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Critical Phenomena, Strings, and Interfaces: Some points concerning the relation of strings to interfaces in statistical
systems are discussed.
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Supercurrent in p-wave Holographic Superconductor: The p-wave and $p+ip$-wave holographic superconductors with fixed DC
supercurrent are studied by introducing a non-vanishing vector potential. We
find that close to the critical temperature $T_c$ of zero current, the
numerical results of both the p wave model and the $p+ip$ model are the same as
those of Ginzburg-Landau (G-L) theory, for example, the critical current $j_c
\sim (T_c-T)^{3/2}$ and the phase transition in the presence of a DC current is
a first order transition. Besides the similar results between both models, the
$p+ip$ superconductor shows isotropic behavior for the supercurrent, while the
p-wave superconductor shows anisotropic behavior for the supercurrent.
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Spiky Strings, Giant Magnons and beta-deformations: We study rigid string solutions rotating on the S^3 subspace of the
beta-deformed AdS_5xS^5 background found by Lunin and Maldacena. For particular
values of the parameters of the solutions we find the known giant magnon and
single spike strings. We present a single spike string solution on the deformed
S^3 and find how the deformation affects the dispersion relation. The possible
relation of this string solution to spin chains and the connection of the
solutions on the undeformed S^3 to the sine-Gordon model are briefly discussed.
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F and M Theories as Gauge Theories of Area Preserving Algebra: F theory and M theory are formulated as gauge theories of area preserving
diffeomorphism algebra. Our M theory is shown to be 1-brane formulation rather
than 0-brane formulation of M theory of Banks, Fischler, Shenker and Susskind
and the F theory is shown to be 1-brane formulation rather than -1-brane
formulation of type IIB matrix theory of Ishibashi, Kawai, Kitazawa and
Tsuchiya.
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Chiral algebras from Ω-deformation: In the presence of an $\Omega$-deformation, local operators generate a chiral
algebra in the topological-holomorphic twist of a four-dimensional $\mathcal{N}
= 2$ supersymmetric field theory. We show that for a unitary $\mathcal{N} = 2$
superconformal field theory, the chiral algebra thus defined is isomorphic to
the one introduced by Beem et al. Our definition of the chiral algebra covers
nonconformal theories with insertions of suitable surface defects.
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The Renormalization Group and the Effective Potential in a Curved
Spacetime with Torsion: The renormalization group method is employed to study the effective potential
in curved spacetime with torsion. The renormalization-group improved effective
potential corresponding to a massless gauge theory in such a spacetime is found
and in this way a generalization of Coleman-Weinberg's approach corresponding
to flat space is obtained. A method which works with the renormalization group
equation for two-loop effective potential calculations in torsionful spacetime
is developed. The effective potential for the conformal factor in the conformal
dynamics of quantum gravity with torsion is thereby calculated explicitly.
Finally, torsion-induced phase transitions are discussed.
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Some Remarks on the Two Parameters Quantum Algebra $SU_{p,k}$}: The two parameters quantum algebra $SU_{p,k}(2)$ can be obtained from a
single parameter algebra $SU_q(2)$. This fact gives some relations between
$SU_{p,k}(2)$ quantities and the corresponding ones of the $SU_q(2)$ algebra.
In this paper are mentioned the relations concerning: Casimir operators,
eigenvectors, matrix elements, Clebsch Gordan coefficients and irreducible
tensors.
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BPS Electromagnetic Waves on Giant Gravitons: We find new 1/8-BPS giant graviton solutions in $AdS_5 \times S^5$, carrying
three angular momenta along $S^5$, and investigate their properties.
Especially, we show that nonzero worldvolume gauge fields are admitted
preserving supersymmetry. These gauge field modes can be viewed as
electromagnetic waves along the compact D3 brane, whose Poynting vector
contributes to the BPS angular momenta. We also analyze the (nearly-)spherical
giant gravitons with worldvolume gauge fields in detail. Expressing the $S^3$
in Hopf fibration ($S^1$ fibred over $S^2$), the wave propagates along the
$S^1$ fiber.
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On the Null Energy Condition and Cosmology: Field theories which violate the null energy condition (NEC) are of interest
for the solution of the cosmological singularity problem and for models of
cosmological dark energy with the equation of state parameter $w<-1$. We
discuss the consistency of two recently proposed models that violate the NEC.
The ghost condensate model requires higher-order derivative terms in the
action. It leads to a heavy ghost field and unbounded energy. We estimate the
rates of particles decay and discuss possible mass limitations to protect
stability of matter in the ghost condensate model. The nonlocal stringy model
that arises from a cubic string field theory and exhibits a phantom behavior
also leads to unbounded energy. In this case the spectrum of energy is
continuous and there are no particle like excitations. This model admits a
natural UV completion since it comes from superstring theory.
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SU(2) Poisson-Lie T duality: Poisson-Lie target space duality is a framework where duality transformations
are properly defined. In this letter we investigate the pair of sigma models
defined by the double SO(3,1) in the Iwasawa decomposition.
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Super-Geometrodynamics: We present explicit solutions of the time-symmetric initial value
constraints, expressed in terms of freely specfiable harmonic functions for
examples of supergravity theories, which emerge as effective theories of
compactified string theory. These results are a prequisite for the study of the
time-evolution of topologically non-trivial initial data for supergravity
theories, thus generalising the "Geometrodynamics" program of Einstein-Maxwell
theory to that of supergravity theories. Specifically, we focus on examples of
multiple electric Maxwell and scalar fields, and analyse the initial data
problem for the general Einstein-Maxwell-Dilaton theory both with one and two
Maxwell fields, and the STU model. The solutions are given in terms of up to
eight arbitrary harmonic functions in the STU model. As a by-product, in order
compare our results with known static solutions, the metric in isotropic
coordinates and all the sources of the non-extremal black holes are expressed
entirely in terms of harmonic functions. We also comment on generalizations to
time-nonsymmetric initial data and their relation to cosmological solutions of
gauged so-called fake supergravities with positive cosmological constant.
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Dynamics of dark energy: In this paper we review in detail a number of approaches that have been
adopted to try and explain the remarkable observation of our accelerating
Universe. In particular we discuss the arguments for and recent progress made
towards understanding the nature of dark energy. We review the observational
evidence for the current accelerated expansion of the universe and present a
number of dark energy models in addition to the conventional cosmological
constant, paying particular attention to scalar field models such as
quintessence, K-essence, tachyon, phantom and dilatonic models. The importance
of cosmological scaling solutions is emphasized when studying the dynamical
system of scalar fields including coupled dark energy. We study the evolution
of cosmological perturbations allowing us to confront them with the observation
of the Cosmic Microwave Background and Large Scale Structure and demonstrate
how it is possible in principle to reconstruct the equation of state of dark
energy by also using Supernovae Ia observational data. We also discuss in
detail the nature of tracking solutions in cosmology, particle physics and
braneworld models of dark energy, the nature of possible future singularities,
the effect of higher order curvature terms to avoid a Big Rip singularity, and
approaches to modifying gravity which leads to a late-time accelerated
expansion without recourse to a new form of dark energy.
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Infrared behavior of dynamical fermion mass generation in QED$_{3}$: Extensive investigations show that QED$_{3}$ exhibits dynamical fermion mass
generation at zero temperature when the fermion flavor $N$ is sufficiently
small. However, it seems difficult to extend the theoretical analysis to finite
temperature. We study this problem by means of Dyson-Schwinger equation
approach after considering the effect of finite temperature or disorder-induced
fermion damping. Under the widely used instantaneous approximation, the
dynamical mass displays an infrared divergence in both cases. We then adopt a
new approximation that includes an energy-dependent gauge boson propagator and
obtain results for dynamical fermion mass that do not contain infrared
divergence. The validity of the new approximation is examined by comparing to
the well-established results obtained at zero temperature.
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A Lie Algebra for Closed Strings, Spin Chains and Gauge Theories: We consider quantum dynamical systems whose degrees of freedom are described
by $N \times N$ matrices, in the planar limit $N \to \infty$. Examples are
gauge theoires and the M(atrix)-theory of strings. States invariant under U(N)
are `closed strings', modelled by traces of products of matrices. We have
discovered that the U(N)-invariant opertors acting on both open and closed
string states form a remarkable new Lie algebra which we will call the heterix
algebra. (The simplest special case, with one degree of freedom, is an
extension of the Virasoro algebra by the infinite-dimensional general linear
algebra.) Furthermore, these operators acting on closed string states only form
a quotient algebra of the heterix algebra. We will call this quotient algebra
the cyclix algebra. We express the Hamiltonian of some gauge field theories
(like those with adjoint matter fields and dimensionally reduced pure QCD
models) as elements of this Lie algebra. Finally, we apply this cyclix algebra
to establish an isomorphism between certain planar matrix models and quantum
spin chain systems. Thus we obtain some matrix models solvable in the planar
limit; e.g., matrix models associated with the Ising model, the XYZ model,
models satisfying the Dolan-Grady condition and the chiral Potts model. Thus
our cyclix Lie algebra described the dynamical symmetries of quantum spin chain
systems, large-N gauge field theories, and the M(atrix)-theory of strings.
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Surface defects and elliptic quantum groups: A brane construction of an integrable lattice model is proposed. The model is
composed of Belavin's R-matrix, Felder's dynamical R-matrix, the
Bazhanov-Sergeev-Derkachov-Spiridonov R-operator and some intertwining
operators. This construction implies that a family of surface defects act on
supersymmetric indices of four-dimensional $\mathcal{N} = 1$ supersymmetric
field theories as transfer matrices related to elliptic quantum groups.
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Multifield Dynamics in Higgs-otic Inflation: In Higgs-otic inflation a complex neutral scalar combination of the $h^0$ and
$H^0$ MSSM Higgs fields plays the role of inflaton in a chaotic fashion. The
potential is protected from large trans-Planckian corrections at large inflaton
if the system is embedded in string theory so that the Higgs fields parametrize
a D-brane position. The inflaton potential is then given by a DBI+CS D-brane
action yielding an approximate linear behaviour at large field. The inflaton
scalar potential is a 2-field model with specific non-canonical kinetic terms.
Previous computations of the cosmological parameters (i.e. scalar and tensor
perturbations) did not take into account the full 2-field character of the
model, ignoring in particular the presence of isocurvature perturbations and
their coupling to the adiabatic modes. It is well known that for generic
2-field potentials such effects may significantly alter the observational
signatures of a given model. We perform a full analysis of adiabatic and
isocurvature perturbations in the Higgs-otic 2-field model. We show that the
predictivity of the model is increased compared to the adiabatic approximation.
Isocurvature perturbations moderately feed back into adiabatic fluctuations.
However, the isocurvature component is exponentially damped by the end of
inflation. The tensor to scalar ratio varies in a region $r=0.08-0.12$,
consistent with combined Planck/BICEP results.
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Stability and Negative Tensions in 6D Brane Worlds: We investigate the dynamical stability of warped, axially symmetric
compactifications in anomaly free 6D gauged supergravity. The solutions have
conical defects, which we source by 3-branes placed on orbifold fixed points,
and a smooth limit to the classic sphere-monopole compactification. Like for
the sphere, the extra fields that are generically required by anomaly freedom
are especially relevant for stability. With positive tension branes only, there
is a strict stability criterion (identical to the sphere case) on the charges
present under the monopole background. Thus brane world models with positive
tensions can be embedded into anomaly free theories in only a few ways.
Meanwhile, surprisingly, in the presence of a negative tension brane the
stability criteria can be relaxed. We also describe in detail the geometries
induced by negative tension codimension two branes.
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Quantization of the Superstring with Manifest U(5) Super-Poincare
Invariance: The superstring is quantized in a manner which manifestly preserves a U(5)
subgroup of the (Wick-rotated) ten-dimensional super-Poincar\'e invariance.
This description of the superstring contains critical N=2 worldsheet
superconformal invariance and is a natural covariantization of the
U(4)-invariant light-cone Green-Schwarz description.
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The Operator Product Expansion of the Lowest Higher Spin Current at
Finite N: For the N=2 Kazama-Suzuki(KS) model on CP^3, the lowest higher spin current
with spins (2, 5/2, 5/2,3) is obtained from the generalized GKO coset
construction. By computing the operator product expansion of this current and
itself, the next higher spin current with spins (3, 7/2, 7/2, 4) is also
derived. This is a realization of the N=2 W_{N+1} algebra with N=3 in the
supersymmetric WZW model. By incorporating the self-coupling constant of lowest
higher spin current which is known for the general (N,k), we present the
complete nonlinear operator product expansion of the lowest higher spin current
with spins (2, 5/2, 5/2, 3) in the N=2 KS model on CP^N space. This should
coincide with the asymptotic symmetry of the higher spin AdS_3 supergravity at
the quantum level. The large (N,k) 't Hooft limit and the corresponding
classical nonlinear algebra are also discussed.
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Minimal Scales from an Extended Hilbert Space: We consider an extension of the conventional quantum Heisenberg algebra,
assuming that coordinates as well as momenta fulfil nontrivial commutation
relations. As a consequence, a minimal length and a minimal mass scale are
implemented. Our commutators do not depend on positions and momenta and we
provide an extension of the coordinate coherent state approach to
Noncommutative Geometry. We explore, as toy model, the corresponding quantum
field theory in a (2+1)-dimensional spacetime. Then we investigate the more
realistic case of a (3+1)-dimensional spacetime, foliated into noncommutative
planes. As a result, we obtain propagators, which are finite in the ultraviolet
as well as the infrared regime.
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The 1/2 BPS Wilson loop in ABJM theory at two loops: We compute the expectation value of the 1/2 BPS circular Wilson loop in ABJM
theory at two loops in perturbation theory. The result shows perfect agreement
with the prediction from localization and the proposed framing factor.
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Electric shocks: bounding Einstein-Maxwell theory with time delays on
boosted RN backgrounds: The requirement that particles propagate causally on non-trivial backgrounds
implies interesting constraints on higher-derivative operators. This work is
part of a systematic study of the positivity bounds derivable from time delays
on shockwave backgrounds. First, we discuss shockwaves in field theory, which
are infinitely boosted Coulomb-like field configurations. We show how a
positive time delay implies positivity of four-derivative operators in scalar
field theory and electromagnetism, consistent with the results derived using
dispersion relations, and we comment on how additional higher-derivative
operators could be included.
We then turn to gravitational shockwave backgrounds. We compute the infinite
boost limit of Reissner-Nordstr\"om black holes to derive charged shockwave
backgrounds. We consider photons traveling on these backgrounds and interacting
through four-derivative corrections to Einstein-Maxwell theory. The inclusion
of gravity introduces a logarithmic term into the time delay that interferes
with the straightforward bounds derivable in pure field theory, a fact
consistent with CEMZ and with recent results from dispersion relations. We
discuss two ways to extract a physically meaningful quantity from the
logarithmic time delay -- by introducing an IR cutoff, or by considering the
derivative of the time delay -- and comment on the bounds implied in each case.
Finally, we review a number of additional shockwave backgrounds which might be
of use in future applications, including spinning shockwaves, those in higher
dimensions or with a cosmological constant, and shockwaves from boosted
extended objects.
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Enhanced corrections near holographic entanglement transitions: a
chaotic case study: Recent work found an enhanced correction to the entanglement entropy of a
subsystem in a chaotic energy eigenstate. The enhanced correction appears near
a phase transition in the entanglement entropy that happens when the subsystem
size is half of the entire system size. Here we study the appearance of such
enhanced corrections holographically. We show explicitly how to find these
corrections in the example of chaotic eigenstates by summing over contributions
of all bulk saddle point solutions, including those that break the replica
symmetry. With the help of an emergent rotational symmetry, the sum over all
saddle points is written in terms of an effective action for cosmic branes. The
resulting Renyi and entanglement entropies are then naturally organized in a
basis of fixed-area states and can be evaluated directly, showing an enhanced
correction near holographic entanglement transitions. We comment on several
intriguing features of our tractable example and discuss the implications for
finding a convincing derivation of the enhanced corrections in other, more
general holographic examples.
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On the constraints defining BPS monopoles: We discuss the explicit formulation of the transcendental constraints
defining spectral curves of SU(2) BPS monopoles in the twistor approach of
Hitchin, following Ercolani and Sinha. We obtain an improved version of the
Ercolani-Sinha constraints, and show that the Corrigan-Goddard conditions for
constructing monopoles of arbitrary charge can be regarded as a special case of
these. As an application, we study the spectral curve of the tetrahedrally
symmetric 3-monopole, an example where the Corrigan-Goddard conditions need to
be modified. A particular 1-cycle on the spectral curve plays an important role
in our analysis.
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Microcausality and quantization of the fermionic Myers-Pospelov model: We study the fermionic sector of the Myers and Pospelov theory with a general
background $n$. The spacelike case without temporal component is well defined
and no new ingredients came about, apart from the explicit Lorentz invariance
violation. The lightlike case is ill defined and physically discarded. However,
the other case where a nonvanishing temporal component of the background is
present, the theory is physically consistent. We show that new modes appear as
a consequence of higher time derivatives. We quantize the timelike theory and
calculate the microcausality violation which turns out to occur near the light
cone.
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Quasilocal Thermodynamics of Kerr de Sitter Spacetimes and the dS/CFT
Correspondence: We consider the quasilocal thermodynamics of rotating black holes in
asymptotic de Sitter spacetimes. Using the minimal number of intrinsic boundary
counterterms, we carry out an analysis of the quasilocal thermodynamics of
Kerr-de Sitter black holes for virtually all possible values of the mass,
rotation parameter and cosmological constant that leave the quasilocal boundary
inside the cosmological event horizon. Specifically, we compute the quasilocal
energy, the conserved charges, the temperature and the heat capacity for the
$(3+1)$-dimensional Kerr-dS black holes. We perform a quasilocal stability
analysis and find phase behavior that is commensurate with previous analysis
carried out through the use of Arnowitt-Deser-Misner (ADM) parameters. Finally,
we investigate the non-rotating case analytically.
