at large $N$ and low momentum is recovered in this limit. Based on
this $\imath \epsilon$ prescription we introduce an effective field theory
Lagrangian for the infrared SYK model.
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Holonomies of gauge fields in twistor space 2: Hecke algebra,
diffeomorphism, and graviton amplitudes: We define a theory of gravity by constructing a gravitational holonomy
operator in twistor space. The theory is a gauge theory whose Chan-Paton factor
is given by a trace over elements of Poincar\'{e} algebra and Iwahori-Hecke
algebra. This corresponds to a fact that, in a spinor-momenta formalism,
gravitational theories are invariant under spacetime translations and
diffeomorphism. The former symmetry is embedded in tangent spaces of frame
fields while the latter is realized by a braid trace. We make a detailed
analysis on the gravitational Chan-Paton factor and show that an S-matrix
functional for graviton amplitudes can be expressed in terms of a
supersymmetric version of the holonomy operator. This formulation will shed a
new light on studies of quantum gravity and cosmology in four dimensions.
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Further discussion of Tomboulis' approach to the confinement problem: We discuss in some detail certain gaps and open problems in the recent paper
by E. T. Tomboulis, which claims to give a rigorous proof of quark confinement
in 4D lattice Yang-Mills theory for all values of the bare coupling. We also
discuss what would be needed to fill the gaps in his proof.
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On the Invariance of Residues of Feynman Graphs: We use simple iterated one-loop graphs in massless Yukawa theory and QED to
pose the following question: what are the symmetries of the residues of a graph
under a permutation of places to insert subdivergences. The investigation
confirms partial invariance of the residue under such permutations: the highest
weight transcendental is invariant under such a permutation. For QED this
result is gauge invariant, ie the permutation invariance holds for any gauge.
Computations are done making use of the Hopf algebra structure of graphs and
employing GiNaC to automate the calculations.
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The DeWitt Equation in Quantum Field Theory: We take a new look at the DeWitt equation, a defining equation for the
effective action functional in quantum field theory. We present a formal
solution to this equation, and discuss the equation in various contexts, and in
particular for models where it can be made completely well defined, such as the
Wess-Zumino model in two dimensions.
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A note on singular D-branes in group manifolds: After reviewing D-branes as conjugacy classes and various charge
quantizations (modulo $k$) in WZW model, we develop the classification and
systematic construction of all possible untwisted D-branes in Lie groups of
A-D-E series. D-branes are classified according to their positions in the
maximal torus. The moduli space of D-branes is naturally identified with a unit
cell in the weight space which is exponentiated to be the maximal torus.
However, for the D-brane classification, one may consider only the fundamental
Weyl domain that is surrounded by the hyperplanes defined by Weyl reflections.
We construct all the D-branes by the method of iterative deletion in the Dynkin
diagram. The dimension of a D-brane always becomes an even number and it
reduces as we go from a generic point of the fundamental domain to its higher
co-dimensional boundaries. Quantum mechanical stability requires that only
D-branes at discrete positions are allowed.
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Cargese lectures on string theory with eight supercharges: These lectures give an introduction to the interrelated topics of Calabi-Yau
compactification of the type II string, black hole attractors, the all-orders
entropy formula, the dual (0,4) CFT, topological strings and the OSV
conjecture. Based on notes by MG of lectures by AS at the 2006 Cargese summer
school.
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Backreaction of excitations on a vortex: Excitations of a vortex are usually considered in a linear approximation
neglecting their backreaction on the vortex. In the present paper we
investigate backreaction of Proca type excitations on a straightlinear vortex
in the Abelian Higgs model. We propose exact Ansatz for fields of the excited
vortex. From initial set of six nonlinear field equations we obtain (in a limit
of weak excitations) two linear wave equations for the backreaction
corrections. Their approximate solutions are found in the cases of plane wave
and wave packet type excitations. We find that the excited vortex radiates
vector field and that the Higgs field has a very broad oscillating component.