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Pomeron-Odderon Interactions: A Functional RG Flow Analysis: In the quest for an effective field theory which could help to understand
some non perturbative feature of the QCD in the Regge limit, we consider a
Reggeon Field Theory (RFT) for both Pomeron and Odderon interactions and
perform an analysys of the critical theory using functional renormalization
group techniques, unveiling a novel symmetry structure.
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The Newman-Penrose Map and the Classical Double Copy: Gauge-gravity duality is arguably our best hope for understanding quantum
gravity. Considerable progress has been made in relating scattering amplitudes
in certain gravity theories to those in gauge theories---a correspondence
dubbed the "double copy". Recently, double copies have also been realized in a
classical setting, as maps between exact solutions of gauge theories and
gravity. We present here a novel map between a certain class of real, exact
solutions of Einstein's equations and self-dual solutions of the flat-space
vacuum Maxwell equations. This map, which we call the "Newman-Penrose map", is
well-defined even for non-vacuum, non-stationary spacetimes, providing a
systematic framework for exploring gravity solutions in the context of the
double copy that have not been previously studied in this setting. To
illustrate this, we present here the Newman-Penrose map for the Schwarzschild
and Kerr black holes, and Kinnersley's photon rocket.
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$1/L^2$ corrected soft photon theorem from a CFT$_3$ Ward identity: Classical soft theorems applied to probe scattering processes on AdS$_4$
spacetimes predict the existence of $1/L^2$ corrections to the soft photon and
soft graviton factors of asymptotically flat spacetimes. In this paper, we
establish that the $1/L^2$ corrected soft photon theorem can be derived from a
large $N$ CFT$_3$ Ward identity. We derive a perturbed soft photon mode
operator on a flat spacetime patch in global AdS$_4$ in terms of an integrated
expression of the boundary CFT current. Using the same in the CFT$_3$ Ward
identity, we recover the $1/L^2$ corrected soft photon theorem derived from
classical soft theorems.
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Weyl Connections and their Role in Holography: It is a well-known property of holographic theories that diffeomorphism
invariance in the bulk space-time implies Weyl invariance of the dual
holographic field theory in the sense that the field theory couples to a
conformal class of background metrics. The usual Fefferman-Graham formalism,
which provides us with a holographic dictionary between the two theories,
breaks explicitly this symmetry by choosing a specific boundary metric and a
corresponding specific metric ansatz in the bulk. In this paper, we show that a
simple extension of the Fefferman-Graham formalism allows us to sidestep this
explicit breaking; one finds that the geometry of the boundary includes an
induced metric and an induced connection on the tangent bundle of the boundary
that is a Weyl connection (rather than the more familiar Levi-Civita connection
uniquely determined by the induced metric). Properly invoking this boundary
geometry has far-reaching consequences: the holographic dictionary extends and
naturally encodes Weyl-covariant geometrical data, and, most importantly, the
Weyl anomaly gains a clearer geometrical interpretation, cohomologically
relating two Weyl-transformed volumes. The boundary theory is enhanced due to
the presence of the Weyl current, which participates with the stress tensor in
the boundary Ward identity.
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Lorentz symmetry breaking and supersymmetry: We discuss three manners to implement Lorentz symmetry breaking in a
superfield theory formulated within the superfield formalism, that is,
deformation of the supersymmetry algebra, introducing of an extra superfield
whose components can depend on Lorentz-violating (LV) vectors (tensors), and
adding of new terms proportional to LV vectors (tensors) to the superfield
action. We illustrate these methodologies with examples of quantum
calculations.
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Geometric Aspects of Holographic Bit Threads: We revisit the recent reformulation of the holographic prescription to
compute entanglement entropy in terms of a convex optimization problem,
introduced by Freedman and Headrick. According to it, the holographic
entanglement entropy associated to a boundary region is given by the maximum
flux of a bounded, divergenceless vector field, through the corresponding
region. Our work leads to two main results: (i) We present a general algorithm
that allows the construction of explicit thread configurations in cases where
the minimal surface is known. We illustrate the method with simple examples:
spheres and strips in vacuum AdS, and strips in a black brane geometry.
Studying more generic bulk metrics, we uncover a sufficient set of conditions
on the geometry and matter fields that must hold to be able to use our
prescription. (ii) Based on the nesting property of holographic entanglement
entropy, we develop a method to construct bit threads that maximize the flux
through a given bulk region. As a byproduct, we are able to construct more
general thread configurations by combining (i) and (ii) in multiple patches. We
apply our methods to study bit threads which simultaneously compute the
entanglement entropy and the entanglement of purification of mixed states and
comment on their interpretation in terms of entanglement distillation. We also
consider the case of disjoint regions for which we can explicitly construct the
so-called multi-commodity flows and show that the monogamy property of mutual
information can be easily illustrated from our constructions.
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The Most General Propagator in Quantum Field Theory: One of the most important mathematical tools necessary for Quantum Field
Theory calculations is the field propagator. Applications are always done in
terms of plane waves and although this has furnished many magnificent results,
one may still be allowed to wonder what is the form of the most general
propagator that can be written. In the present paper, by exploiting what is
called polar form, we find the most general propagator in the case of spinors,
whether regular or singular, and we give a general discussion in the case of
vectors.
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Double Ernst Solution in Einstein-Kalb-Ramond Theory: The K\"ahler formulation of 5-dimensional Einstein-Kalb-Ramond (EKR) theory
admitting two commuting Killing vectors is presented. Three different
Kramer-Neugebauer-like maps are established for the 2-dimensional case. A class
of solutions constructed on the double Ernst one is obtained. It is shown that
the double Kerr solution corresponds to a EKR dipole configuration with
horizon.
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Bi-partite entanglement entropy in massive two-dimensional quantum field
theory: Recently, Cardy, Castro Alvaredo and the author obtained the first
exponential correction to saturation of the bi-partite entanglement entropy at
large region length, in massive two-dimensional integrable quantum field
theory. It only depends on the particle content of the model, and not on the
way particles scatter. Based on general analyticity arguments for form factors,
we propose that this result is universal, and holds for any massive
two-dimensional model (also out of integrability). We suggest a link of this
result with counting pair creations far in the past.
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Brief review on higher spin black holes: We review some relevant results in the context of higher spin black holes in
three-dimensional spacetimes, focusing on their asymptotic behaviour and
thermodynamic properties. For simplicity, we mainly discuss the case of gravity
nonminimally coupled to spin-3 fields, being nonperturbatively described by a
Chern-Simons theory of two independent sl(3,R) gauge fields. Since the analysis
is particularly transparent in the Hamiltonian formalism, we provide a concise
discussion of their basic aspects in this context; and as a warming up
exercise, we briefly analyze the asymptotic behaviour of pure gravity, as well
as the BTZ black hole and its thermodynamics, exclusively in terms of gauge
fields. The discussion is then extended to the case of black holes endowed with
higher spin fields, briefly signaling the agreements and discrepancies found
through different approaches. We conclude explaining how the puzzles become
resolved once the fall off of the fields is precisely specified and extended to
include chemical potentials, in a way that it is compatible with the asymptotic
symmetries. Hence, the global charges become completely identified in an
unambiguous way, so that different sets of asymptotic conditions turn out to
contain inequivalent classes of black hole solutions being characterized by a
different set of global charges.
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Interpolating Gauges,Parameter Differentiability,WT-identities and the
epsilon term: Evaluation of variation of a Green's function in a gauge field theory with a
gauge parameter theta involves field transformations that are (close to)
singular. Recently, we had demonstrated {hep-th/0106264}some unusual results
that follow from this fact for an interpolating gauge interpolating between the
Feynman and the Coulomb gauge (formulated by Doust). We carry out further
studies of this model. We study properties of simple loop integrals involved in
an interpolating gauge. We find that the proof of continuation of a Green's
function from the Feynman gauge to the Coulomb gauge via such a gauge in a
gauge-invariant manner seems obstructed by the lack of differentiability of the
path-integral with respect to theta (at least at discrete values for a specific
Green's function considered) and/or by additional contributions to the
WT-identities. We show this by the consideration of simple loop diagrams for a
simple scattering process. The lack of differentiability, alternately, produces
a large change in the path-integral for a small enough change in theta near
some values. We find several applications of these observations in a gauge
field theory. We show that the usual procedure followed in the derivation of
the WT-identity that leads to the evaluation of a gauge variation of a Green's
function involves steps that are not always valid in the context of such
interpolating gauges. We further find new results related to the need for
keeping the epsilon-term in the in the derivation of the WT-identity and and a
nontrivial contribution to gauge variation from it. We also demonstrate how
arguments using Wick rotation cannot rid us of these problems. This work brings
out the pitfalls in the use of interpolating gauges in a clearer focus.
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Low-energy general relativity with torsion: a systematic derivative
expansion: We attempt to build systematically the low-energy effective Lagrangian for
the Einstein--Cartan formulation of gravity theory that generally includes the
torsion field. We list all invariant action terms in certain given order; some
of the invariants are new. We show that in the leading order the fermion action
with torsion possesses additional U(1)_L x U(1)_R gauge symmetry, with 4+4
components of the torsion (out of the general 24) playing the role of Abelian
gauge bosons. The bosonic action quadratic in torsion gives masses to those
gauge bosons. Integrating out torsion one obtains a point-like 4-fermion action
of a general form containing vector-vector, axial-vector and axial-axial
interactions. We present a quantum field-theoretic method to average the
4-fermion interaction over the fermion medium, and perform the explicit
averaging for free fermions with given chemical potential and temperature. The
result is different from that following from the "spin fluid" approach used
previously. On the whole, we arrive to rather pessimistic conclusions on the
possibility to observe effects of the torsion-induced 4-fermion interaction,
although under certain circumstances it may have cosmological consequences.
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Non-Linear Resonance in Relativistic Preheating: Inflation in the early Universe can be followed by a brief period of
preheating, resulting in rapid and non-equilibrium particle production through
the dynamics of parametric resonance. However, the parametric resonance effect
is very sensitive to the linearity of the reheating sector. Additional
self-interactions in the reheating sector, such as non-canonical kinetic terms
like the DBI Lagrangian, may enhance or frustrate the parametric resonance
effect of preheating. In the case of a DBI reheating sector, preheating is
described by parametric resonance of a damped relativistic harmonic oscillator.
In this paper, we illustrate how the non-linear terms in the relativistic
oscillator shut down the parametric resonance effect. This limits the
effectiveness of preheating when there are non-linear self-interactions.
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(2+1)-dimensional Chern-Simons bi-gravity with AdS Lie bialgebra as an
interacting theory of two massless spin-2 fields: We introduce a new Lie bialgebra structure for the anti de Sitter (AdS) Lie
algebra in (2+1)-dimensional spacetime. By gauging the resulting \textit{AdS
Lie bialgebra}, we write a Chern-Simons gauge theory of bi-gravity involving
two dreibeins rather than two metrics, which describes two interacting massless
spin-2 fields. Our ghost-free bi-gravity model which has no any local degrees
of freedom, has also a suitable free field limit. By solving its equations of
motion, we obtain a \textit{new black hole} solution which has two curvature
singularities and two horizons. We also study cosmological implications of this
massless bi-gravity model.
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Casimir Self-Entropy of a Spherical Electromagnetic $δ$-Function
Shell: In this paper we continue our program of computing Casimir self-entropies of
idealized electrical bodies. Here we consider an electromagnetic
$\delta$-function sphere ("semitransparent sphere") whose electric
susceptibility has a transverse polarization with arbitrary strength.
Dispersion is incorporated by a plasma-like model. In the strong coupling
limit, a perfectly conducting spherical shell is realized. We compute the
entropy for both low and high temperatures. The TE self-entropy is negative as
expected, but the TM self-entropy requires ultraviolet and infrared
subtractions, and, surprisingly, is only positive for sufficiently strong
coupling. Results are robust under different regularization schemes.
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Krylov Complexity in Calabi-Yau Quantum Mechanics: Recently, a novel measure for the complexity of operator growth is proposed
based on Lanczos algorithm and Krylov recursion method. We study this Krylov
complexity in quantum mechanical systems derived from some well-known local
toric Calabi-Yau geometries, as well as some non-relativistic models. We find
that for the Calabi-Yau models, the Lanczos coefficients grow slower than
linearly for small $n$'s, consistent with the behavior of integrable models. On
the other hand, for the non-relativistic models, the Lanczos coefficients
initially grow linearly for small $n$'s, then reach a plateau. Although this
looks like the behavior of a chaotic system, it is mostly likely due to
saddle-dominated scrambling effects instead, as argued in the literature. In
our cases, the slopes of linearly growing Lanczos coefficients almost saturate
a bound by the temperature. During our study, we also provide an alternative
general derivation of the bound for the slope.
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Interplay between reflection positivity and crossing symmetry in the
bootstrap approach to CFT: Crossing symmetry (CS) is the main tool in the bootstrap program applied to
CFT models. This consists in an equality which imposes restrictions on the CFT
data of a model, i.e, the OPE coefficients and the conformal dimensions.
Reflection positivity (RP) has also played a role, since this condition lead to
the unitary bound and reality of the OPE coefficients. In this paper we show
that RP can still reveal more information, showing how RP itself can capture an
important part of the restrictions imposed by the full CS equality. In order to
do that, we use a connection used by us in a previous work between RP and
positive definiteness of a function of a single variable. This allows to write
constraints on the OPE coefficients in a concise way, encoding in the
conditions that certain functions of the crossratio will be positive defined
and in particular completely monotonic. We will consider how the bounding of
scalar conformal dimensions and OPE coefficients arise in this RP based
approach. We will illustrate the conceptual and practical value of this view
trough examples of general CFT models in $d$-dimensions.
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Horizons and Correlation Functions in 2D Schwarzschild-de Sitter
Spacetime: Two-dimensional Schwarzschild-de Sitter is a convenient spacetime in which to
study the effects of horizons on quantum fields since the spacetime contains
two horizons, and the wave equation for a massless minimally coupled scalar
field can be solved exactly. The two-point correlation function of a massless
scalar is computed in the Unruh state. It is found that the field correlations
grow linearly in terms of a particular time coordinate that is good in the
future development of the past horizons, and that the rate of growth is equal
to the sum of the black hole plus cosmological surface gravities. This time
dependence results from additive contributions of each horizon component of the
past Cauchy surface that is used to define the state. The state becomes the
Bunch-Davies vacuum in the cosmological far field limit. The two point function
for the field velocities is also analyzed and a peak is found when one point is
between the black hole and cosmological horizons and one point is outside the
future cosmological horizon.
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Generalized Drinfeld-Sokolov Hierarchies II: The Hamiltonian Structures: In this paper we examine the bi-Hamiltonian structure of the generalized
KdV-hierarchies. We verify that both Hamiltonian structures take the form of
Kirillov brackets on the Kac-Moody algebra, and that they define a coordinated
system. Classical extended conformal algebras are obtained from the second
Poisson bracket. In particular, we construct the $W_n^l$ algebras, first
discussed for the case $n=3$ and $l=2$ by A. Polyakov and M. Bershadsky.
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Defects, modular differential equations, and free field realization of N
= 4 VOAs: For all 4d $\mathcal{N} = 4$ SYM theories with simple gauge groups $G$, we
show that the residues of the integrands in the $\mathcal{N} = 4$ Schur
indices, which are related to Gukov-Witten type surface defects in the
theories, equal the vacuum characters of rank$G$ copies of $bc \beta \gamma$
systems that provide the free field realization of associated $\mathcal{N} = 4$
VOAs. This result predicts that these residues, as module characters, are
additional solutions to the flavored modular differential equations satisfied
by the original Schur index. The prediction is verified in the $G = SU(2)$
case, where an additional logarithmic solution is constructed.
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Free Energy of D_n Quiver Chern-Simons Theories: We apply the matrix model of Kapustin, Willett and Yaakov to compute the free
energy of N=3 Chern-Simons matter theories with D_n quivers in the large N
limit. We conjecture a general expression for the free energy that is
explicitly invariant under Seiberg duality and show that it can be interpreted
as a sum over certain graphs known as signed graphs. Through the AdS/CFT
correspondence, this leads to a prediction for the volume of certain tri-Sasaki
Einstein manifolds. We also study the unfolding procedure, which relates these
D_n quivers to A_{2n-5} quivers. Furthermore, we consider the addition of
massive fundamental flavor fields, verifying that integrating these out
decreases the free energy in accordance with the F-theorem.
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States and Observables in Semiclassical Field Theory: a Manifestly
Covariant Approach: A manifestly covariant formulation of quantum field Maslov complex-WKB theory
(semiclassical field theory) is investigated for the case of scalar field. The
main object of the theory is "semiclassical bundle". Its base is the set of all
classical states, fibers are Hilbert spaces of quantum states in the external
field. Semiclassical Maslov states may be viewed as points or surfaces on the
semiclassical bundle. Semiclassical analogs of QFT axioms are formulated. A
relationship between covariant semiclassical field theory and Hamiltonian
formulation is discussed. The constructions of axiomatic field theory
(Schwinger sources, Bogoliubov $S$-matrix, Lehmann-Symanzik-Zimmermann
$R$-functions) are used in constructing the covariant semiclassical theory. A
new covariant formulation of classical field theory and semiclassical
quantization proposal are discussed.
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Action-angle variables for dihedral systems on the circle: A nonrelativistic particle on a circle and subject to a cos^{-2}(k phi)
potential is related to the two-dimensional (dihedral) Coxeter system I_2(k),
for k in N. For such `dihedral systems' we construct the action-angle variables
and establish a local equivalence with a free particle on the circle. We
perform the quantization of these systems in the action-angle variables and
discuss the supersymmetric extension of this procedure. By allowing radial
motion one obtains related two-dimensional systems, including A_2, BC_2 and G_2
three-particle rational Calogero models on R, which we also analyze.
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K-field kinks in two-dimensional dilaton gravity: In this work, kinks with non-canonical kinetic energy terms are studied in a
type of two-dimensional dilaton gravity model. The linear stability issue is
generally discussed for arbitrary static solutions, and the stability criteria
are obtained. As an explicit example, a model with cuscuton term is studied.
After rewriting the equations of motion into simpler first-order formalism and
choosing a polynomial superpotential, an exact self-gravitating kink solution
is obtained. The impacts of the cuscuton term are discussed.
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To Half--Be or Not To Be?: It has recently been argued that half degrees of freedom could emerge in
Lorentz and parity invariant field theories, using a non-linear Proca field
theory dubbed Proca-Nuevo as a specific example. We provide two proofs, using
the Lagrangian and Hamiltonian pictures, that the theory possesses a pair of
second class constraints, leaving $D-1$ degrees of freedom in $D$ spacetime
dimensions, as befits a consistent Proca model. Our proofs are explicit and
straightforward in two dimensions and we discuss how they generalize to an
arbitrary number of dimensions. We also clarify why local Lorentz and parity
invariant field theories cannot hold half degrees of freedom.
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Higher-Derivative Gravitation in Bosonic and Superstring Theories and a
New Mechanism for Supersymmetry Breaking: A discussion of the number of degrees of freedom, and their dynamical
properties, in higher derivative gravitational theories is presented. The
complete non-linear sigma model for these degrees of freedom is exhibited using
the method of auxiliary fields. As a by-product we present a consistent
non-linear coupling of a spin-2 tensor to gravitation. It is shown that
non-vanishing $(C_{\mu\nu\alpha\beta})^{2}$ terms arise in $N=1$, $D=4$
superstring Lagrangians due to one-loop radiative corrections with light field
internal lines. We discuss the general form of quadratic $(1,1)$ supergravity
in two dimensions, and show that this theory is equivalent to two scalar
supermultiplets coupled to the usual Einstein supergravity. It is demonstrated
that the theory possesses stable vacua with vanishing cosmological constant
which spontaneously break supersymmetry.
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Dilaton tadpoles and D-brane interactions in compact spaces: We analyse some physical consequences when supersymmetry is broken by a set
of D-branes and/or orientifold planes in Type II string theories. Generically,
there are global dilaton tadpoles at the disk level when the transverse space
is compact. By taking the toy model of a set of electric charges in a compact
space, we discuss two different effects appearing when global tadpoles are not
cancelled. On the compact directions a constant term appears that allows to
solve the equations of motion. On the non-compact directions Poincar\'e
invariance is broken. We analyse some examples where the Poincar\'e invariance
is broken along the time direction (cosmological models).After that, we discuss
how to obtain a finite interaction between D-branes and orientifold planes in
the compact space at the supergravity level.
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Effective Matter Cosmologies of Massive Gravity I: Non-Physical Fluids: For the massive gravity, after decoupling from the metric equation we find a
broad class of solutions of the Stuckelberg sector by solving the background
metric in the presence of a diagonal physical metric. We then construct the
dynamics of the corresponding FLRW cosmologies which inherit effective matter
contribution through the decoupling solution mechanism of the scalar sector.
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Quantum field theory on a discrete space and noncommutative geometry: We analyse in detail the quantization of a simple noncommutative model of
spontaneous symmetry breaking in zero dimensions taking into account the
noncommutative setting seriously. The connection to the counting argument of
Feyman diagrams of the corresponding theory in four dimensions is worked out
explicitly. Special emphasis is put on the motivation as well as the
presentation of some well-known basic notions of quantum field theory which in
the zero-dimensional theory can be studied without being spoiled by technical
complications due to the absence of divergencies.
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Constrained Dynamics in the Hamiltonian formalism: These are pedagogical notes on the Hamiltonian formulation of constrained
dynamical systems. All the examples are finite dimensional, field theories are
not covered, and the notes could be used by students for a preliminary study
before the infinite dimensional phase space of field theory is tackled.
Holonomic constraints in configuration space are considered first and Dirac
brackets introduced for such systems. It is shown that Dirac brackets are a
projection of Poisson brackets onto the constrained phase space and the
projection operator is constructed explicitly. More general constraints on
phase space are then considered and exemplified by a particle in a strong
magnetic field. First class constraints on phases are introduced using the
example of motion on the complex projective space ${\mathbf{C P}}^{n-1}$.
Motion of a relativistic particle in Minkowski space with a reparameterisation
invariant world-line is also discussed.
These notes are based on a short lecture course given at Bhubaneswar Indian
Institute of Technology in November 2021.
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Functional RG flow of the effective Hamiltonian action: After a brief review of the definition and properties of the quantum
effective Hamiltonian action we describe its renormalization flow by a
functional RG equation. This equation can be used for a non-perturbative
quantization and study also of theories with bare Hamiltonians which are not
quadratic in the momenta. As an example the vacuum energy and gap of quantum
mechanical models are computed. Extensions of this framework to quantum field
theories are discussed. In particular one possible Lorentz covariant approach
for simple scalar field theories is developed. Fermionic degrees of freedom,
being naturally described by a first order formulation, can be easily
accommodated in this approach.
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Holographic anatomy of fuzzballs: We present a comprehensive analysis of 2-charge fuzzball solutions, that is,
horizon-free non-singular solutions of IIB supergravity characterized by a
curve on R^4. We propose a precise map that relates any given curve to a
specific superposition of R ground states of the D1-D5 system. To test this
proposal we compute the holographic 1-point functions associated with these
solutions, namely the conserved charges and the vacuum expectation values of
chiral primary operators of the boundary theory, and find perfect agreement
within the approximations used. In particular, all kinematical constraints are
satisfied and the proposal is compatible with dynamical constraints although
detailed quantitative tests would require going beyond the leading supergravity
approximation. We also discuss which geometries may be dual to a given R ground
state. We present the general asymptotic form that such solutions must have and
present exact solutions which have such asymptotics and therefore pass all
kinematical constraints. Dynamical constraints would again require going beyond
the leading supergravity approximation.
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On the phase structure of extra-dimensional gauge theories with fermions: We study the phase structure of five-dimensional Yang-Mills theories coupled
to Dirac fermions. In order to tackle their non-perturbative character, we
derive the flow equations for the gauge coupling and the effective potential
for the Aharonov-Bohm phases employing the Functional Renormalisation Group. We
analyse the infrared and ultraviolet fixed-point solutions in the flow of the
gauge coupling as a function of the compactification radius of the fifth
dimension. We discuss various types of trajectories which smoothly connect both
dimensional limits. Last, we investigate the phase diagram and vacuum structure
of the gauge potential for different fermion content.
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The timbre of Hawking gravitons: an effective description of energy
transport from holography: Planar black holes in AdS, which are holographically dual to compressible
relativistic fluids, have a long-lived phonon mode that captures the physics of
attenuated sound propagation and transports energy in the plasma. We describe
the open effective field theory of this fluctuating phonon degree of freedom.
The dynamics of the phonon is encoded in a single scalar field whose
gravitational coupling has non-trivial spatial momentum dependence. This
description fits neatly into the paradigm of classifying gravitational modes by
their Markovianity index, depending on whether they are long-lived. The sound
scalar is a non-Markovian field with index (3-d) for a d-dimensional fluid. We
reproduce (and extend) the dispersion relation of the holographic sound mode to
quartic order in derivatives, constructing in the process the effective field
theory governing its attenuated dynamics and associated stochastic
fluctuations. We also remark on the presence of additional spatially
homogeneous zero modes in the gravitational problem, which remain disconnected
from the phonon Goldstone mode.
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Integrable deformations of AdS/CFT: In this paper we study in detail the deformations introduced in [1] of the
integrable structures of the AdS$_{2,3}$ integrable models. We do this by
embedding the corresponding scattering matrices into the most general solutions
of the Yang-Baxter equation. We show that there are several non-trivial
embeddings and corresponding deformations. We work out crossing symmetry for
these models and study their symmetry algebras and representations. In
particular, we identify a new elliptic deformation of the $\rm AdS_3 \times S^3
\times M^4$ string sigma model.
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Non-Supersymmetric Seiberg Duality, Orientifold QCD and Non-Critical
Strings: We propose an electric-magnetic duality and conjecture an exact conformal
window for a class of non-supersymmetric U(N_c) gauge theories with fermions in
the (anti)symmetric representation of the gauge group and N_f additional scalar
and fermion flavors. The duality exchanges N_c with N_f -N_c \mp 4 leaving N_f
invariant, and has common features with Seiberg duality in N=1 SQCD with SU or
SO/Sp gauge group. At large N the duality holds due to planar equivalence with
N=1 SQCD. At finite N we embed these gauge theories in a setup with D-branes
and orientifolds in a non-supersymmetric, but tachyon-free, non-critical type
0B string theory and argue in favor of the duality in terms of boundary and
crosscap state monodromies as in analogous supersymmetric situations. One can
verify explicitly that the resulting duals have matching global anomalies.
Finally, we comment on the moduli space of these gauge theories and discuss
other potential non-supersymmetric examples that could exhibit similar
dualities.
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Unitary Representations of Some Infinite Dimensional Lie Algebras
Motivated by String Theory on AdS_3: We consider some unitary representations of infinite dimensional Lie algebras
motivated by string theory on AdS_3. These include examples of two kinds: the
A,D,E type affine Lie algebras and the N=4 superconformal algebra. The first
presents a new construction for free field representations of affine Lie
algebras. The second is of a particular physical interest because it provides
some hints that a hybrid of the NSR and GS formulations for string theory on
AdS_3 exists.
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Six-loop divergences in the supersymmetric Kahler sigma model: The two-dimensional supersymmetric $\s$-model on a K\"ahler manifold has a
non-vanishing $\b$-function at four loops, but the $\b$-function at five loops
can be made to vanish by a specific choice of renormalisation scheme. We
investigate whether this phenomenon persists at six loops, and conclude that it
does not; there is a non-vanishing six-loop $\b$-function irrespective of
renormalisation scheme ambiguities.
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w(1+infinity) Algebra with a Cosmological Constant and the Celestial
Sphere: It is shown that in the presence of a nonvanishing cosmological constant,
Strominger's infinite-dimensional $\mathrm{w_{1+\infty}}$ algebra of soft
graviton symmetries is modified in a simple way. The deformed algebra contains
a subalgebra generating $ SO(1,4)$ or $SO(2,3)$ symmetry groups of
$\text{dS}_4$ or $\text{AdS}_4$, depending on the sign of the cosmological
constant. The transformation properties of soft gauge symmetry currents under
the deformed $\mathrm{w_{1+\infty}}$ are also discussed.
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Transmission matrices in gl(N) & U_q(gl(N)) quantum spin chains: The gl(N) and U_q(gl(N)) quantum spin chains in the presence of integrable
spin impurities are considered. Within the Bethe ansatz formulation, we derive
the associated transmission amplitudes, and the corresponding transmission
matrices -representations of the underlying quadratic algebra- that physically
describe the interaction between the various particle-like excitations
displayed by these models and the spin impurity.
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Casimir effect, loop corrections and topological mass generation for
interacting real and complex scalar fields in Minkowski spacetime with
different conditions: In this paper the Casimir energy density, loop corrections, and generation of
topological mass are investigated for a system consisting of two interacting
real and complex scalar fields. The interaction considered is the quartic
interaction in the form of a product of the modulus square of the complex field
and the square of the real field. In addition, it is also considered the
self-interaction associated with each field. In this theory, the scalar field
is constrained to always obey periodic condition while the complex field obeys
in one case a quasiperiodic condition and in other case mixed boundary
conditions. The Casimir energy density, loop corrections, and topological mass
are evaluated analytically for the massive and massless scalar fields
considered. An analysis of possible different stable vacuum states and the
corresponding stability condition is also provided. In order to better
understand our investigation, some graphs are also presented. The formalism we
use here to perform such investigation is the effective potential, which is
written as loop expansions via path integral in quantum field theory.
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Nonlocal charges from marginal deformations of 2D CFTs: Holographic $T
\bar T$, $T \bar J$ and Yang-Baxter deformations: In this paper we study generic features of nonlocal charges obtained from
marginal deformations of WZNW models. Using free-fields representations of CFTs
based on simply laced Lie algebras, one can use simple arguments to build the
nonlocal charges; but for more general Lie algebras these methods are not
strong enough to be generally used. We propose a brute force calculation where
the nonlocality is associated to a new Lie algebra valued field, and from this
prescription we impose several constraints on the algebra of nonlocal charges.
Possible applications for Yang-Baxter and holographic \(T\bar{T}\) and
\(T\bar{J}\) deformations are also discussed.
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Hamiltonian reduction of the $U_{EM}(1)$ gauged three flavour WZW model: The three-flavour Wess-Zumino model coupled to electromagnetism is treated as
a constraint system using the Faddeev-Jackiw method. Expanding into series of
powers of the Goldstone boson fields and keeping terms up to second and third
order we obtain Coulomb-gauge hamiltonian densities.
|
Proper time method in de Sitter space: We use the proper time formalism to study a (non-self-interacting) massive
Klein-Gordon theory in the two dimensional de Sitter space. We determine the
exact Green's function of the theory by solving the DeWitt-Schwinger equation
as well as by calculating the operator matrix element. We point out how the one
parameter family of arbitrariness in the Green's function arises in this
method.
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Double Metric, Generalized Metric and $α'$-Geometry: We relate the unconstrained `double metric' of the `$\alpha'$-geometry'
formulation of double field theory to the constrained generalized metric
encoding the spacetime metric and b-field. This is achieved by integrating out
auxiliary field components of the double metric in an iterative procedure that
induces an infinite number of higher-derivative corrections. As an application
we prove that, to first order in $\alpha'$ and to all orders in fields, the
deformed gauge transformations are Green-Schwarz-deformed diffeomorphisms. We
also prove that to first order in $\alpha'$ the spacetime action encodes
precisely the Green-Schwarz deformation with Chern-Simons forms based on the
torsionless gravitational connection. This seems to be in tension with
suggestions in the literature that T-duality requires a torsionful connection,
but we explain that these assertions are ambiguous since actions that use
different connections are related by field redefinitions.
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Prescriptive Unitarity for Non-Planar Six-Particle Amplitudes at Two
Loops: We extend the applications of prescriptive unitarity beyond the planar limit
to provide local, polylogarithmic, integrand-level representations of
six-particle MHV scattering amplitudes in both maximally supersymmetric
Yang-Mills theory and gravity. The integrand basis we construct is diagonalized
on a spanning set of non-vanishing leading singularities that ensures the
manifest matching of all soft-collinear singularities in both theories. As a
consequence, this integrand basis naturally splits into infrared-finite and
infrared-divergent parts, with hints toward an integrand-level exponentiation
of infrared divergences. Importantly, we use the same basis of integrands for
both theories, so that the presence or absence of residues at infinite loop
momentum becomes a feature detectable by inspecting the cuts of the theory.
Complete details of our results are provided as ancillary files.
This work has been updated to take into account the results of
[arXiv:1911.09106], which leads to a simpler and more uniform representation of
these amplitudes.
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Motion of a Particle with Isospin in the Presence of a Monopole: From a consistent expression for the quadriforce describing the interaction
between a coloured particle and gauge fields, we investigate the relativistic
motion of a particle with isospin interacting with a BPS monopole and with a
Julia-Zee dyon. The analysis of such systems reveals the existence of
unidimensional unbounded motion and asymptotic trajectories restricted to
conical surfaces, which resembles the equivalent case of Electromagnetism.
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A Note on the Swampland Distance Conjecture: We discuss the Swampland Distance Conjecture in the framework of black hole
thermodynamics. In particular, we consider black holes in de Sitter space and
we show that the Swampland Distance Conjecture is a consequence of the fact
that apparent horizons are always inside cosmic event horizons whenever they
exist in the case of fast-roll inflation. In addition, we show that the
Bekenstein and the Hubble entropy bounds for the entropy in a region of
spacetime lead similarly to the same conjecture.
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Hawking Radiation from Elko Particles Tunnelling across Black Strings
Horizon: We apply the tunnelling method for the emission and absorption of Elko
particles in the event horizon of a black string solution. We show that Elko
particles are emitted at the expected Hawking temperature from black strings,
but with a quite different signature with respect to the Dirac particles. We
employ the Hamilton-Jacobi technique to black hole tunnelling, by applying the
WKB approximation to the coupled system of Dirac-like equations governing the
Elko particle dynamics. As a typical signature, different Elko particles are
shown to produce the same standard Hawking temperature for black strings.
However we prove that they present the same probability irrespective of
outgoing or ingoing the black hole horizon. It provides a typical signature for
mass dimension one fermions, that is different from the mass dimension three
halves fermions inherent to Dirac particles, as different Dirac spinor fields
have distinct inward and outward probability of tunnelling.
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Yang-Baxter $σ$-models and dS/AdS T-duality: We point out the existence of nonlinear $\sigma$-models on group manifolds
which are left symmetric and right Poisson-Lie symmetric. We discuss the
corresponding rich T-duality story with particular emphasis on two examples:
the anisotropic principal chiral model and the $SL(2,C)/SU(2)$ WZW model. The
latter has the de Sitter space as its (conformal) non-Abelian dual.