|
On the regularization scheme and gauge choice ambiguities in
topologically massive gauge theories: It is demonstrated that in the (2+1)-dimensional topologically massive gauge
theories an agreement of the Pauli-Villars regularization scheme with the other
schemes can be achieved by employing pairs of auxiliary fermions with the
opposite sign masses. This approach does not introduce additional violation of
discrete (P and T) symmetries. Although it breaks the local gauge symmetry only
in the regulator fields' sector, its trace disappears completely after removing
the regularization as a result of superrenormalizability of the model. It is
shown also that analogous extension of the Pauli-Villars regularization in the
vector particle sector can be used to agree the arbitrary covariant gauge
results with the Landau ones. The source of ambiguities in the covariant gauges
is studied in detail. It is demonstrated that in gauges that are softer in the
infrared region (e.g. Coulomb or axial) nonphysical ambiguities inherent to the
covariant gauges do not arise.
|
Mapping relativistic to ultra/non-relativistic conformal symmetries in
2D and finite $\sqrt{T\bar{T}}$ deformations: The conformal symmetry algebra in 2D (Diff($S^{1}$)$\oplus$Diff($S^{1}$)) is
shown to be related to its ultra/non-relativistic version
(BMS$_{3}$$\approx$GCA$_{2}$) through a nonlinear map of the generators,
without any sort of limiting process. For a generic classical CFT$_{2}$, the
BMS$_{3}$ generators then emerge as composites built out from the chiral
(holomorphic) components of the stress-energy tensor, $T$ and $\bar{T}$,
closing in the Poisson brackets at equal time slices. Nevertheless,
supertranslation generators do not span Noetherian symmetries. BMS$_{3}$
becomes a bona fide symmetry once the CFT$_{2}$ is marginally deformed by the
addition of a $\sqrt{T\bar{T}}$ term to the Hamiltonian. The generic deformed
theory is manifestly invariant under diffeomorphisms and local scalings, but it
is no longer a CFT$_{2}$ because its energy and momentum densities fulfill the
BMS$_{3}$ algebra. The deformation can also be described through the original
CFT$_{2}$ on a curved metric whose Beltrami differentials are determined by the
variation of the deformed Hamiltonian with respect to $T$ and $\bar{T}$.
BMS$_{3}$ symmetries then arise from deformed conformal Killing equations,
corresponding to diffeomorphisms that preserve the deformed metric and
stress-energy tensor up to local scalings. As an example, we briefly address
the deformation of $\mathrm{N}$ free bosons, which coincides with
ultra-relativistic limits only for $\mathrm{N}=1$. Furthermore, Cardy formula
and the S-modular transformation of the torus become mapped to their
corresponding BMS$_{3}$ (or flat) versions.
|
More on Non-supersymmetric Asymmetric Orbifolds with Vanishing
Cosmological Constant: We explore various non-supersymmetric type II string vacua constructed based
on asymmetric orbifolds of tori with vanishing cosmological constant at the one
loop. The string vacua we present are modifications of the models studied in
arXiv:1512.05155[hep-th], of which orbifold group is just generated by a single
element. We especially focus on two types of modifications: (i) the orbifold
twists include different types of chiral reflections not necessarily removing
massless Rarita-Schwinger fields in the 4-dimensional space-time, (ii) the
orbifold twists do not include the shift operator. We further discuss the
unitarity and stability of constructed non-supersymmetric string vacua, with
emphasizing the common features of them.
|
Q-lumps on a Domain Wall with a Spin-Orbit Interaction: The nonlinear O(3) sigma-model in (2+1) dimensions with an additional
potential term admits solutions called Q-lumps, having both topological and
Noether charges. We consider in 3+1-dimensional spacetime the theory with
Q-lumps on a domain wall in the presence of spin-orbit interaction in the bulk
and find interaction effects for a two-particle solution through perturbation
theory and adiabatic approximation.
|
Long quantum superstrings in AdS_5 x S^5: Following hep-th/0001204 we discuss the computation of quantum corrections
near long IIB superstring configurations in AdS_5 x S^5 which are related to
the Wilson loop expectation values in the strong coupling expansion of the dual
n=4 SYM theory with large N. We use the Green-Schwarz description of
superstrings in curved R-R backgrounds and demonstrate that it is well-defined
and useful for developing perturbation theory near long string backgrounds.