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A Pure Spinor Twistor Description of Ambitwistor Strings: We present a novel ten-dimensional description of ambitwistor strings. This
formulation is based on a set of supertwistor variables involving pure spinors
and a set of constraints previously introduced in the context of the $D=10$
superparticle following a ten-dimensional twistor-like construction introduced
by Berkovits. We perform a detailed quantum-mechanical analysis of the
constraint algebra, we show that the corresponding central charges vanish, and
after considering a convenient gauge fixing procedure, physical states are
found. Vertex operators are explicitly constructed and, by noticing a relation
with the standard pure spinor formalism, scattering amplitudes are shown to
correctly describe $D=10$ super-Yang-Mills interactions. As in other
ambitwistor string models, amplitudes are found to be localized on the support
of the scattering equations, and thus this work provides a bridge between
Berkovits' construction and the Cachazo-He-Yuan formulae. After extending the
pure spinor twistor transform to include an additional supersymmetry, our
results are immediately generalized to Type IIB supergravity.
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Operator lifetime and the force-free electrodynamic limit of magnetised
holographic plasma: Using the framework of higher-form global symmetries, we examine the regime
of validity of force-free electrodynamics by evaluating the lifetime of the
electric field operator, which is non-conserved due to screening effects. We
focus on a holographic model which has the same global symmetry as that of low
energy plasma and obtain the lifetime of (non-conserved) electric flux in a
strong magnetic field regime. The lifetime is inversely correlated to the
magnetic field strength and thus suppressed in the strong field regime.
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Phase Transition of Charged-AdS Black Holes and Quasinormal Modes : a
Time Domain Analysis: In this work we use the quasinormal mode of a massless scalar perturbation to
probe the phase transition of the charged-AdS black hole in time profile. The
signature of the critical behavior of this black hole solution is detected in
the isobaric process. This paper is a natural extension of [1, 2] to the time
domain analysis. More precisely, our study shows a clear signal in term of the
damping rate and the oscillation frequencies of the scalar field perturbation.
We conclude that the quasinormal modes can be an efficient tool to detect the
signature of thermodynamic phase transition in the isobaric process far from
the critical temperature, but fail to disclose this signature at the critical
temperature
|
On the renormalization of a generalized supersymmetric version of the
maximal Abelian gauge: In this work we present an algebraic proof of the renormazibility of the
super-Yang-Mills action quantized in a generalized supersymmetric version of
the maximal Abelian gauge. The main point stated here is that the generalized
gauge depends on a set of infinity gauge parameters in order to take into
account all possible composite operators emerging from the dimensionless
character of the vector superfield. At the end, after the removal of all
ultraviolet divergences, it is possible to specify values to the gauge
parameters in order to return to the original supersymmetric maximal Abelian
gauge, first presented in Phys. Rev. D91, no. 12, 125017 (2015), Ref. [1].
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Spinor-vector supersymmetry algebra in three dimensions: We focus on a spin-3/2 supersymmetry (SUSY) algebra of Baaklini in D = 3 and
explicitly show a nonlinear realization of the SUSY algebra. The unitary
representation of the spin-3/2 SUSY algebra is discussed and compared with the
ordinary (spin-1/2) SUSY algebra.
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Prescriptive Unitarity: We introduce a prescriptive approach to generalized unitarity, resulting in a
strictly-diagonal basis of loop integrands with coefficients given by
specifically-tailored residues in field theory. We illustrate the power of this
strategy in the case of planar, maximally supersymmetric Yang-Mills theory,
where we construct closed-form representations of all ($n$-point N$^k$MHV)
scattering amplitudes through three loops. The prescriptive approach contrasts
with the ordinary description of unitarity-based methods by avoiding any need
for linear algebra to determine integrand coefficients. We describe this
approach in general terms as it should have applications to many quantum field
theories, including those without planarity, supersymmetry, or massless spectra
defined in any number of dimensions.
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Quantum fluctuations of topological ${\mathbb S}^3$-kinks: The kink Casimir effect in the massive non-linear $S^3$-sigma model is
analyzed.
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Brane-worlds and theta-vacua: Reductions from odd to even dimensionalities ($5\to 4$ or $3\to 2$), for
which the effective low-energy theory contains chiral fermions, present us with
a mismatch between ultraviolet and infrared anomalies. This applies to both
local (gauge) and global currents; here we consider the latter case. We show
that the mismatch can be explained by taking into account a change in the
spectral asymmetry of the massive modes--an odd-dimensional analog of the
phenomenon described by the Atiyah-Patodi-Singer theorem in even
dimensionalities. The result has phenomenological implications: we present a
scenario in which a QCD-like $\theta$-angle relaxes to zero on a certain
(possibly, cosmological) timescale, despite the absence of any light axion-like
particle.
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Seeking the Ground State of String Theory: Recently, a number of authors have challenged the conventional assumption
that the string scale, Planck mass, and unification scale are roughly
comparable. It has been suggested that the string scale could be as low as a
TeV. The greatest obstacle to developing a string phenomenology is our lack of
understanding of the ground state. We explain why the dynamics which determines
this state is not likely to be accessible to any systematic approximation. We
note that the racetrack scheme, often cited as a counterexample, suffers from
similar difficulties. We stress that the weakness of the gauge couplings, the
gauge hierarchy, and coupling unification suggest that it may be possible to
extract some information in a systematic approximation. We review the ideas of
Kahler stabilization, an attempt to reconcile these facts. We consider whether
the system is likely to sit at extremes of the moduli space, as in recent
proposals for a low string scale. Finally we discuss the idea of Maximally
Enhanced Symmetry, a hypothesis which is technically natural, compatible with
basic facts about cosmology, and potentially predictive.
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Topics on the geometry of D-brane charges and Ramond-Ramond fields: In this paper we discuss some topics on the geometry of type II superstring
backgrounds with D-branes, in particular on the geometrical meaning of the
D-brane charge, the Ramond-Ramond fields and the Wess-Zumino action. We see
that, depending on the behaviour of the D-brane on the four non-compact
space-time directions, we need different notions of homology and cohomology to
discuss the associated fields and charge: we give a mathematical definition of
such notions and show their physical applications. We then discuss the problem
of corretly defining Wess-Zumino action using the theory of p-gerbes. Finally,
we recall the so-called *-problem and make some brief remarks about it.
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Degenerations of K3, Orientifolds and Exotic Branes: A recently constructed limit of K3 has a long neck consisting of segments,
each of which is a nilfold fibred over a line, that are joined together with
Kaluza-Klein monopoles. The neck is capped at either end by a Tian-Yau space,
which is non-compact, hyperkahler and asymptotic to a nilfold fibred over a
line. We show that the type IIA string on this degeneration of K3 is dual to
the type I$'$ string, with the Kaluza-Klein monopoles dual to the D8-branes and
the Tian-Yau spaces providing a geometric dual to the O8 orientifold planes. At
strong coupling, each O8-plane can emit a D8-brane to give an O8$^*$ plane, so
that there can be up to 18 D8-branes in the type I$'$ string. In the IIA dual,
this phenomenon occurs at weak coupling and there can be up to 18 Kaluza-Klein
monopoles in the dual geometry. We consider further duals in which the
Kaluza-Klein monopoles are dualised to NS5-branes or exotic branes. A 3-torus
with $H$-flux can be realised in string theory as an NS5-brane wrapped on
$T^3$, with the 3-torus fibred over a line. T-dualising gives a 4-dimensional
hyperkahler manifold which is a nilfold fibred over a line, which can be viewed
as a Kaluza-Klein monopole wrapped on $T^2$. Further T-dualities then give
non-geometric spaces fibred over a line and can be regarded as wrapped exotic
branes. These are all domain wall configurations, dual to the D8-brane. Type
I$'$ string theory is the natural home for D8-branes, and we dualise this to
find string theory homes for each of these branes. The Kaluza-Klein monopoles
arise in the IIA string on the degenerate K3. T-duals of this give exotic
branes on non-geometric spaces.
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Energy radiated from a fluctuating selfdual string: We compute the energy that is radiated from a fluctuating selfdual string in
the large $N$ limit of $A_{N-1}$ theory using the AdS-CFT correspondence. We
find that the radiated energy is given by a non-local expression integrated
over the string world-sheet. We also make the corresponding computation for a
charged string in six-dimensional classical electrodynamics, thereby
generalizing the Larmor formula for the radiated energy from an accelerated
point particle.
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Gravity-Matter Couplings from Liouville Theory: The three-point functions for minimal models coupled to gravity are derived
in the operator approach to Liouville theory which is based on its $U_q(sl(2))$
quantum group structure. The result is shown to agree with matrix-model
calculations on the sphere. The precise definition of the corresponding
cosmological constant is given in the operator solution of the quantum
Liouville theory. It is shown that the symmetry between quantum-group spins $J$
and $-J-1$ previously put forward by the author is the explanation of the
continuation in the number of screening operators discovered by Goulian and Li.
Contrary to the previous discussions of this problem, the present approach
clearly separates the emission operators for each leg. This clarifies the
structure of the dressing by gravity. It is shown, in particular that the end
points are not treated on the same footing as the mid point. Since the outcome
is completely symmetric this suggests the existence of a picture-changing
mechanism in two dimensional gravity.
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Axion-Dilaton Black Holes: In this talk some essential features of stringy black holes are described. We
consider charged four-dimensional axion-dilaton black holes. The Hawking
temperature and the entropy of all solutions are shown to be simple functions
of the squares of supercharges, defining the positivity bounds. Spherically
symmetric and multi black hole solutions are presented. The extreme solutions
have some unbroken supersymmetries. Axion-dilaton black holes with zero entropy
and zero area of the horizon form a family of stable particle-like objects,
which we call holons. We discuss the possibility of splitting of nearly extreme
black holes into holons.
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The correspondence between rotating black holes and fundamental strings: The correspondence principle between strings and black holes is a general
framework for matching black holes and massive states of fundamental strings at
a point where their physical properties (such as mass, entropy and temperature)
smoothly agree with each other. This correspondence becomes puzzling when
attempting to include rotation: At large enough spins, there exist degenerate
string states that seemingly cannot be matched to any black hole. Conversely,
there exist black holes with arbitrarily large spins that cannot correspond to
any single-string state. We discuss in detail the properties of both types of
objects and find that a correspondence that resolves the puzzles is possible by
adding dynamical features and non-stationary configurations to the picture. Our
scheme incorporates all black hole and string phases as part of the
correspondence, save for one outlier which remains enigmatic: the near-extremal
Kerr black hole. Along the way, we elaborate on general aspects of the
correspondence that have not been emphasized before.
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On the duality of massive Kalb-Ramond and Proca fields: We compare the massive Kalb-Ramond and Proca fields with a quartic
self-interaction and show that the same strong coupling scale is present in
both theories. In the Proca theory, the longitudinal mode enters the strongly
coupled regime beyond this scale, while the two transverse modes propagate
further and survive in the massless limit. In contrast, in case of the massive
Kalb-Ramond field, the two transverse modes become strongly coupled beyond the
Vainshtein scale, while the pseudo-scalar mode remains in the weak coupling
regime and survives in the massless limit. This indicates a contradiction with
the numerous claims in the literature that these theories are dual to each
other.
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Noncompact Symmetries in String Theory: Noncompact groups, similar to those that appeared in various supergravity
theories in the 1970's, have been turning up in recent studies of string
theory. First it was discovered that moduli spaces of toroidal compactification
are given by noncompact groups modded out by their maximal compact subgroups
and discrete duality groups. Then it was found that many other moduli spaces
have analogous descriptions. More recently, noncompact group symmetries have
turned up in effective actions used to study string cosmology and other
classical configurations. This paper explores these noncompact groups in the
case of toroidal compactification both from the viewpoint of low-energy
effective field theory, using the method of dimensional reduction, and from the
viewpoint of the string theory world sheet. The conclusion is that all these
symmetries are intimately related. In particular, we find that Chern--Simons
terms in the three-form field strength $H_{\mu\nu\rho}$ play a crucial role.
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Fractional Effective Quark-Antiquark Interaction in Symplectic Quantum
Mechanics: We investigate within the formalism of Symplectic Quantum Mechanics a
two-dimensional non-relativistic strong interacting system that represents the
bound heavy quark-antiquark state, where it was considered a linear potential
in the context of generalized fractional derivatives. For this purpose, it was
solved the Schr\"odinger equation in phase space with the linear potential. The
solution (ground state) is obtained, analyzed through the Wigner function
comparing with the original solution, the Airy function for the meson
$c\overline{c}$. The identified eigenfunctions are connected to the Wigner
function via the Weyl product and the Galilei group representation theory in
phase space. In some ways, compared to the wave function, the Wigner function
makes it simpler to see how the meson system is non-classical.
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Correlator correspondences for subregular $\mathcal{W}$-algebras and
principal $\mathcal{W}$-superalgebras: We examine a strong/weak duality between a Heisenberg coset of a theory with
$\mathfrak{sl}_n$ subregular $\mathcal{W}$-algebra symmetry and a theory with a
$\mathfrak{sl}_{n|1}$-structure. In a previous work, two of the current authors
provided a path integral derivation of correlator correspondences for a series
of generalized Fateev-Zamolodchikov-Zamolodchikov (FZZ-)duality. In this paper,
we derive correlator correspondences in a similar way but for a different
series of generalized duality. This work is a part of the project to realize
the duality of corner vertex operator algebras proposed by Gaiotto and
Rap\v{c}\'ak and partly proven by Linshaw and one of us in terms of two
dimensional conformal field theory. We also examine another type of duality
involving an additional pair of fermions, which is a natural generalization of
the fermionic FZZ-duality. The generalization should be important since a
principal $\mathcal{W}$-superalgebra appears as its symmetry and the properties
of the superalgebra are less understood than bosonic counterparts.
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Physicists' $d=3+1$, $N=1$ superspace-time and supersymmetric QFTs from
a tower construction in complexified ${\Bbb Z}/2$-graded $C^\infty$-Algebraic
Geometry and a purge-evaluation/index-contracting map: The complexified ${\Bbb Z}/2$-graded $C^\infty$-Algebraic Geometry aspect of
a superspace(-time) $\widehat{X}$ in Sec.\,1 of D(14.1) (arXiv:1808.05011
[math.DG]) together with the Spin-Statistics Theorem in Quantum Field Theory,
which requires fermionic components of a superfield be anticommuting, lead us
to the notion of towered superspace(-time) $\widehat{X}^{\widehat{\boxplus}}$
and the built-in purely even physics sector $X^{\mbox{physics}}$ from
$\widehat{X}^{\widehat{\boxplus}}$. We use this to reproduce the $d=3+1$, $N=1$
Wess-Zumino model and the $d=3+1$, $N=1$ supersymmetric $U(1)$ gauge theory
with matter --- as in, e.g., Chap.\,V and Chap.\,VI \& part of Chap.\,VII of
the classical Supersymmetry \& Supergravity textbook by Julius Wess and
Jonathan Bagger --- and, hence, recast physicists' two most basic
supersymmetric quantum field theories solidly into the realm of (complexified
${\Bbb Z}/2$-graded) $C^\infty$-Algebraic Geometry. Some traditional
differential geometers' ways of understanding supersymmetric quantum field
theories are incorporated into the notion of a
purge-evaluation/index-contracting map ${\cal
P}:C^\infty(X^{\mbox{physics}})\rightarrow C^\infty(\widehat{X})$ in the
setting. This completes for the current case a $C^\infty$-Algebraic Geometry
language we sought for in D(14.1), footnote 2, that can directly link to the
study of supersymmetry in particle physics. Once generalized to the nonabelian
case in all dimensions and extended $N\ge 2$, this prepares us for a
fundamental (as opposed to solitonic) description of super D-branes parallel to
Ramond-Neveu-Schwarz fundamental superstrings
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Super-Zeeman Embedding Models on N-Supersymmetric World-Lines: We construct a model of an electrically charged magnetic dipole with
arbitrary N-extended world-line supersymmetry, which exhibits a supersymmetric
Zeeman effect. By including supersymmetric constraint terms, the ambient space
of the dipole may be tailored into an algebraic variety, and the supersymmetry
broken for almost all parameter values. The so exhibited obstruction to
supersymmetry breaking refines the standard one, based on the Witten index
alone.
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Fractional Branes and N=1 Gauge Theories: We discuss fractional D3-branes on the orbifold C^3/Z_2*Z_2. We study the
open and the closed string spectrum on this orbifold. The corresponding N=1
theory on the brane has, generically, a U(N_1)*U(N_2)*U(N_3)*U(N_4) gauge group
with matter in the bifundamental. In particular, when only one type of brane is
present, one obtains pure N=1 Yang-Mills. We study the coupling of the branes
to the bulk fields and present the corresponding supergravity solution, valid
at large distances. By using a probe analysis, we are able to obtain the
Wilsonian beta-function for those gauge theories that possess some chiral
multiplet. Although, due to the lack of moduli, the probe technique is not
directly applicable to the case of pure N=1 Yang-Mills, we point out that the
same formula gives the correct result also for this case.
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Back-door fine-tuning in supersymmetric low scale inflation: Low scale inflation has many virtues and it has been claimed that its natural
realisation in supersymmetric standard model can be achieved rather easily. In
this letter we have demonstrated that also in this case the dynamics of the
hidden sector responsible for supersymmetry breakdown and the structure of the
soft terms affects significantly, and in fact often spoils, the would-be
inflationary dynamics. Also, we point out that the issue if the cosmological
constant cancellation in the post-inflationary vacuum strongly affects
supersymmetric inflation. It is important to note the crucial difference
between freezing of the modulus and actually stabilising it - the first
approach misses parts of the scalar potential which turn out to be relevant for
inflation. We argue, that it is more likely that the low scale supersymmetric
inflation occurs at a critical point at the origin in the field space than at
an inflection point away from the origin, as the necessary fine-tuning in the
second case is typically larger.
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Linear Models for Flux Vacua: We construct worldsheet descriptions of heterotic flux vacua as the IR limits
of N=2 gauge theories. Spacetime torsion is incorporated via a 2d Green-Schwarz
mechanism in which a doublet of axions cancels a one-loop gauge anomaly.
Manifest (0,2) supersymmetry and the compactness of the gauge theory instanton
moduli space suggest that these models, which include Fu-Yau models, are stable
against worldsheet instanton effects, implying that they, like Calabi-Yaus, may
be smoothly extended to solutions of the exact beta functions. Since Fu-Yau
compactifications are dual to KST-type flux compactifications, this provides a
microscopic description of these IIB RR-flux vacua.
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Weak cosmic censorship conjecture with pressure and volume in the
Gauss-Bonnet AdS black hole: With the Hamilton-Jacobi equation, we obtain the energy-momentum relation of
a charged particle as it is absorbed by the Gauss-Bonnet AdS black hole. On the
basis of the energy-momentum relation at the event horizon, we investigate the
first law, second law, and weak cosmic censorship conjecture in both the normal
phase space and extended phase space. Our results show that the first law,
second law as well as the weak cosmic censorship conjecture are valid in the
normal phase space for all the initial states are black holes. However, in the
extended phase space, the second law is violated for the extremal and
near-extremal black holes, and the weak cosmic censorship conjecture is
violable for the near-extremal black hole, though the first law is still valid.
In addition, in both the the normal and extended phase spaces, we find the
absorbed particle changes the configuration of the near-extremal black hole,
while don't change that of the extremal black hole.
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Smooth tensionful higher-codimensional brane worlds with bulk and brane
form fields: Completely regular tensionful codimension-n brane world solutions are
discussed, where the core of the brane is chosen to be a thin codimension-(n-1)
shell in an infinite volume flat bulk, and an Einstein-Hilbert term localized
on the brane is included (Dvali-Gabadadze-Porrati models). In order to support
such localized sources we enrich the vacuum structure of the brane by the
inclusion of localized form fields. We find that phenomenological constraints
on the size of the internal core seem to impose an upper bound to the brane
tension. Finite transverse-volume smooth solutions are also discussed.
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Two-dimensional gauge anomalies and $p$-adic numbers: We show how methods of number theory can be used to study anomalies in gauge
quantum field theories in spacetime dimension two. To wit, the anomaly
cancellation conditions for the abelian part of the local anomaly admit
solutions if and only if they admit solutions in the reals and in the $p$-adics
for every prime $p$ and we use this to build an algorithm to find all
solutions.
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Vector-Tensor multiplet in N=2 superspace with central charge: We use the four-dimensional N=2 central charge superspace to give a
geometrical construction of the Abelian vector-tensor multiplet consisting,
under N=1 supersymmetry, of one vector and one linear multiplet. We derive the
component field supersymmetry and central charge transformations, and show that
there is a super-Lagrangian, the higher components of which are all total
derivatives, allowing us to construct superfield and component actions.
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Supersymmetry of IIA warped flux AdS and flat backgrounds: We identify the fractions of supersymmetry preserved by the most general
warped flux AdS and flat backgrounds in both massive and standard IIA
supergravities. We find that $AdS_n\times_w M^{10-n}$ preserve $2^{[{n\over2}]}
k$ for $n\leq 4$ and $2^{[{n\over2}]+1} k$ for $4<n\leq 7$ supersymmetries,
$k\in \bN_{>0}$. In addition we show that, for suitably restricted fields and
$M^{10-n}$, the killing spinors of AdS backgrounds are given in terms of the
zero modes of Dirac like operators on $M^{10-n}$. This generalizes the
Lichnerowicz theorem for connections whose holonomy is included in a general
linear group. We also adapt our results to $\bR^{1,n-1}\times_w M^{10-n}$
backgrounds which underpin flux compactifications to $\bR^{1,n-1}$ and show
that these preserve $2^{[{n\over2}]} k$ for $2<n\leq 4$, $2^{[{n+1\over2}]} k$
for $4<n\leq 8$, and $2^{[{n\over2}]} k$ for $n=9, 10$ supersymmetries.
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Low Energy Gauge Unification Theory: Because of the problems arising from the fermion unification in the
traditional Grand Unified Theory and the mass hierarchy between the
4-dimensional Planck scale and weak scale, we suggest the low energy gauge
unification theory with low high-dimensional Planck scale. We discuss the
non-supersymmetric SU(5) model on $M^4\times S^1/Z_2 \times S^1/Z_2$ and the
supersymmetric SU(5) model on $M^4\times S^1/(Z_2\times Z_2') \times
S^1/(Z_2\times Z_2')$. The SU(5) gauge symmetry is broken by the orbifold
projection for the zero modes, and the gauge unification is accelerated due to
the SU(5) asymmetric light KK states. In our models, we forbid the proton
decay, still keep the charge quantization, and automatically solve the fermion
mass problem. We also comment on the anomaly cancellation and other possible
scenarios for low energy gauge unification.
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The Spectral Action Principle: We propose a new action principle to be associated with a noncommutative
space $(\Ac ,\Hc ,D)$. The universal formula for the spectral action is $(\psi
,D\psi) + \Trace (\chi (D /$ $\Lb))$ where $\psi$ is a spinor on the Hilbert
space, $\Lb$ is a scale and $\chi$ a positive function. When this principle is
applied to the noncommutative space defined by the spectrum of the standard
model one obtains the standard model action coupled to Einstein plus Weyl
gravity. There are relations between the gauge coupling constants identical to
those of $SU(5)$ as well as the Higgs self-coupling, to be taken at a fixed
high energy scale.
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Dielectric-Branes: We extend the usual world-volume action for a Dp-brane to the case of N
coincident Dp-branes where the world-volume theory involves a U(N) gauge
theory. The guiding principle in our construction is that the action should be
consistent with the familiar rules of T-duality. The resulting action involves
a variety of potential terms, i.e., nonderivative interactions, for the
nonabelian scalar fields. This action also shows that Dp-branes naturally
couple to RR potentials of all form degrees, including both larger and smaller
than p+1. We consider the dynamics resulting from this action for Dp-branes
moving in nontrivial background fields, and illustrate how the Dp-branes are
``polarized'' by external fields. In a simple example, we show that a system of
D0-branes in an external RR four-form field expands into a noncommutative
two-sphere, which is interpreted as the formation of a spherical D2-D0 bound
state.
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Schrödinger Fields on the Plane with $[U(1)]^N$ Chern-Simons
Interactions and Generalized Self-dual Solitons: A general non-relativistic field theory on the plane with couplings to an
arbitrary number of abelian Chern-Simons gauge fields is considered. Elementary
excitations of the system are shown to exhibit fractional and mutual
statistics. We identify the self-dual systems for which certain classical and
quantal aspects of the theory can be studied in a much simplified mathematical
setting. Then, specializing to the general self-dual system with two
Chern-Simons gauge fields (and non-vanishing mutual statistics parameter), we
present a systematic analysis for the static vortexlike classical solutions,
with or without uniform background magnetic field. Relativistic generalizations
are also discussed briefly.
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BRST, Ward identities, gauge dependence, and a functional
renormalization group: Basic properties of gauge theories in the framework of Faddeev-Popov (FP)
method, Batalin-Vilkovisky (BV) formalism, functional renormalization group
(FRG) approach are considered. The FP and BV quantizations are characterized by
the Becchi-Rouet-Stora-Tyutin (BRST) symmetry while the BRST symmetry is broken
in the FRG approach. It is shown that the FP method, the BV formalism and the
FRG approach can be provided with the Slavnov-Taylor identity, the Ward
identity and the modified Slavnov-Taylor identity, respectively. It is proven
that using the background field method the background gauge invariance of
effective action within the FP and FRG quantization procedures can be achieved
in nonlinear gauges. The gauge-dependence problem within the FP, BV and FRG
quantizations is studied. Arguments allowing us to state the existence of
principal problems of the FRG in the case of gauge theories are given.
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Chiral Symmetry Breaking in the Nambu-Jona-Lasinio Model in Curved
Spacetime with Non-Trivial Topology: We discuss the phase structure (in the $1/N$-expansion) of the
Nambu-Jona-Lasinio model in curved spacetime with non-trivial topology ${\cal
M}^3 \times {\rm S}^1$. The evaluation of the effective potential of the
composite field $\bar{\psi} \psi$ is presented in the linear curvature
approximation (topology is treated exactly) and in the leading order of the
$1/N$-expansion. The combined influence of topology and curvature to the phase
transitions is investigated. It is shown, in particular, that at zero curvature
and for small radius of the torus there is a second order phase transition from
the chiral symmetric to the chiral non-symmetric phase. When the curvature
grows and (or) the radius of ${\rm S}^1$ decreases, then the phase transition
is in general of first order. The dynamical fermionic mass is also calculated
in a number of different situations.
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Bose and Fermi Statistics and the Regularization of the Nonrelativistic
Jacobian for the Scale Anomaly: We regulate in Euclidean space the Jacobian under scale transformations for
two-dimensional nonrelativistic fermions and bosons interacting via contact
interactions and compare the resulting scaling anomalies. For fermions,
Grassmannian integration inverts the Jacobian: however, this effect is
cancelled by the regularization procedure and a result similar to that of
bosons is attained. We show the independence of the result with respect to the
regulating function, and show the robustness of our methods by comparing the
procedure with an effective potential method using both cutoff and
$\zeta$-function regularization.
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Complexity Geometry and Schwarzian Dynamics: A celebrated feature of SYK-like models is that at low energies, their
dynamics reduces to that of a single variable. In many setups, this
"Schwarzian" variable can be interpreted as the extremal volume of the dual
black hole, and the resulting dynamics is simply that of a 1D Newtonian
particle in an exponential potential. On the complexity side, geodesics on a
simplified version of Nielsen's complexity geometry also behave like a 1D
particle in a potential given by the angular momentum barrier. The agreement
between the effective actions of volume and complexity succinctly summarizes
various strands of evidence that complexity is closely related to the dynamics
of black holes.
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Perturbations on a moving D3-brane and mirage cosmology: We study the evolution of perturbations on a moving probe D3-brane coupled to
a 4-form field in an AdS$_5$-Schwarzschild bulk. The unperturbed dynamics are
parametrised by a conserved energy $E$ and lead to Friedmann-Robertson-Walker
`mirage' cosmology on the brane with scale factor $a(\tau)$. The fluctuations
about the unperturbed worldsheet are then described by a scalar field
$\phi(\tau,\vec{x})$. We derive an equation of motion for $\phi$, and find that
in certain regimes of $a$ the effective mass squared is negative. On an
expanding BPS brane with E=0 superhorizon modes grow as $a^4$ whilst subhorizon
modes are stable. When the brane contracts, all modes grow. We also briefly
discuss the case when $E>0$, BPS anti-branes as well as non-BPS branes.
Finally, the perturbed brane embedding gives rise to scalar perturbations in
the FRW universe. We show that $\phi$ is proportional to the gauge invariant
Bardeen potentials on the brane.
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First Order Description of Black Holes in Moduli Space: We show that the second order field equations characterizing extremal
solutions for spherically symmetric, stationary black holes are in fact implied
by a system of first order equations given in terms of a prepotential W. This
confirms and generalizes the results in [14]. Moreover we prove that the
squared prepotential function shares the same properties of a c-function and
that it interpolates between M^2_{ADM} and M^2_{BR}, the parameter of the
near-horizon Bertotti-Robinson geometry. When the black holes are solutions of
extended supergravities we are able to find an explicit expression for the
prepotentials, valid at any radial distance from the horizon, which reproduces
all the attractors of the four dimensional N>2 theories. Far from the horizon,
however, for N-even our ansatz poses a constraint on one of the U-duality
invariants for the non-BPS solutions with Z \neq 0. We discuss a possible
extension of our considerations to the non extremal case.
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Bosonization of Nonrelativistic Fermions and W-infinity Algebra: We discuss the bosonization of non-relativistic fermions in one space
dimension in terms of bilocal operators which are naturally related to the
generators of $W$-infinity algebra. The resulting system is analogous to the
problem of a spin in a magnetic field for the group $W$-infinity. The new
dynamical variables turn out to be $W$-infinity group elements valued in the
coset $W$-infinity/$H$ where $H$ is a Cartan subalgebra. A classical action
with an $H$ gauge invariance is presented. This action is three-dimensional. It
turns out to be similiar to the action that describes the colour degrees of
freedom of a Yang-Mills particle in a fixed external field. We also discuss the
relation of this action with the one we recently arrived at in the Euclidean
continuation of the theory using different coordinates.
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Remodeling the Effective One-Body Formalism in Post-Minkowskian Gravity: The Effective One-Body formalism of the gravitational two-body problem in
general relativity is reconsidered in the light of recent scattering amplitude
calculations. Based on the kinematic relationship between momenta and the
effective potential, we consider an energy-dependent effective metric
describing the scattering in terms of an Effective One-Body problem for the
reduced mass. The identification of the effective metric simplifies
considerably in isotropic coordinates when combined with a redefined angular
momentum map. While the effective energy-dependent metric as expected is not
unique, solutions can be chosen perturbatively in the Post-Minkowskian
expansion without the need to introduce non-metric corrections. By a canonical
transformation, our condition maps to the one based on the standard angular
momentum map. Expanding our metric around the Schwarzschild solution we recover
the solution based on additional non-metric contributions.
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Holographic reconstruction of asymptotically flat spacetimes: We present a "holographic" reconstruction of bulk spacetime geometry using
correlation functions of a massless field living at the "future boundary" of
the spacetime, namely future null infinity $\mathscr{I}^+$. It is holographic
in the sense that there exists a one-to-one correspondence between correlation
functions of a massless field in four-dimensional spacetime $\mathcal{M}$ and
those of another massless field living in three-dimensional null boundary
$\mathscr{I}^+$. The idea is to first reconstruct the bulk metric $g_{\mu\nu}$
by "inverting" the bulk correlation functions and re-express the latter in
terms of boundary correlators via the correspondence. This effectively allows
asymptotic observers close to $\mathscr{I}^+$ to reconstruct the deep interior
of the spacetime using only correlation functions localized near
$\mathscr{I}^+$.
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Multidimensional Residues for Feynman Integrals with Generic Power of
Propagators: We propose that the concept of multidimensional residues can be used to
directly extracting the coefficients of scalar master integrals (with single
propagators only) from one-loop Feynman integrals with generic power of
propagators. Unlike the usual integration-by-parts (IBP) technique, where one
has to solve iteratively a complicated set of equations to carry out the
reduction and determine the coefficients of scalar master integrals, using
multidimensional residues provides the possibility of directly extracting the
coefficients of the master integrals. As the first application of this idea, we
show how to directly extract the scalar box integral coefficients.
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Action, entropy and pair creation rate of charged black holes in de
Sitter space: We compute and clarify the interpretation of the on-shell Euclidean action
for Reissner-Nordstr\"{o}m black holes in de Sitter space. We show the on-shell
action is minus the sum of the black hole and cosmological horizon entropy for
arbitrary mass and charge in any number of dimensions. This unifying expression
helps to clear up a confusion about the Euclidean actions of extremal and
ultracold black holes in de Sitter, as they can be understood as special cases
of the general expression. We then use this result to estimate the probability
for the pair creation of black holes with arbitrary mass and charge in an empty
de Sitter background, by employing the formalism of constrained instantons.
Finally, we suggest that the decay of charged de Sitter black holes is governed
by the gradient flow of the entropy function and that, as a consequence, the
regime of light, superradiant, rapid charge emission should describe the
potential decay of extreme charged Nariai black holes to singular geometries.
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Gribov horizon and BRST symmetry: a few remarks: The issue of the BRST symmetry in presence of the Gribov horizon is addressed
in Euclidean Yang-Mills theories in the Landau gauge. The positivity of the
Faddeev-Popov operator within the Gribov region enables us to convert the soft
breaking of the BRST invariance exhibited by the Gribov-Zwanziger action into a
non-local exact symmetry, displaying explicit dependence from the
non-perturbative Gribov parameter. Despite its non-locality, this symmetry
turns out to be useful in order to establish non-perturbative Ward identities,
allowing us to evaluate the vacuum expectation value of quantities which are
BRST exact. These results are generalized to the refined Gribov-Zwanziger
action introduced in [1], which yields a gluon propagator which is
non-vanishing at the origin in momentum space, and a ghost propagator which is
not enhanced in the infrared.
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Three-BMN Correlation Functions: Integrability vs. String Field Theory
One-Loop Mismatch: We compare calculations of the three-point correlation functions of BMN
operators at the one-loop (next-to-leading) order in the scalar SU(2) sector
from the integrability expression recently suggested by Gromov and Vieira, and
from the string field theory expression based on the effective interaction
vertex by Dobashi and Yoneya. A disagreement is found between the form-factors
of the correlation functions in the one-loop contributions. The order-of-limits
problem is suggested as a possible explanation of this discrepancy.