|
Constraints on Interacting Scalars in 2T Field Theory and No Scale
Models in 1T Field Theory: In this paper I determine the general form of the physical and mathematical
restrictions that arise on the interactions of gravity and scalar fields in the
2T field theory setting, in d+2 dimensions, as well as in the emerging shadows
in d dimensions. These constraints on scalar fields follow from an underlying
Sp(2,R) gauge symmetry in phase space. Determining these general constraints
provides a basis for the construction of 2T supergravity, as well as physical
applications in 1T-field theory, that are discussed briefly here, and more
detail elsewhere. In particular, no scale models that lead to a vanishing
cosmological constant at the classical level emerge naturally in this setting.
|
Non-Abelian discrete gauge symmetries in 4d string models: We study the realization of non-Abelian discrete gauge symmetries in 4d field
theory and string theory compactifications. The underlying structure
generalizes the Abelian case, and follows from the interplay between gaugings
of non-Abelian isometries of the scalar manifold and field identifications
making axion-like fields periodic. We present several classes of string
constructions realizing non-Abelian discrete gauge symmetries. In particular,
compactifications with torsion homology classes, where non-Abelianity arises
microscopically from the Hanany-Witten effect, or compactifications with
non-Abelian discrete isometry groups, like twisted tori. We finally focus on
the more interesting case of magnetized branes in toroidal compactifications
and quotients thereof (and their heterotic and intersecting duals), in which
the non-Abelian discrete gauge symmetries imply powerful selection rules for
Yukawa couplings of charged matter fields. In particular, in MSSM-like models
they correspond to discrete flavour symmetries constraining the quark and
lepton mass matrices, as we show in specific examples.
|
On P_T-distribution of gluon production rate in constant chromoelectric
field: A complete expression for the p_T-distribution of the gluon production rate
in the homogeneous chromoelectric field has been obtained. Our result contains
a new additional term proportional to the singular function \delta(p_T^2). We
demonstrate that the presence of this term is consistent with the dual symmetry
of QCD effective action and allows to reproduce the known result for the total
imaginary part of the effective action after integration over transverse
momentum.
|
Localization of Scalar Fluctuations in a Dilatonic Brane-World Scenario: We derive and solve the full set of scalar perturbation equations for a class
of $Z_2$-symmetric five-dimensional geometries generated by a bulk cosmological
constant and by a 3-brane non-minimally coupled to a bulk dilaton field. The
massless scalar modes, like their tensor analogues, are localized on the brane,
and provide long-range four-dimensional dilatonic interactions, which are
generically present even when matter on the brane carries no dilatonic charge.
The shorter-range corrections induced by the continuum of massive scalar modes
are always present: they persist even in the case of a trivial dilaton
background (the standard Randall--Sundrum configuration) and vanishing
dilatonic charges.
|
On the group generated by $\mathbf C$, $\mathbf{P}$ and $\mathbf T$:
$\mathbf {I^2 = T^2 = P^2 = I T P= -1}$, with applications to pseudo-scalar
mesons: We study faithful representations of the discrete Lorentz symmetry operations
of parity $\mathbf P$ and time reversal $\mathbf T$, which involve complex
phases when acting on fermions. If the phase of $\mathbf P$ is a rational
multiple of $\pi$ then $\mathbf P^{2 n}=1$ for some positive integer $n$ and it
is shown that, when this is the case, $\mathbf P$ and $\mathbf T$ generate a
discrete group, a dicyclic group (also known as a generalised quaternion group)
which are generalisations of the dihedral groups familiar from crystallography.
Charge conjugation $\mathbf C$ introduces another complex phase and, again
assuming rational multiples of $\pi$ for complex phases, $\mathbf T \mathbf C$
generates a cyclic group of order $2 m$ for some positive integer $m$.There is
thus a doubly infinite series of possible finite groups labelled by $n$ and
$m$. Demanding that $\mathbf C$ commutes with $\mathbf P$ and $\mathbf T$
forces $n=m=2$ and the group generated by $\mathbf P$ and $\mathbf T$ is
uniquely determined to be the quaternion group.