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Thermodynamics of noncommutative high-dimensional AdS black holes with
non-Gaussian smeared matter distributions: Considering non-Gaussian smeared matter distributions, we investigate
thermodynamic behaviors of the noncommutative high-dimensional
Schwarzschild-Tangherlini anti-de Sitter black hole, and obtain the condition
for the existence of extreme black holes. We indicate that the Gaussian smeared
matter distribution, which is a special case of non-Gaussian smeared matter
distributions, is not applicable for the 6- and higher-dimensional black holes
due to the hoop conjecture. In particular, the phase transition is analyzed in
detail. Moreover, we point out that the Maxwell equal area law maintains for
the noncommutative black hole whose Hawking temperature is within a specific
range, but fails for that whose the Hawking temperature is beyond this range.
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Supersymmetry and Attractors: We find a general principle which allows one to compute the area of the
horizon of N=2 extremal black holes as an extremum of the central charge. One
considers the ADM mass equal to the central charge as a function of electric
and magnetic charges and moduli and extremizes this function in the moduli
space (a minimum corresponds to a fixed point of attraction). The extremal
value of the square of the central charge provides the area of the horizon,
which depends only on electric and magnetic charges. The doubling of unbroken
supersymmetry at the fixed point of attraction for N=2 black holes near the
horizon is derived via conformal flatness of the Bertotti-Robinson-type
geometry. These results provide an explicit model independent expression for
the macroscopic Bekenstein-Hawking entropy of N=2 black holes which is
manifestly duality invariant. The presence of hypermultiplets in the solution
does not affect the area formula. Various examples of the general formula are
displayed. We outline the attractor mechanism in N=4,8 supersymmetries and the
relation to the N=2 case. The entropy-area formula in five dimensions, recently
discussed in the literature, is also seen to be obtained by extremizing the 5d
central charge.
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Quaternionic Formulation of the Exact Parity Model: The exact parity model (EPM) is a simple extension of the Standard Model
which reinstates parity invariance as an unbroken symmetry of nature. The
mirror matter sector of the model can interact with ordinary matter through
gauge boson mixing, Higgs boson mixing and, if neutrinos are massive, through
neutrino mixing. The last effect has experimental support through the observed
solar and atmospheric neutrino anomalies. In this paper we show that the exact
parity model can be formulated in a quaternionic framework. This suggests that
the idea of mirror matter and exact parity may have profound implications for
the mathematical formulation of quantum theory.
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Massless scalar particle on AdS spacetime: Hamiltonian reduction and
quantization: We investigate the massless scalar particle dynamics on $AdS_{N+1} ~ (N>1)$
by the method of Hamiltonian reduction. Using the dynamical integrals of the
conformal symmetry we construct the physical phase space of the system as a
$SO(2,N+1)$ orbit in the space of symmetry generators. The symmetry generators
themselves are represented in terms of $(N+1)$-dimensional oscillator
variables. The physical phase space establishes a correspondence between the
$AdS_{N+1}$ null-geodesics and the dynamics at the boundary of $AdS_{N+2}$. The
quantum theory is described by a UIR of $SO(2,N+1)$ obtained at the unitarity
bound. This representation contains a pair of UIR's of the isometry subgroup
SO(2,N) with the Casimir number corresponding to the Weyl invariant mass value.
The whole discussion includes the globally well-defined realization of the
conformal group via the conformal embedding of $AdS_{N+1}$ in the ESU
$\rr\times S^N$.
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From U(1) Maxwell Chern-Simons to Azbel-Hofstadter: Testing Magnetic
Monopoles and Gravity to $\sim 10^{-15}$\textit{m}?: It is built a map between an Abelian Topological Quantum Field Theory, $2+1D$
compact U(1) gauge Maxwell Chern-Simons Theory and the nonrelativistic quantum
mechanics Azbel-Hofstadter model of Bloch electrons. The $U_q(sl_2)$ quantum
group and the magnetic translations group of the Azbel-Hofstadter model
correspond to discretized subgroups of U(1) with linear gauge parameters. The
magnetic monopole confining and condensate phases in the Topological Quantum
Field Theory are identified with the extended (energy bands) and localized
(gaps) phases of the Bloch electron. The magnetic monopole condensate is
associated, at the nonrelativistic level, with gravitational white holes due to
deformed classical gauge fields. These gravitational solutions render the
existence of finite energy pure magnetic monopoles possible. This mechanism
constitutes a dynamical symmetry breaking which regularizes the solutions on
those localized phases allowing physical solutions of the Shr\"odinger equation
which are chains of electron filaments connecting several monopole-white
holes.To test these results would be necessary a strong external magnetic field
$B\sim 5 T$ at low temperature $T<1 K$. To be accomplished, it would test the
existence of magnetic monopoles and classical gravity to a scale of $\sim
10^{-15}$ \textit{meters}, the dimension of the monopole-white hole. A proper
discussion of such experiment is out of the scope of this theoretical work.
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Casimir Energy of the Universe and the Dark Energy Problem: We regard the Casimir energy of the universe as the main contribution to the
cosmological constant. Using 5 dimensional models of the universe, the flat
model and the warped one, we calculate Casimir energy. Introducing the new
regularization, called {\it sphere lattice regularization}, we solve the
divergence problem. The regularization utilizes the closed-string
configuration. We consider 4 different approaches: 1) restriction of the
integral region (Randall-Schwartz), 2) method of 1) using the minimal area
surfaces, 3) introducing the weight function, 4) {\it generalized
path-integral}. We claim the 5 dimensional field theories are quantized
properly and all divergences are renormalized. At present, it is explicitly
demonstrated in the numerical way, not in the analytical way. The
renormalization-group function ($\be$-function) is explicitly obtained. The
renormalization-group flow of the cosmological constant is concretely obtained.
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Monodromy of an Inhomogeneous Picard-Fuchs Equation: The global behaviour of the normal function associated with van Geemen's
family of lines on the mirror quintic is studied. Based on the associated
inhomogeneous Picard-Fuchs equation, the series expansions around large complex
structure, conifold, and around the open string discriminant are obtained. The
monodromies are explicitly calculated from this data and checked to be
integral. The limiting value of the normal function at large complex structure
is an irrational number expressible in terms of the di-logarithm.
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UV cancelations in gravity loop integrands: In this work we explore the properties of four-dimensional gravity integrands
at large loop momenta. This analysis can not be done directly for the full
off-shell integrand but only becomes well-defined on cuts that allow us to
unambiguously specify labels for the loop variables. The ultraviolet region of
scattering amplitudes originates from poles at infinity of the loop integrands
and we show that in gravity these integcrands conceal a number of surprising
features. In particular, certain poles at infinity are absent which requires a
conspiracy between individual Feynman integrals contributing to the amplitude.
We suspect that this non-trivial behavior is a consequence of yet-to-be found
symmetry or hidden property of gravity amplitudes. We discuss mainly amplitudes
in $\mathcal{N}=8$ supergravity but most of the statements are valid for pure
gravity as well.
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Holography of Wrapped M5-branes and Chern-Simons theory: We study three-dimensional superconformal field theories on wrapped
M5-branes. Applying the gauge/gravity duality and the recently proposed 3d-3d
relation, we deduce quantitative predictions for the perturbative free energy
of a Chern-Simons theory on hyperbolic 3-space. Remarkably, the perturbative
expansion is expected to terminate at two-loops in the large N limit. We check
the correspondence numerically in a number of examples, and confirm the N^3
scaling with precise coefficients.
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Two-dimensional SUSY-pseudo-Hermiticity without separation of variables: We study SUSY-intertwining for non-Hermitian Hamiltonians with special
emphasis to the two-dimensional generalized Morse potential, which does not
allow for separation of variables. The complexified methods of SUSY-separation
of variables and two-dimensional shape invariance are used to construct
particular solutions - both for complex conjugated energy pairs and for
non-paired complex energies.
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Magnetic monopole - domain wall collisions: Interactions of different types of topological defects can play an important
role in the aftermath of a phase transition. We study interactions of
fundamental magnetic monopoles and stable domain walls in a Grand Unified
theory in which $SU(5) \times Z_2$ symmetry is spontaneously broken to
$SU(3)\times SU(2)\times U(1)/Z_6$. We find that there are only two distinct
outcomes depending on the relative orientation of the monopole and the wall in
internal space. In one case, the monopole passes through the wall, while in the
other it unwinds on hitting the wall.
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Quantum Theory, Noncommutativity and Heuristics: Noncommutative field theories are a class of theories beyond the standard
model of elementary particle physics. Their importance may be summarized in two
facts. Firstly as field theories on noncommutative spacetimes they come with
natural regularization parameters. Secondly they are related in a natural way
to theories of quantum gravity which typically give rise to noncommutative
spacetimes. Therefore noncommutative field theories can shed light on the
problem of quantizing gravity. An attractive aspect of noncommutative field
theories is that they can be formulated so as to preserve spacetime symmetries
and to avoid the introduction of irrelevant degrees freedom and so they provide
models of consistent fundamental theories. In these notes we review the
formulation of symmetry aspects of noncommutative field theories on the
simplest type of noncommutative spacetime, the Moyal plane. We discuss
violations of Lorentz, P, CP, PT and CPT symmetries as well as causality. Some
experimentally detectable signatures of these violations involving Planck scale
physics of the early universe and linear response finite temperature field
theory are also presented.
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De Sitter Uplift with Dynamical Susy Breaking: We propose the use of D-brane realizations of Dynamical Supersymmetry
Breaking (DSB) gauge sectors as sources of uplift in compactifications with
moduli stabilization onto de Sitter vacua. This construction is fairly
different from the introduction of anti D-branes, yet allows for tunably small
contributions to the vacuum energy via their embedding into warped throats. The
idea is explicitly exemplified by the embedding of the 1-family $SU(5)$ DSB
model in a local warped throat with fluxes, which we discuss in detail in terms
of orientifolds of dimer diagrams.
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Massless Charged Particles Tunneling Radiation from a RN-dS Horizon and
the Linear and Quadratic GUP: In this paper, we investigate the massless Reissner-Nordstrom de Sitter
metric in the context of minimal length scenarios. We prove not only the
confinement of the energy density of massless charged particles, both fermions
and bosons, but also their ability to tunnel through the cosmological horizon.
These massless particles might be interacting with Dirac sea and in this case
they will appear outside the cosmological horizon in the context of dS/CFT
holography. This result may formulate a fundamental reason for the expansion of
the Dirac sea. Therefore, a spacetime Big Crunch may occur.
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Superselection Sectors of $\son$ Wess-Zumino-Witten Models: The superselection structure of $\son$ WZW models is investigated from the
point of view of algebraic quantum field theory. At level $1$ it turns out that
the observable algebras of the WZW theory can be constructed in terms of even
CAR algebras. This fact allows to give a formulation of these models close to
the DHR framework. Localized endomorphisms are constructed explicitly in terms
of Bogoliubov transformations, and the WZW fusion rules are proven using the
DHR sector product.
At level $2$ it is shown that most of the sectors are realized in
$\HNSh=\HNS\otimes\HNS$ where $\HNS$ is the Neveu-Schwarz sector of the level
$1$ theory. The level $2$ characters are derived and $\HNSh$ is decomposed
completely into tensor products of the sectors of the WZW chiral algebra and
irreducible representation spaces of the coset Virasoro algebra. Crucial for
this analysis is the DHR decomposition of $\HNSh$ into sectors of a gauge
invariant fermion algebra since the WZW chiral algebra as well as the coset
Virasoro algebra are invariant under the gauge group $\Oz$.
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Flowing from relativistic to non-relativistic string vacua in AdS$_5
\times$S$^5$: We find the connection between relativistic and non-relativistic string vacua
in AdS$_5 \times$S$^5$ in terms of a free parameter $c$ flow. First, we show
that the famous relativistic BMN vacuum flows in the large $c$ parameter to an
unphysical solution of the non-relativistic theory. Then, we consider the
simplest non-relativistic vacuum, found in arXiv:2109.13240 (called BMN-like),
and we identify its relativistic origin, namely a non-compact version of the
folded string with zero spin, ignored in the past due to its infinite energy.
We show that, once the critical closed B-field required by the non-relativistic
limit is included, the total energy of such relativistic solution is finite,
and in the large $c$ parameter it precisely matches the one of the BMN-like
string. We also analyse the case with spin in the transverse AdS directions.
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Three-dimensional BF Theories and the Alexander-Conway Invariant of
Knots: We study 3-dimensional BF theories and define observables related to knots
and links. The quantum expectation values of these observables give the
coefficients of the Alexander-Conway polynomial.
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Dimensional continuation without perturbation theory: A formula is proposed for continuing physical correlation functions to
non-integer numbers of dimensions, expressing them as infinite weighted sums
over the same correlation functions in arbitrary integer dimensions. The
formula is motivated by studying the strong coupling expansion, but the end
result makes no reference to any perturbation theory. It is shown that the
formula leads to the correct dimension dependence in weak coupling perturbation
theory at one loop.
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M5-branes in ABJM theory and Nahm equation: We construct BPS solutions representing M2-M5 bound state in the ABJM action
explicitly. They include the funnel type solutions and 't Hooft Polyakov
monopole solutions. Furthermore, we give a one to one correspondence between
the solutions of the BPS equation and the ones of an extended Nahm equation
which includes the Nahm equation. This enables us to construct infinitely many
conserved quantities from the Lax form of the Nahm equation.
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θ-angle monodromy in two dimensions: "\theta-angle monodromy" occurs when a theory possesses a landscape of
metastable vacua which reshuffle as one shifts a periodic coupling \theta by a
single period. "Axion monodromy" models arise when this parameter is promoted
to a dynamical pseudoscalar field. This paper studies the phenomenon in
two-dimensional gauge theories which possess a U(1) factor at low energies: the
massive Schwinger and gauged massive Thirring models, the U(N) 't Hooft model,
and the {\mathbb CP}^N model. In all of these models, the energy dependence of
a given metastable false vacuum deviates significantly from quadratic
dependence on \theta just as the branch becomes completely unstable (distinct
from some four-dimensional axion monodromy models). In the Schwinger, Thirring,
and 't Hooft models, the meson masses decrease as a function of \theta. In the
U(N) models, the landscape is enriched by sectors with nonabelian \theta terms.
In the {\mathbb CP}^N model, we compute the effective action and the size of
the mass gap is computed along a metastable branch.
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Toward getting finite results from N=4 SYM with alpha'-corrections: We take our first step toward getting finite results from the
alpha'-corrected D=4 N=4 SYM theory with emphasis on the field theory
techniques. Starting with the classical action of N=4 SYM with the leading
alpha'-corrections, we examine new divergence at one loop due to the presence
of the alpha'-terms. The new vertices do not introduce additional divergence to
the propagators or to the three-point correlators. However they do introduce
new divergence, e.g., to the scalar four-point function which should be
canceled by extra counter-terms. We expect that the counter-terms will appear
in the 1PI effective action that is obtained by considering the string annulus
diagram. We work out the structure of the divergence and comment on an
application to the anomalous dimension of the SYM operators in the context of
AdS/CFT.
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Lagrangian Formulation for Free Mixed-Symmetry Bosonic Gauge Fields in
(A)dS(d): Covariant Lagrangian formulation for free bosonic massless fields of
arbitrary mixed-symmetry type in (A)dS(d) space-time is presented. The analysis
is based on the frame-like formulation of higher-spin field dynamics [1] with
higher-spin fields described as p-forms taking values in appropriate modules of
the (A)dS(d). The problem of finding free field action is reduced to the
analysis of an appropriate differential complex, with the derivation Q
associated with the variation of the action. The constructed action exhibits
additional gauge symmetries in the flat limit in agreement with the general
structure of gauge symmetries for mixed-symmetry fields in Minkowski and
(A)dS(d) spaces.
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Biharmonic Superspace for N=4 Mechanics: We develop a new superfield approach to N=4 supersymmetric mechanics based on
the concept of biharmonic superspace (bi-HSS). It is an extension of the
N=4,d=1 superspace by two sets of harmonic variables associated with the two
SU(2) factors of the R-symmetry group SO(4) of the N=4, d=1 super Poincar\'e
algebra. There are three analytic subspaces in it: two of the Grassmann
dimension 2 and one of the dimension 3. They are closed under the
infinite-dimensional "large" N=4 superconformal group, as well as under the
finite-dimensional superconformal group D(2,1;\alpha). The main advantage of
the bi-HSS approach is that it gives an opportunity to treat N=4
supermultiplets with finite numbers of off-shell components on equal footing
with their ``mirror'' counterparts. We show how such multiplets and their
superconformal properties are described in this approach. We also define
nonpropagating gauge multiplets which can be used to gauge various isometries
of the bi-HSS actions. We present an example of nontrivial N=4 mechanics model
with a seven-dimensional target manifold obtained by gauging an U(1) isometry
in a sum of the free actions of the multiplet (4,4,0) and its mirror
counterpart.
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Neutrino mixing and mass hierarchy in Gaussian landscapes: The flavor structure of the Standard Model may arise from random selection on
a landscape. In a class of simple models, called "Gaussian landscapes," Yukawa
couplings derive from overlap integrals of Gaussian zero-mode wavefunctions on
an extra-dimensional space. Statistics of vacua are generated by scanning the
peak positions of these wavefunctions, giving probability distributions for all
flavor observables. Gaussian landscapes can account for all of the major
features of flavor, including both the small electroweak mixing in the quark
sector and the large mixing observed in the lepton sector. We find that large
lepton mixing stems directly from lepton doublets having broad wavefunctions on
the internal manifold. Assuming the seesaw mechanism, we find the mass
hierarchy among neutrinos is sensitive to the number of right-handed neutrinos,
and can provide a good fit to neutrino oscillation measurements.
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Horava-Lifshitz Gravity And Ghost Condensation: In this paper we formulate RFDiff invariant f(R) Horava-Lifshitz gravity and
we show that it is related to the ghost condensation in the projectable version
of Horava-Lifshitz gravity.
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Quotient Stacks and String Orbifolds: In this short review we outline some recent developments in understanding
string orbifolds. In particular, we outline the recent observation that string
orbifolds do not precisely describe string propagation on quotient spaces, but
rather are literally sigma models on objects called quotient stacks, which are
closely related to (but not quite the same as) quotient spaces. We show how
this is an immediate consequence of definitions, and also how this explains a
number of features of string orbifolds, from the fact that the CFT is
well-behaved to orbifold Euler characteristics. Put another way, many features
of string orbifolds previously considered ``stringy'' are now understood as
coming from the target-space geometry; one merely needs to identify the correct
target-space geometry.
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Renormalizability of the Dynamical Two-Form: A proof of renormalizability of the theory of the dynamical non-Abelian
two-form is given using the Zinn-Justin equation. Two previously unknown
symmetries of the quantum action, different from the BRST symmetry, are needed
for the proof. One of these is a gauge fermion dependent nilpotent symmetry,
while the other mixes different fields with the same transformation properties.
The BRST symmetry itself is extended to include a shift transformation by use
of an anticommuting constant. These three symmetries restrict the form of the
quantum action up to arbitrary order in perturbation theory. The results show
that it is possible to have a renormalizable theory of massive vector bosons in
four dimensions without a residual Higgs boson.
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Arithmetic Spacetime Geometry from String Theory: An arithmetic framework to string compactification is described. The approach
is exemplified by formulating a strategy that allows to construct geometric
compactifications from exactly solvable theories at $c=3$. It is shown that the
conformal field theoretic characters can be derived from the geometry of
spacetime, and that the geometry is uniquely determined by the two-dimensional
field theory on the world sheet. The modular forms that appear in these
constructions admit complex multiplication, and allow an interpretation as
generalized McKay-Thompson series associated to the Mathieu and Conway groups.
This leads to a string motivated notion of arithmetic moonshine.
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Ultra-violet Behavior of Bosonic Quantum Membranes: We treat the action for a bosonic membrane as a sigma model, and then compute
quantum corrections by integrating out higher membrane modes. As in string
theory, where the equations of motion of Einstein's theory emerges by setting
$\beta = 0$, we find that, with certain assumptions, we can recover the
equations of motion for the background fields. Although the membrane theory is
non-renormalizable on the world volume by power counting, the investigation of
the ultra-violet behavior of membranes may give us insight into the
supersymmetric case, where we hope to obtain higher order M-theory corrections
to 11 dimensional supergravity.
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Perturbative Expansion around the Gaussian Effective Action: The
Background Field Method: We develop a systematic method of the perturbative expansion around the
Gaussian effective action based on the background field method. We show, by
applying the method to the quantum mechanical anharmonic oscillator problem,
that even the first non-trivial correction terms greatly improve the Gaussian
approximation.
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Three-quark clusters at finite temperatures and densities: We present a relativistic three-body equation to study correlations in a
medium of finite temperatures and densities. This equation is derived within a
systematic Dyson equation approach and includes the dominant medium effects due
to Pauli blocking and self energy corrections. Relativity is implemented
utilizing the light front form. The equation is solved for a zero-range force
for parameters close to the confinement-deconfinement transition of QCD. We
present correlations between two- and three-particle binding energies and
calculate the three-body Mott transition.
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Exact renormalization flow and domain walls from holography: The holographic correspondence between 2d, N=2 quantum field theories and
classical 4d, N=2 supergravity coupled to hypermultiplet matter is proposed.
The geometrical constraints on the target space of the 4d, N=2 non-linear
sigma-models in N=2 supergravity background are interpreted as the exact
renormalization group flow equations in two dimensions. Our geometrical
description of the renormalization flow is manifestly covariant under general
reparametrization of the 2d coupling constants. An explicit exact solution to
the 2d renormalization flow, based on its dual holographic description in terms
of the Zamolodchikov metric, is considered in the particular case of the
four-dimensional NLSM target space described by the SU(2)-invariant (Weyl)
anti-self-dual Einstein metrics. The exact regular (Tod-Hitchin) solutions to
these metrics are governed by the Painlev'e VI equation, and describe domain
walls.
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Closed universes can satisfy the holographic principle in three
dimensions: We examine in details Friedmann-Robertson-Walker models in 2+1 dimensions in
order to investigate the cosmic holographic principle suggested by Fischler and
Susskind. Our results are rigorously derived differing from the previous one
found by Wang and Abdalla. We discuss the erroneous assumptions done in this
work. The matter content of the models is composed of a perfect fluid, with a
$\gamma$-law equation of state. We found that closed universes satisfy the
holographic principle only for exotic matter with a negative pressure. We also
analyze the case of a collapsing flat universe.
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Superfluid properties of BPS monopoles: This paper is devoted to demonstrating manifest superfluid properties of the
Minkowskian Higgs model with vacuum BPS monopole solutions at assuming the
"continuous" $\sim S^2$ vacuum geometry in that model. It will be also argued
that point hedgehog topological defects are present in the Minkowskian Higgs
model with BPS monopoles. It turns out, and we show this, that the enumerated
phenomena are compatible with the Faddeev-Popov "heuristic" quantization of the
Minkowskian Higgs model with vacuum BPS monopoles, coming to fixing the Weyl
(temporal) gauge $A_0=0$ for gauge fields $A$ in the Faddeev-Popov path
integral.
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S-confinements from deconfinements: We consider four dimensional $\mathcal{N}=1$ gauge theories that are
S-confining, that is they are dual to a Wess-Zumino model. S-confining theories
with a simple gauge group have been classified. We prove all the S-confining
dualities in the list, when the matter fields transform in rank-$1$ and/or
rank-$2$ representations. Our only assumptions are the S-confining dualities
for $SU(N)$ with $N+1$ flavors and for $Usp(2N)$ with $2N+4$ fundamentals. The
strategy consists in a sequence of deconfinements and re-confinements. We pay
special attention to the explicit superpotential at each step.
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Twisted holography without conformal symmetry: We discuss the notion of translation-invariant vacua for 2d chiral algebras
and relate it to the notion of the associated variety. The two-dimensional
chiral algebra associated to four-dimensional ${\cal N}=4$ $U(N)$ SYM has a
conjectural holographic dual involving the B-model topological string theory.
We study the effect of non-zero vacuum expectation values on the chiral algebra
correlation functions and derive a holographic dual Calabi-Yau geometry. We
test our proposal by a large $N$ analysis of correlation functions of
determinant operators, whose saddles can be matched with semi-classical
configurations of "Giant Graviton" D-branes in the bulk
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Killing-Yano equations with torsion, worldline actions and G-structures: We determine the geometry of the target spaces of supersymmetric
non-relativistic particles with torsion and magnetic couplings, and with
symmetries generated by the fundamental forms of G-structures for $G= U(n),
SU(n), Sp(n), Sp(n)\cdot Sp(1), G_2$ and $Spin(7)$. We find that the
Killing-Yano equation, which arises as a condition for the invariance of the
worldline action, does not always determine the torsion coupling uniquely in
terms of the metric and fundamental forms. We show that there are several
connections with skew-symmetric torsion for $G=U(n), SU(n)$ and $G_2$ that
solve the invariance conditions. We describe all these compatible connections
for each of the $G$-structures and explain the geometric nature of the
couplings.
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Quantum Corrections in Collective Field Theory: We review and extend the computation of scattering amplitudes of tachyons in
the $c=1$ matrix model using a manifestly finite prescription for the
collective field hamiltonian. We give further arguments for the exactness of
the cubic hamiltonian by demonstrating the equality of the loop corrections in
the collective field theory with those calculated in the fermionic picture.
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Instanton Effects in Matrix Models and String Effective Lagrangians: We perform an explicit calculation of the lowest order effects of single
eigenvalue instantons on the continuous sector of the collective field theory
derived from a $d=1$ bosonic matrix model. These effects consist of certain
induced operators whose exact form we exhibit.
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About Symmetries in Physics: The goal of this introduction to symmetries is to present some general ideas,
to outline the fundamental concepts and results of the subject and to situate a
bit the following lectures of this school. [These notes represent the write-up
of a lecture presented at the fifth ``Seminaire Rhodanien de Physique: Sur les
Symetries en Physique" held at Dolomieu (France), 17-21 March 1997. Up to the
appendix and the graphics, it is to be published in "Symmetries in Physics",
F.Gieres, M.Kibler,C.Lucchesi and O.Piguet, eds. (Editions Frontieres, 1998).]
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BPS Quantization of the Five-Brane: We give a unified description of all BPS states of M-theory compactified on
$T^5$ in terms of the five-brane. We compute the mass spectrum and degeneracies
and find that the $SO(5,5,Z)$ U-duality symmetry naturally arises as a
T-duality by assuming that the world-volume theory of the five-brane itself is
described by a string theory. We also consider the compactification on $S^1/Z_2
\times T^4$, and give a new explanation for its correspondence with heterotic
string theory by exhibiting its dual equivalence to M-theory on $K3\times S^1$.
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Tunnelling Effects in a Brane System and Quantum Hall Physics: We argue that a system of interacting D-branes, generalizing a recent
proposal, can be modelled as a Quantum Hall fluid. We show that tachyon
condensation in such a system is equivalent to one particle tunnelling. In a
conformal field theory effective description, that induces a transition from a
theory with central charge c=2 to a theory with c=3/2, with a corresponding
symmetry enhancement.
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Tensor and Vector Multiplets in Six-Dimensional Supergravity: We construct the complete coupling of $(1,0)$ supergravity in six dimensions
to $n$ tensor multiplets, extending previous results to all orders in the fermi
fields. We then add couplings to vector multiplets, as dictated by the
generalized Green-Schwarz mechanism. The resulting theory embodies factorized
gauge and supersymmetry anomalies, to be disposed of by fermion loops, and is
determined by corresponding Wess-Zumino consistency conditions, aside from a
quartic coupling for the gaugini. The supersymmetry algebra contains a
corresponding extension that plays a crucial role for the consistency of the
construction. We leave aside gravitational and mixed anomalies, that would only
contribute to higher-derivative couplings.
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Integrable Models and Confinement in (2+1)-Dimensional Weakly-Coupled
Yang-Mills Theory: We generalize the (2+1)-dimensional Yang-Mills theory to an anisotropic form
with two gauge coupling constants $e$ and $e^{\prime}$. In an axial gauge, a
regularized version of the Hamiltonian of this gauge theory is
$H_{0}+{e^{\prime}}^{2}H_{1}$, where $H_{0}$ is the Hamiltonian of a set of
(1+1)-dimensional principal chiral nonlinear sigma models. We treat $H_{1}$ as
the interaction Hamiltonian. For gauge group SU(2), we use form factors of the
currents of the principal chiral sigma models to compute the string tension for
small $e^{\prime}$, after reviewing exact S-matrix and form-factor methods. In
the anisotropic regime, the dependence of the string tension on the coupling
constant is not in accord with generally-accepted dimensional arguments.
|
Matrix Gravity and Massive Colored Gravitons: We formulate a theory of gravity with a matrix-valued complex vierbein based
on the SL(2N,C)xSL(2N,C) gauge symmetry. The theory is metric independent, and
before symmetry breaking all fields are massless. The symmetry is broken
spontaneously and all gravitons corresponding to the broken generators acquire
masses. If the symmetry is broken to SL(2,C) then the spectrum would correspond
to one massless graviton coupled to $2N^2 -1$ massive gravitons. A novel
feature is the way the fields corresponding to non-compact generators acquire
kinetic energies with correct signs. Equally surprising is the way Yang-Mills
gauge fields acquire their correct kinetic energies through the coupling to the
non-dynamical antisymmetric components of the vierbeins.
|
Algebro-geometric approach to a fermion self-consistent field theory on
coset space SU(m+n)/S(U(m) x U(n)): The integrability-condition method is regarded as a mathematical tool to
describe the symmetry of collective sub-manifold. We here adopt the
particle-hole representation. In the conventional time-dependent (TD)
self-consistent field (SCF) theory, we take the one-form linearly composed of
the TD SCF Hamiltonian and the infinitesimal generator induced by the
collective-variable differential of canonical transformation on a group.
Standing on the differential geometrical viewpoint, we introduce a
Lagrange-like manner familiar to fluid dynamics to describe collective
coordinate systems. We construct a geometric equation, noticing the structure
of coset space SU(m+n)/S(U(m) x U(n)). To develop a perturbative method with
the use of the collective variables, we aim at constructing a new fermion SCF
theory, i.e., renewal of TD Hartree-Fock (TDHF) theory by using the canonicity
condition under the existence of invariant subspace in the whole HF space. This
is due to a natural consequence of the maximally decoupled theory because there
exists an invariant subspace, if the invariance principle of Schredinger
equation is realized. The integrability condition of the TDHF equation
determining a collective sub-manifold is studied, standing again on the
differential geometric viewpoint. A geometric equation works well over a wide
range of physics beyond the random phase approximation.
|
Gauge invariance induced relations and the equivalence between distinct
approaches to NLSM amplitudes: In this paper, we derive generalized Bern-Carrasco-Johansson relations for
color-ordered Yang-Mills amplitudes by imposing gauge invariance conditions and
dimensional reduction appropriately on the new discovered graphic expansion of
Einstein-Yang-Mills amplitudes. These relations are also satisfied by
color-ordered amplitudes in other theories such as color-scalar theory,
bi-scalar theory and nonlinear sigma model (NLSM). As an application of the
gauge invariance induced relations, we further prove that the three types of
BCJ numerators in NLSM , which are derived from Feynman rules, Abelian Z-theory
and Cachazo-He- Yuan formula respectively, produce the same total amplitudes.
In other words, the three distinct approaches to NLSM amplitudes are equivalent
to each other.
|
On the Unlikeliness of Multi-Field Inflation: Bounded Random Potentials
and our Vacuum: Based on random matrix theory, we compute the likelihood of saddles and
minima in a class of random potentials that are softly bounded from above and
below, as required for the validity of low energy effective theories. Imposing
this bound leads to a random mass matrix with non-zero mean of its entries. If
the dimensionality of field-space is large, inflation is rare, taking place
near a saddle point (if at all), since saddles are more likely than minima or
maxima for common values of the potential. Due to the boundedness of the
potential, the latter become more ubiquitous for rare low/large values
respectively. Based on the observation of a positive cosmological constant, we
conclude that the dimensionality of field-space after (and most likely during)
inflation has to be low if no anthropic arguments are invoked, since the
alternative, encountering a metastable deSitter vacuum by chance, is extremely
unlikely.
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Is There Scale Invariance in N=1 Supersymmetric Field Theories ?: In two dimensions, it is well known that the scale invariance can be
considered as conformal invariance. However, there is no solid proof of this
equivalence in four or higher dimensions. We address this issue in the context
of 4d $\mathcal{N}=1$ SUSY theories. The SUSY version of dilatation current for
theories without conserved $R$ symmetry is constructed through the
FZ-multiplet. We discover that the scale-invariant SUSY theory is also
conformal when the real superfield in the dilatation current multiplet is
conserved. Otherwise, it is only scale-invariant, despite of the transformation
of improvement.
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Proving the Absence of the Perturbative Corrections to the N=2 U(1)
Kähler Potential Using the N=1 Supergraph Techniques: Perturbative N=2 non-renormalization theorem states that there is no
perturbative correction to the Kahler potential \int d^4\theta
K(\Phi,\bar{\Phi}). We prove this statement by using the N=1 supergraph
techniques. We consider the N=2 supersymmetric U(1) gauge theory which
possesses general prepotential F(\Psi).
|
Noncommutative Quantum Hall Effect and Aharonov-Bohm Effect: We study a system of electrons moving on a noncommutative plane in the
presence of an external magnetic field which is perpendicular to this plane.