Neutral pseudo-scalar mesons can be simultaneous $\mathbf C$ and $\mathbf P$
eigenstates. $\mathbf T$ commutes with $\mathbf P$ and $\mathbf C$ when acting
on fermion bi-linears so neutral pseudo-scalar mesons can also be $\mathbf T$
eigenstates. The $\mathbf T$-parity should therefore be experimentally
observable and the $\mathbf{CPT}$ theorem dictates that $T= C P$.
|
BMS type symmetries at null-infinity and near horizon of non-extermal
black holes: In this paper we consider a generally covariant theory of gravity, and extend
the generalized off-shell ADT current such that it becomes conserved for field
dependent (asymptotically) Killing vector field. Then we define the extended
off-shell ADT current and the extended off-shell ADT charge. Consequently, we
define the conserved charge perturbation by integrating from the extended
off-shell ADT charge over a spacelike codimension two surface. Eventually, we
use the presented formalism to find the conserved charge perturbation of an
asymptotically flat spacetime. The conserved charge perturbation we obtain is
exactly matched with the result of the paper \cite{6'}. These charges are as
representations of the $BMS_4$ symmetry algebra. Also, we find that the near
horizon conserved charges of a non-extremal black hole with extended symmetries
are the Noether charges. For this case our result is also exactly matched with
that of the paper \cite{15}.
|
Cosmology in General Massive Gravity Theories: We study the cosmology of general massive gravity theories with five
propagating degrees of freedom. This large class of theories includes both the
case with a residual Lorentz invariance as the cases with simpler rotational
invariance. We find that the existence of a nontrivial homogeneous FRW
background, in addition to selecting the lorentz-breaking case, implies in
general that perturbations around strict Minkowski or dS space are strongly
coupled. The result is that dark energy can be naturally accounted for in
massive gravity but its equation of state w_eff has to deviate from -1. We find
indeed a relation between the strong coupling scale of perturbations and the
deviation of w_eff from -1. Taking into account current limits on w_eff and
submillimiter tests of the Newton's law as a limit on the possible strong
coupling regime, we find that it is still possible to have a weakly coupled
theory in a quasi dS background. Future experimental improvements may be used
to predict w_eff in a weakly coupled massive gravity theory
|
Charged Vector Inflation: We present a model of inflation in which the inflaton field is charged under
a triplet of $U(1)$ gauge fields. The model enjoys an internal $O(3)$ symmetry
supporting the isotropic FRW solution. With an appropriate coupling between the
gauge fields and the inflaton field, the system reaches an attractor regime in
which the gauge fields furnish a small constant fraction of the total energy
density. We decompose the scalar perturbations into the adiabatic and entropy
modes and calculate the contributions of the gauge fields into the curvature
perturbations power spectrum. We also calculate the entropy power spectrum and
the adiabatic-entropy cross correlation. In addition to the metric tensor
perturbations, there are tensor perturbations associated with the gauge field
perturbations which are coupled to metric tensor perturbations. We show that
the correction in primordial gravitational tensor power spectrum induced from
the matter tensor perturbation is a sensitive function of the gauge coupling.
|
On Newton's law in supersymmetric braneworld models: We study the propagation of gravitons within 5-D supersymmetric braneworld
models with a bulk scalar field. The setup considered here consists of a 5-D
bulk spacetime bounded by two 4-D branes localized at the fixed points of an
$S^1/Z_2$ orbifold. There is a scalar field $\phi$ in the bulk which, provided
a superpotential $W(\phi)$, determines the warped geometry of the 5-D
spacetime. This type of scenario is common in string theory, where the bulk
scalar field $\phi$ is related to the volume of small compact extra dimensions.
We show that, after the moduli are stabilized by supersymmetry breaking terms
localized on the branes, the only relevant degrees of freedom in the bulk
consist of a 5-D massive spectrum of gravitons. Then we analyze the
gravitational interaction between massive bodies localized at the positive
tension brane mediated by these bulk gravitons. It is shown that the Newtonian
potential describing this interaction picks up a non-trivial contribution at
short distances that depends on the shape of the superpotential $W(\phi)$. We
compute this contribution for dilatonic braneworld scenarios $W(\phi) =
e^{\alpha \phi}$ (where $\alpha$ is a constant) and discuss the particular case
of 5-D Heterotic M-theory: It is argued that a specific footprint at micron
scales could be observable in the near future.
|
Five-Dimensional Gauged Supergravity Black Holes with Independent
Rotation Parameters: We construct new non-extremal rotating black hole solutions in SO(6) gauged
five-dimensional supergravity. Our solutions are the first such examples in
which the two rotation parameters are independently specifiable, rather than
being set equal. The black holes carry charges for all three of the gauge
fields in the U(1)^3 subgroup of SO(6), albeit with only one independent charge
parameter. We discuss the BPS limits, showing in particular that these include
the first examples of regular supersymmetric black holes with independent
angular momenta in gauged supergravity. We also find non-singular BPS solitons.
Finally, we obtain another independent class of new rotating non-extremal black
hole solutions with just one non-vanishing rotation parameter, and one
non-vanishing charge.
|
$SU(2)$ Yang-Mills solitons in $R^2$ gravity: We construct new family of spherically symmetric regular solutions of $SU(2)$
Yang-Mills theory coupled to pure $R^2$ gravity. The particle-like field
configurations possess non-integer non-Abelian magnetic charge. A discussion of
the main properties of the solutions and their differences from the usual
Bartnik-McKinnon solitons in the asymptotically flat case is presented. It is
shown that there is continuous family of linearly stable non-trivial solutions
in which the gauge field has no nodes.
|
On the Covariant Quantization of Green-Schwarz Superstring and
Brink--Schwarz Superparticle: The effective action for the Brink-Schwarz Superparticle is constructed in an
infinite dimensional phase space using a gauge invariant formulation.
|
Schwinger's Dynamical Casimir Effect: Bulk Energy Contribution: Schwinger's Dynamical Casimir Effect is one of several candidate explanations
for sonoluminescence. Recently, several papers have claimed that Schwinger's
estimate of the Casimir energy involved is grossly inaccurate. In this letter,
we show that these calculations omit the crucial volume term. When the missing
term is correctly included one finds full agreement with Schwinger's result for
the Dynamical Casimir Effect. We have nothing new to say about sonoluminescence
itself except to affirm that the Casimir effect is energetically adequate as a
candidate explanation.
|
Borel resummation of secular divergences in stochastic inflation: We make use of Borel resummation to extract the exact time dependence from
the divergent series found in the context of stochastic inflation. Correlation
functions of self-interacting scalar fields in de Sitter spacetime are known to
develop secular IR divergences via loops, and the first terms of the divergent
series have been consistently computed both with standard techniques for curved
spacetime quantum field theory and within the framework of stochastic
inflation. We show that Borel resummation can be used to interpret the
divergent series and to correctly infer the time evolution of the correlation
functions. In practice, we adopt a method called Borel--Pad\'{e} resummation
where we approximate the Borel transformation by a Pad\'{e} approximant. We
also discuss the singularity structures of Borel transformations and mention
possible applications to cosmology.
|
Equations on knot polynomials and 3d/5d duality: We briefly review the current situation with various relations between
knot/braid polynomials (Chern-Simons correlation functions), ordinary and
extended, considered as functions of the representation and of the knot
topology. These include linear skein relations, quadratic Plucker relations, as
well as "differential" and (quantum) A-polynomial structures. We pay a special
attention to identity between the A-polynomial equations for knots and Baxter
equations for quantum relativistic integrable systems, related through
Seiberg-Witten theory to 5d super-Yang-Mills models and through the AGT
relation to the q-Virasoro algebra. This identity is an important ingredient of
emerging a 3d-5d generalization of the AGT relation. The shape of the Baxter
equation (including the values of coefficients) depend on the choice of the
knot/braid. Thus, like the case of KP integrability, where (some, so far torus)
knots parameterize particular points of the Universal Grassmannian, in this
relation they parameterize particular points in the moduli space of many-body
integrable systems of relativistic type.