For generality we assume that the coordinates and the momenta are both
noncommutative. We make a transformation from the noncommutative coordinates to
a set of commuting coordinates and then we write the Hamiltonian for this
system. The energy spectrum and the expectation value of the current can then
be calculated and the Hall conductivity can be extracted. We use the same
method to calculate the phase shift for the Aharonov-Bohm effect. Precession
measurements could allow strong upper limits to be imposed on the
noncommutativity coordinate and momentum parameters $\Theta$ and $\Xi$.
|
Magnetic Mass in 4D AdS Gravity: We provide a fully-covariant expression for the diffeomorphic charge in 4D
anti-de Sitter gravity, when the Gauss-Bonnet and Pontryagin terms are added to
the action. The couplings of these topological invariants are such that the
Weyl tensor and its dual appear in the on-shell variation of the action, and
such that the action is stationary for asymptotic (anti) self-dual solutions in
the Weyl tensor. In analogy with Euclidean electromagnetism, whenever the
self-duality condition is global, both the action and the total charge are
identically vanishing. Therefore, for such configurations the magnetic mass
equals the Ashtekhar-Magnon-Das definition.
|
Graph duality as an instrument of Gauge-String correspondence: We explore an identity between two branching graphs and propose a physical
meaning in the context of the gauge-gravity correspondence. From the
mathematical point of view, the identity equates probabilities associated with
$\mathbb{GT}$, the branching graph of the unitary groups, with probabilities
associated with $\mathbb{Y}$, the branching graph of the symmetric groups. In
order to furnish the identity with physical meaning, we exactly reproduce these
probabilities as the square of three point functions involving certain
hook-shaped backgrounds. We study these backgrounds in the context of LLM
geometries and discover that they are domain walls interpolating two AdS spaces
with different radii. We also find that, in certain cases, the probabilities
match the eigenvalues of some observables, the embedding chain charges. We
finally discuss a holographic interpretation of the mathematical identity
through our results.
|
Shifting Spin on the Celestial Sphere: We explore conformal primary wavefunctions for all half integer spins up to
the graviton. Half steps are related by supersymmetry, integer steps by the
classical double copy. The main results are as follows: we 1) introduce a
convenient spin frame and null tetrad to organize all radiative modes of
varying spin; 2) identify the massless spin-3/2 conformal primary wavefunction
as well as the conformally soft Goldstone mode corresponding to large
supersymmetry transformations; 3) indicate how to express a conformal primary
of arbitrary spin in terms of differential operators acting on a scalar
primary; 4) demonstrate that conformal primary metrics satisfy the double copy
in a variety of forms -- operator, Weyl, and Kerr-Schild -- and are exact,
albeit complex, solutions to the fully non-linear Einstein equations of Petrov
type N; 5) propose a novel generalization of conformal primary wavefunctions;
and 6) show that this generalization includes a large class of physically
interesting metrics corresponding to ultra-boosted black holes, shockwaves and
more.
|
Casimir force between Chern-Simons surfaces: We calculate the Casimir force between two parallel plates if the boundary
conditions for the photons are modified due to presence of the Chern-Simons
term. We show that this effect should be measurable within the present
experimental technique.
|
Compact T-branes: We analyse global aspects of 7-brane backgrounds with a non-commuting profile
for their worldvolume scalars, also known as T-branes. In particular, we
consider configurations with no poles and globally well-defined over a compact
K\"ahler surface. We find that such T-branes cannot be constructed on surfaces
of positive or vanishing Ricci curvature. For the existing T-branes, we discuss
their stability as we move in K\"ahler moduli space at large volume and provide
examples of T-branes splitting into non-mutually-supersymmetric constituents as
they cross a stability wall.
|
Polarized Dirac fermions in de Sitter spacetime: The tetrad gauge invariant theory of the free Dirac field in two special
moving charts of the de Sitter spacetime is investigated pointing out the
operators that commute with the Dirac one. These are the generators of the
symmetry transformations corresponding to isometries that give rise to
conserved quantities according to the Noether theorem. With their help the
plane wave spinor solutions of the Dirac equation with given momentum and
helicity are derived and the final form of the quantum Dirac field is
established. It is shown that the canonical quantization leads to a correct
physical interpretation of the massive or massless fermion quantum fields.
|
The 1/2 BPS 't Hooft loops in N=4 SYM as instantons in 2d Yang-Mills: We extend the recent conjecture on the relation between a certain 1/8 BPS
subsector of 4d N=4 SYM on S^2 and 2d Yang-Mills theory by turning on circular
1/2 BPS 't Hooft operators linked with S^2. We show that localization predicts
that these 't Hooft operators and their correlation functions with Wilson
operators on S^2 are captured by instanton contributions to the partition
function of the 2d Yang-Mills theory. Based on this prediction, we compute
explicitly correlation functions involving the 't Hooft operator, and observe
precise agreement with S-duality predictions.
|
Holographic entanglement entropy and thermodynamic instability of planar
R-charged black holes: The holographic entanglement entropy of an infinite strip subsystem on the
asymptotic AdS boundary is used as a probe to study the thermodynamic
instabilities of planar R-charged black holes (or their dual field theories).
We focus on the single-charge AdS black holes in $D=5$, which correspond to
spinning D3-branes with one non-vanishing angular momentum. Our results show
that the holographic entanglement entropy indeed exhibits the thermodynamic
instability associated with the divergence of the specific heat. When the width
of the strip is large enough, the finite part of the holographic entanglement
entropy as a function of the temperature resembles the thermal entropy, as is
expected. As the width becomes smaller, however, the two entropies behave
differently. In particular, there exists a critical value for the width of the
strip, below which the finite part of the holographic entanglement entropy as a
function of the temperature develops a self-intersection. We also find similar
behavior in the single-charge black holes in $D=4$ and $7$.
|
Gauge-Invariant Operators for Singular Knots in Chern-Simons Gauge
Theory: We construct gauge invariant operators for singular knots in the context of
Chern-Simons gauge theory. These new operators provide polynomial invariants
and Vassiliev invariants for singular knots. As an application we present the
form of the Kontsevich integral for the case of singular knots.
|
Spinning strings and correlation functions in the AdS/CFT correspondence: In this thesis we present some computations made in both sides of the AdS/CFT
holographic correspondence using the integrability of both theories.
Regarding the string theory side, this thesis is focused in the computation
of the dispersion relation of closed spinning strings in some deformed $AdS_3
\times S^3$ backgrounds. In particular we are going to focus in the deformation
provided by the mixing of R-R and NS-NS fluxes and the so-called
$\eta$-deformation. These computations are made using the classical
integrability of these two deformed string theories, which is provided by the
presence of a set of conserved quantities called "Uhlenbeck constants". The
existence of the Uhlenbeck constants is central for the method used to derive
the dispersion relations.
Regarding the gauge theory side, we are interested in the computation of two
and three-point correlation functions. Concerning the two-point function a
computation of correlation functions involving different operators and
different number of excitations is performed using the Algebraic Bethe Ansatz
and the Quantum Inverse Scattering Method. These results are compared with
computations done with the Coordinate Bethe Ansatz and with
Zamolodchikov-Faddeev operators. Concerning the three-point functions, we will
explore the novel construction given by the hexagon framework. In particular we
are going to start from the already proposed hexagon form factor and rewrite it
in a language more resembling of the Algebraic Bethe Ansatz. For this intent we
construct an invariant vertex using Zamolodchikov-Faddeev operators, which is
checked for some simple cases.
|
Rigid open membrane and non-abelian non-commutative Chern-Simons theory: In the Berkooz-Douglas matrix model of M theory in the presence of
longitudinal $M5$-brane, we investigate the effective dynamics of the system by
considering the longitudinal $M5$-brane as the background and the spherical
$M5$-brane related with the other space dimensions as the probe brane. Due to
there exists the background field strength provided by the source of the
longitudinal $M5$-brane, an open membrane should be ended on the spherical
$M5$-brane based on the topological reason. The formation of the bound brane
configuration for the open membrane ending on the 5-branes in the background of
longitudinal 5-brane can be used to model the 4-dimensional quantum Hall system
proposed recently by Zhang and Hu. The description of the excitations of the
quantum Hall soliton brane configuration is established by investigating the
fluctuations of $D0$-branes living on the bound brane around their classical
solution derived by the transformations of area preserving diffeomorphisms of
the open membrane. We find that this effective field theory for the
fluctuations is an SO(4) non-commutative Chern-Simons field theory. The matrix
regularized version of this effective field theory is given in order to allow
the finite $D0$-branes to live on the bound brane. We also discuss some
possible applications of our results to the related topics in M-theory and to
the 4-dimensional quantum Hall system.
|
A note on C-Parity Conservation and the Validity of Orientifold Planar
Equivalence: We analyze the possibility of a spontaneous breaking of C-invariance in gauge
theories with fermions in vector-like - but otherwise generic - representations
of the gauge group. QCD, supersymmetric Yang-Mills theory, and orientifold
field theories, all belong to this class. We argue that charge conjugation is
not spontaneously broken as long as Lorentz invariance is maintained.
Uniqueness of the vacuum state in pure Yang-Mills theory (without fermions) and
convergence of the expansion in fermion loops are key ingredients. The fact
that C-invariance is conserved has an interesting application to our proof of
planar equivalence between supersymmetric Yang-Mills theory and orientifold
field theory on R4, since it allows the use of charge conjugation to connect
the large-N limit of Wilson loops in different representations.
|
Operator Mixing and the AdS/CFT correspondence: We provide a direct prescription for computing the mixing among gauge
invariant operators in N=4 SYM. Our approach is based on the action of the
superalgebra on the states of the theory and thus it can be also applied to
resolve the mixing in the dual string description. As an example, we focus on
the supermultiplet containing the BMN operators with two impurities. On the
field theory side, we derive the leading planar quantum corrections to the
naive expression of the highest weight state. Then we use the same prescription
in the BMN limit of the AdS5xS5 string theory and derive the form of the
2-impurity highest weight state. The string expression matches nicely the SYM
result and provides a prediction for the mixing due to higher order quantum
corrections in field theory.
|
Classification and a toolbox for orientifold models: We provide the general tadpole conditions for a class of supersymmetric
orientifold models by studing the general properties of the elements included
in the orientifold group. In this talk, we concentrate on orientifold models of
the type $T^6/Z_M\times Z_N$.
|
Higher-order field theories: $φ^6$, $φ^8$ and beyond: The $\phi^4$ model has been the "workhorse" of the classical Ginzburg--Landau
phenomenological theory of phase transitions and, furthermore, the foundation
for a large amount of the now-classical developments in nonlinear science.
However, the $\phi^4$ model, in its usual variant (symmetric double-well
potential), can only possess two equilibria. Many complex physical systems
possess more than two equilibria and, furthermore, the number of equilibria can
change as a system parameter (e.g., the temperature in condensed matter
physics) is varied. Thus, "higher-order field theories" come into play. This
chapter discusses recent developments of higher-order field theories,
specifically the $\phi^6$, $\phi^8$ models and beyond. We first establish their
context in the Ginzburg--Landau theory of successive phase transitions,
including a detailed discussion of the symmetric triple well $\phi^6$ potential
and its properties. We also note connections between field theories in
high-energy physics (e.g., "bag models" of quarks within hadrons) and
parametric (deformed) $\phi^6$ models. We briefly mention a few salient points
about even-higher-order field theories of the $\phi^8$, $\phi^{10}$, etc.\
varieties, including the existence of kinks with power-law tail asymptotics
that give rise to long-range interactions. Finally, we conclude with a set of
open problems in the context of higher-order scalar fields theories.
|
Hidden symmetries and Large N factorisation for permutation invariant
matrix observables: Permutation invariant polynomial functions of matrices have previously been
studied as the observables in matrix models invariant under $S_N$, the
symmetric group of all permutations of $N$ objects. In this paper, the
permutation invariant matrix observables (PIMOs) of degree $k$ are shown to be
in one-to-one correspondence with equivalence classes of elements in the
diagrammatic partition algebra $P_k(N)$. On a 4-dimensional subspace of the
13-parameter space of $S_N$ invariant Gaussian models, there is an enhanced
$O(N)$ symmetry. At a special point in this subspace, is the simplest $O(N)$
invariant action. This is used to define an inner product on the PIMOs which is
expressible as a trace of a product of elements in the partition algebra. The
diagram algebra $P_k(N)$ is used to prove the large $N$ factorisation property
of this inner product, which generalizes a familiar large $N$ factorisation for
inner products of matrix traces invariant under continuous symmetries.
|
A Solution of the Randall-Sundrum Model and the Mass Hierarchy Problem: A solution of the Randall-Sundrum model for a simplified case (one wall) is
obtained. It is given by the $1/k^2$-expansion (thin wall expansion) where
$1/k$ is the {\it thickness} of the domain wall. The vacuum setting is done by
the 5D Higgs potential and the solution is for a {\it family} of the Higgs
parameters. The mass hierarchy problem is examined. Some physical quantities in
4D world such as the Planck mass, the cosmological constant, and fermion masses
are focussed. Similarity to the domain wall regularization used in the chiral
fermion problem is explained. We examine the possibility that the 4D massless
chiral fermion bound to the domain wall in the 5D world can be regarded as the
real 4D fermions such as neutrinos, quarks and other leptons.
|
Quantum causal histories: Quantum causal histories are defined to be causal sets with Hilbert spaces
attached to each event and local unitary evolution operators. The reflexivity,
antisymmetry, and transitivity properties of a causal set are preserved in the
quantum history as conditions on the evolution operators. A quantum causal
history in which transitivity holds can be treated as ``directed'' topological
quantum field theory. Two examples of such histories are described.
|
Finite temperature Casimir pistons for electromagnetic field with mixed
boundary conditions and its classical limit: In this paper, the finite temperature Casimir force acting on a
two-dimensional Casimir piston due to electromagnetic field is computed. It was
found that if mixed boundary conditions are assumed on the piston and its
opposite wall, then the Casimir force always tends to restore the piston
towards the equilibrium position, regardless of the boundary conditions assumed
on the walls transverse to the piston. In contrary, if pure boundary conditions
are assumed on the piston and the opposite wall, then the Casimir force always
tend to pull the piston towards the closer wall and away from the equilibrium
position. The nature of the force is not affected by temperature. However, in
the high temperature regime, the magnitude of the Casimir force grows linearly
with respect to temperature. This shows that the Casimir effect has a classical
limit as has been observed in other literatures.
|
Deconstructing Scalar QED at Zero and Finite Temperature: We calculate the effective potential for the WLPNGB in a world with a
circular latticized extra dimension. The mass of the WLPNGB is calculated from
the one-loop quantum effect of scalar fields at zero and finite temperature. We
show that a series expansion by the modified Bessel functions is useful to
calculate the one-loop effective potentials.
|
Gauge/Gravity Duals with Holomorphic Dilaton: We consider configurations of D7-branes and whole and fractional D3-branes
with N=2 supersymmetry. On the supergravity side these have a warp factor,
three-form flux and a nonconstant dilaton. We discuss general IIB solutions of
this type and then obtain the specific solutions for the D7/D3 system. On the
gauge side the D7-branes add matter in the fundamental representation of the
D3-brane gauge theory. We find that the gauge and supergravity metrics on
moduli space agree. However, in many cases the supergravity curvature is large
even when the gauge theory is strongly coupled. In these cases we argue that
the useful supergravity dual must be a IIA configuration.
|
Duality, Monodromy and Integrability of Two Dimensional String Effective
Action: The monodromy matrix, ${\hat{\cal M}}$, is constructed for two dimensional
tree level string effective action. The pole structure of ${\hat{\cal M}}$ is
derived using its factorizability property. It is found that the monodromy
matrix transforms non-trivially under the non-compact T-duality group, which
leaves the effective action invariant and this can be used to construct the
monodromy matrix for more complicated backgrounds starting from simpler ones.
We construct, explicitly, ${\hat{\cal M}}$ for the exactly solvable
Nappi-Witten model, both when B=0 and $B\neq 0$, where these ideas can be
directly checked. We consider well known charged black hole solutions in the
heterotic string theory which can be generated by T-duality transformations
from a spherically symmetric `seed' Schwarzschild solution. We construct the
monodromy matrix for the Schwarzschild black hole background of the heterotic
string theory.
|
Isoperimetric Inequalities and Magnetic Fields at CERN: We discuss the generalization of the classical isoperimetric inequality to
asymptotically hyperbolic Riemannian manifolds. It has been discovered that the
AdS/CFT correspondence in string theory requires that such an inequality hold
in order to be internally consistent. In a particular application, to the
systems formed in collisions of heavy ions in particle colliders, we show how
to formulate this inequality in terms of measurable physical quantities, the
magnetic field and the temperature. Experiments under way at CERN in Geneva can
thus be said to be testing an isoperimetric inequality.
|
On the Scattering Phase for AdS_5 x S^5 Strings: We propose a phase factor of the worldsheet S-matrix for strings on AdS_5 x
S^5 apparently solving Janik's crossing relation.
|
All 4-dimensional static, spherically symmetric, 2-charge abelian
Kaluza-Klein black holes and their CFT duals: We derive the dual CFT Virasoro algebras from the algebra of conserved
diffeomorphism charges, for a large class of abelian Kaluza-Klein black holes.
Under certain conditions, such as non-vanishing electric and magnetic monopole
charges, the Kaluza-Klein black holes have a Reissner-Nordstrom space-time
structure. For the non-extremal charged Kaluza-Klein black holes, we use the
uplifted 6d pure gravity solutions to construct a set of Killing horizon
preserving diffeomorphisms. For the (non-supersymmetric) extremal black holes,
we take the NENH limit, and construct a one-parameter family of diffeomorphisms
which preserve the Hamiltonian constraints at spatial infinity. In each case we
evaluate the algebra of conserved diffeomorphism charges following Barnich,
Brandt and Compere, who used a cohomological approach, and Silva, who employed
a covariant-Lagrangian formalism.
At the Killing horizon, it is only Silva's algebra which acquires a central
charge extension, and which enables us to recover the Bekenstein-Hawking black
hole entropy from the Cardy formula. For the NENH geometry, the extremal black
hole entropy is obtained only when the free parameter of the diffeomorphism
generating vector fields is chosen such that the central terms of the two
algebras are in agreement.
|
Quantum Groups on Fibre Bundles: It is shown that the principle of locality and noncommutative geometry can be
connnected by a sheaf theoretical method. In this framework quantum spaces are
introduced and examples in mathematical physics are given. With the language of
quantum spaces noncommutative principal and vector bundles are defined and
their properties are studied. Important constructions in the classical theory
of principal fibre bundles like associated bundles and differential calculi are
carried over to the quantum case. At the end $q$-deformed instanton models are
introduced for every integral index.
|
Revisiting Schwarzschild black hole singularity through string theory: The resolution of black hole singularities represents an essential problem in
the realm of quantum gravity. Due to the Belinskii, Khalatnikov and Lifshitz
(BKL) proposal, the structure of the black hole interior in vacuum Einstein's
equations can be described by the Kasner universe, which possesses the
$O\left(d,d\right)$ symmetry. It motivates us to use the anisotropic
Hohm-Zwiebach action, known as the string effective action with all orders
$\alpha^{\prime}$ corrections for the $O\left(d,d\right)$ symmetric background,
to study the singularity problem of black hole. In this letter, we obtain the
singular condition for black holes and demonstrate that it is possible to
resolve the Schwarzschild black hole singularity through the non-perturbative
$\alpha^{\prime}$ corrections of string theory.
|
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