|
Black Hole Thermodynamics with Conical Defects: Recently we have shown [1604.08812] how to formulate a thermodynamic first
law for a single (charged) accelerated black hole in AdS space by fixing the
conical deficit angles present in the spacetime. Here we show how to generalise
this result, formulating thermodynamics for black holes with varying conical
deficits. We derive a new potential for the varying tension defects: the
"thermodynamic length", both for accelerating and static black holes. We
discuss possible physical processes in which the tension of a string ending on
a black hole might vary, and also map out the thermodynamic phase space of
accelerating black holes and explore their critical phenomena.
|
Whitham Deformations and Tau Functions in N = 2 Supersymmetric Gauge
Theories: We review new aspects of integrable systems discovered recently in N=2
supersymmetric gauge theories and their topologically twisted versions. The
main topics are (i) an explicit construction of Whitham deformations of the
Seiberg-Witten curves for classical gauge groups, (ii) its application to
contact terms in the u-plane integral of topologically twisted theories, and
(iii) a connection between the tau functions and the blowup formula in
topologically twisted theories.
|
On the Stability of the Classical Vacua in a Minimal SU(5) 5-D
Supergravity Model: We consider a five-dimensional supergravity model with SU(5) gauge symmetry
and the minimal field content. Studying the arising scalar potential we find
that the gauging of the $U(1)_R$ symmetry of the five-dimensional supergravity
causes instabilities. Lifting the instabilities the vacua are of Anti-de-Sitter
type and SU(5) is broken along with supersymmetry. Keeping the $U(1)_R$
ungauged the potential has flat directions along which supersymmetry is
unbroken.
|
Classification of Normal Modes for Multiskyrmions: The normal mode spectra of multiskyrmions play a key role in their
quantisation. We present a general method capable of predicting all the
low-lying vibrational modes of known minimal energy multiskyrmions. In
particular, we explain the origin of the higher multipole breathing modes,
previously observed but not understood. We show how these modes may be
classified according to the symmetry group of the static solution. Our results
provide strong hints that the N-skyrmion moduli space, for N>3, may have a
richer structure than previously thought, incorporating 8N-4 degrees of
freedom.
|
A nonlocal charge for cylindrical gravitational waves: The classical scattering of cylindrical gravitational waves is exactly
solvable. The motivation for this paper is to understand if the quantum
scattering problem is also exactly solvable. The classical dynamics is governed
by a two dimensional sigma model. We study this sigma model's $S$-matrix. We
construct a conserved nonlocal charge and derive the associated tree-level
$S$-matrix conservation law. We check our conservation law directly using
Feynman diagrams. The existence of this symmetry is a hint that cylindrical
gravitational waves might have an exactly solvable $S$-matrix.
|
Interactions of a String Inspired Graviton Field: We continue to explore the possibility that the graviton in two dimensions is
related to a quadratic differential that appears in the anomalous contribution
of the gravitational effective action for chiral fermions. A higher dimensional
analogue of this field might exist as well. We improve the defining action for
this diffeomorphism tensor field and establish a principle for how it interacts
with other fields and with point particles in any dimension. All interactions
are related to the action of the diffeomorphism group. We discuss possible
interpretations of this field.
|
Vacuum polarization by a magnetic flux of special rectangular form: We consider the ground state energy of a spinor field in the background of a
square well shaped magnetic flux tube. We use the zeta- function regularization
and express the ground state energy as an integral involving the Jost function
of a two dimensional scattering problem. We perform the renormalization by
subtracting the contributions from first several heat kernel coefficients. The
ground state energy is presented as a convergent expression suited for
numerical evaluation. We discuss corresponding numerical calculations. Using
the uniform asymptotic expansion of the special functions entering the Jost
function we are able to calculate higher order heat kernel coefficients.
|
Conformal Field Theories in Fractional Dimensions: We study the conformal bootstrap in fractional space-time dimensions,
obtaining rigorous bounds on operator dimensions. Our results show strong
evidence that there is a family of unitary CFTs connecting the 2D Ising model,
the 3D Ising model, and the free scalar theory in 4D. We give numerical
predictions for the leading operator dimensions and central charge in this
family at different values of D and compare these to calculations of phi^4
theory in the epsilon-expansion.
|
AdS_2 D-Branes in Lorentzian AdS_3: The boundary states for AdS_2 D-branes in Lorentzian AdS_3 space-time are
presented. AdS_2 D-branes are algebraically defined by twisted Dirichlet
boundary conditions and are located on twisted conjugacy classes of SL(2,R).
Using free field representation of symmetry currents in the SL(2,R) WZNW model,
the twisted Dirichlet gluing conditions among currents are translated to
matching conditions among free fields and then to boundary conditions among the
modes of free fields. The Ishibashi states are written as coherent states on
AdS_3 in the free field formalism and it is shown that twisted Dirichlet
boundary conditions are satisfied on them. The tree-level amplitude of
propagation of closed strings between two AdS_2 D-branes is evaluated and by
comparing which to the characters of sl(2,R) Kac-Moody algebra it is shown that
only states in the principal continuous series representation of sl(2,R)
Kac-Moody algebra contributes to the amplitude and thus they are the only ones
that couple to AdS_2 D-branes. The form of the character of sl(2,R) principal
continuous series and the boundary condition among the zero modes are used to
determine the physical boundary states for AdS_2 D-branes.
|
AdS pp-waves: We obtain the pp-waves of D=5 and D=4 gauged supergravities supported by
$U(1)^3$ and $U(1)^4$ gauge field strengths respectively. We show that
generically these solutions preserve 1/4 of the supersymmetry, but
supernumerary supersymmetry can arise for appropriately constrained harmonic
functions associated with the pp-waves. In particular it implies that the
solutions are independent of the light-cone coordinate $x^+$. We also obtain
the pp-waves in the Freedman-Schwarz model.
|
Boundary divergences in vacuum self-energies and quantum field theory in
curved spacetime: It is well known that boundary conditions on quantum fields produce
divergences in the renormalized energy-momentum tensor near the boundaries.
Although irrelevant for the computation of Casimir forces between different
bodies, the self-energy couples to gravity, and the divergences may, in
principle, generate large gravitational effects. We present an analysis of the
problem in the context of quantum field theory in curved spaces. Our model
consists of a quantum scalar field coupled to a classical field that, in a
certain limit, imposes Dirichlet boundary conditions on the quantum field. We
show that the model is renormalizable and that the divergences in the
renormalized energy-momentum tensor disappear for sufficiently smooth
interfaces.
|
Noncommutative supergeometry, duality and deformations: We introduce a notion of $Q$-algebra that can be considered as a
generalization of the notion of $Q$-manifold (a supermanifold equipped with an
odd vector field obeying $\{Q,Q\} =0$). We develop the theory of connections on
modules over $Q$-algebras and prove a general duality theorem for gauge
theories on such modules. This theorem containing as a simplest case
$SO(d,d,{\bf Z})$-duality of gauge theories on noncommutative tori can be
applied also in more complicated situations. We show that $Q$-algebras appear
naturally in Fedosov construction of formal deformation of commutative algebras
of functions and that similar $Q$-algebras can be constructed also in the case
when the deformation parameter is not formal.
|
First order phase transition and corrections to its parameters in the
O(N) - model: The temperature phase transition in the $N$-component scalar field theory
with spontaneous symmetry breaking is investigated using the method combining
the second Legendre transform and with the consideration of gap equations in
the extrema of the free energy. After resummation of all super daisy graphs an
effective expansion parameter, $(1/2N)^{1/3}$, appears near $T_c$ for large
$N$. The perturbation theory in this parameter accounting consistently for the
graphs beyond the super daisies is developed. A certain class of such diagrams
dominant in 1/N is calculated perturbatively. Corrections to the
characteristics of the phase transition due to these contributions are obtained
and turn out to be next-to-leading order as compared to the values derived on
the super daisy level and do not alter the type of the phase transition which
is weakly first-order. In the limit $N$ goes to infinity the phase transition
becomes second order. A comparison with other approaches is done.
|
Chirality Changing Phase Transitions in 4d String Vacua: We provide evidence that some four-dimensional N=1 string vacua with
different numbers of generations are connected through phase transitions. The
transitions involve going through a point in moduli space where there is a
nontrivial fixed point governing the low energy field theory. In an M-theory
description, the examples involve wrapped 5-branes leaving one of the ends of
the world.
|
Symmetry Enhancements in 7d Heterotic Strings: We use a moduli space exploration algorithm to produce a complete list of
maximally enhanced gauge groups that are realized in the heterotic string in
7d, encompassing the usual Narain component, and five other components with
rank reduction realized via nontrivial holonomy triples. Using lattice
embedding techniques we find an explicit match with the mechanism of
singularity freezing in M-theory on K3. The complete global data for each gauge
group is explicitly given.
|
Holographic Glueballs and Infrared Wall Driven by Dilaton: We study glueballs in the holographic gauge theories, supersymmetric and
non-super symmetric cases, which are given by the type IIB superstring
solutions with non-trivial dilaton. In both cases, the dilaton reflects the
condensate of the gauge field strength, $<F^2>$, which is responsible to the
linear confining potential between the quark and anti-quark. Then we could see
the meson spectra. On the other hand, the glueball spectra are not found in the
supersymmetric case. We need a sharp wall, which corresponds to an infrared
cutoff, in order to obtain the glueballs. In the non-supersymmetric case, the
quantized glueballs are actually observed due to the existence of such a wall
driven by the dilaton. The strings and D-branes introduced as building blocks
of hadrons are pushed out by this wall, and we could see the Regge behavior of
the higher spin meson and glueball states. We find that the slope of the
glueball trajectory is half of the flavor meson's one. As for the low spin
glueballs, they are studied by solving the fluctuations of the bulk fields, and
their discrete spectra are shown.
|
On Newton-Cartan trace anomalies: We classify the trace anomaly for parity-invariant non-relativistic
Schr\"odinger theories in 2+1 dimensions coupled to background Newton-Cartan
gravity. The general anomaly structure looks very different from the one in the
z=2 Lifshitz theories. The type A content of the anomaly is remarkably
identical to that of the relativistic 3+1 dimensional case, suggesting the
conjecture that an a-theorem should exist also in the Newton-Cartan context.
Erratum: due to an overcounting of the number of linearly-independent terms
in the basis, the type A anomaly disappears if Frobenius condition is imposed.
See appended erratum for details. This crucial mistake was pointed out to us in
arXiv:1601.06795.
|
Counting Chiral Operators in Quiver Gauge Theories: We discuss in detail the problem of counting BPS gauge invariant operators in
the chiral ring of quiver gauge theories living on D-branes probing generic
toric CY singularities. The computation of generating functions that include
counting of baryonic operators is based on a relation between the baryonic
charges in field theory and the Kaehler moduli of the CY singularities. A study
of the interplay between gauge theory and geometry shows that given geometrical
sectors appear more than once in the field theory, leading to a notion of
"multiplicities". We explain in detail how to decompose the generating function
for one D-brane into different sectors and how to compute their relevant
multiplicities by introducing geometric and anomalous baryonic charges. The
Plethystic Exponential remains a major tool for passing from one D-brane to
arbitrary number of D-branes. Explicit formulae are given for few examples,
including C^3/Z_3, F_0, and dP_1.
|
Lectures on Supergravity p-branes: We review the properties of classical p-brane solutions to supergravity
theories, i.e. solutions that may be interpreted as Poincare-invariant
hyperplanes in spacetime. Topics covered include the distinction between
elementary/electric and solitonic/magnetic solutions, examples of singularity
and global structure, relations between mass densities, charge densities and
the preservation of unbroken supersymmetry, diagonal and vertical Kaluza-Klein
reduction families, Scherk-Schwarz reduction and domain walls, and the
classification of multiplicities using duality symmetries.
|
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