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Dynamics of a planar domain wall with oscillating thickness in λ
Φ^{4} model: Domain wall - type solution with oscillating thickness in a real, scalar
field model is investigated with the help of a polynomial approximation. We
propose a simple extension of the polynomial approximation method. In this
approach we calculate higher order corrections to the planar domain wall
solution, find that the domain wall with oscillating thickness radiates, and
compute dumping of oscillations of the domain wall. | Massive spin-2 particle from a rank-2 tensor: Here we obtain all possible second-order theories for a rank-2 tensor which
describe a massive spin-2 particle. We start with a general second-order
Lagrangian with ten real parameters. The absence of lower spin modes and the
existence of two local field redefinitions leads us to only one free parameter.
The solutions split into three one-parameter classes according to the local
symmetries of the massless limit. In the class which contains the usual massive
Fierz-Pauli theory, the subset of spin-1 massless symmetries is maximal. In
another class where the subset of spin-0 symmetries is maximal, the massless
theory is invariant under Weyl transformations and the mass term does not need
to fit in the form of the Fierz-Pauli mass term. In the remaining third class
neither the spin-1 nor the spin-0 symmetry is maximal and we have a new family
of spin-2 massive theories. |
Gauge Symmetry of the Chiral Schwinger model from an improved Gauge
Unfixing formalism: In this paper, the Hamiltonian structure of the bosonized chiral Schwinger
model (BCSM) is analyzed. From the consistency condition of the constraints
obtained from the Dirac method, we can observe that this model presents, for
certain values of the $\alpha$ parameter, two second-class constraints, which
means that this system does not possess gauge invariance. However, we know that
it is possible to disclose gauge symmetries in such a system by converting the
original second-class system into a first-class one. This procedure can be done
through the gauge unfixing (GU) formalism by acting with a projection operator
directly on the original second-class Hamiltonian, without adding any extra
degrees of freedom in the phase space. One of the constraints becomes the gauge
symmetry generator of the theory and the other one is disregarded. At the end,
we have a first-class Hamiltonian satisfying a first-class algebra. Here, our
goal is to apply a new scheme of embedding second-class constrained systems
based on the GU formalism, named improved GU formalism, in the BCSM. The
original second-class variables are directly converted into gauge invariant
variables, called GU variables. We have verified that the Poisson brackets
involving the GU variables are equal to the Dirac brackets between the original
second-class variables. Finally, we have found that our improved GU variables
coincide with those obtained from an improved BFT method after a particular
choice for the Wess-Zumino terms. | Fermion zero modes in a chromomagnetic vortex lattice: We prove the existence of zero modes of massless quarks in a background of
spaghetti vacuum of chromomagnetic vortices in QCD. We find a general solution
for the zero modes and show that the modes can be localized at pairs of
vortices. |
Superconductivity at Any Temperature: We construct a 2+1 dimensional model that sustains superconductivity at all
temperatures. This is achieved by introducing a Chern Simons mixing term
between two Abelian gauge fields A and Z. The superfluid is described by a
complex scalar charged under Z, whereas a sufficiently strong magnetic field of
A forces the superconducting condensate to form at all temperatures. In fact,
at finite temperature, the theory exhibits Berezinsky-Kosterlitz-Thouless phase
transition due to proliferation of topological vortices admitted by our
construction. However, the critical temperature is proportional to the magnetic
field of A, and thus, the phase transition can be postponed to high
temperatures by increasing the strength of the magnetic field. This model can
be a step towards realizing the long sought room temperature superconductivity. | Notes on S-Matrix of Non-critical N=2 String: In this paper we discuss the scattering S-matrix of non-critical N=2 string
at tree level. First we consider the \hat{c}<1 string defined by combining the
N=2 time-like linear dilaton SCFT with the N=2 Liouville theory. We compute
three particle scattering amplitudes explicitly and find that they are actually
vanishing. We also find an evidence that this is true for higher amplitudes.
Next we analyze another \hat{c}<1 string obtained from the N=2 time-like
Liouville theory, which is closely related to the N=2 minimal string. In this
case, we find a non-trivial expression for the three point functions. When we
consider only chiral primaries, the amplitudes are very similar to those in the
(1,n) non-critical bosonic string. |
One Ring to Rule Them All ... and in the Darkness Bind Them?: We construct all eleven-dimensional, three-charge BPS solutions that preserve
a fixed, standard set of supersymmetries. Our solutions include all BPS
three-charge rotating black holes, black rings, supertubes, as well as
arbitrary superpositions of these objects. We find very large families of black
rings and supertubes with profiles that follow arbitrary closed curves in the
spatial R^4 transverse to the branes. The black rings copiously violate black
hole uniqueness. The supertube solutions are completely regular, and
generically have small curvature. They also have the same asymptotics as the
three-charge black hole; and so they might be mapped to microstates of the
D1-D5-p system and used to explain the entropy of this black hole. | Exact calculation of the radiatively-induced Lorentz and CPT violation
in QED: Radiative corrections arising from the axial coupling of charged fermions to
a constant vector b_\mu can induce a Lorentz- and CPT-violating Chern-Simons
term in the QED action. We calculate the exact one-loop correction to this term
keeping the full b_\mu dependence, and show that in the physically interesting
cases it coincides with the lowest-order result. The effect of regularization
and renormalization and the implications of the result are briefly discussed. |
Moduli Stabilisation and the Statistics of Axion Physics in the
Landscape: String theory realisations of the QCD axion are often said to belong to the
anthropic window where the decay constant is around the GUT scale and the
initial misalignment angle has to be tuned close to zero. In this paper we
revisit this statement by studying the statistics of axion physics in the
string landscape. We take moduli stabilisation properly into account since the
stabilisation of the saxions is crucial to determine the physical properties of
the corresponding axionic partners. We focus on the model-independent case of
closed string axions in type IIB flux compactifications and find that their
decay constants and mass spectrum feature a logarithmic, instead of a
power-law, distribution. In the regime where the effective field theory is
under control, most of these closed string axions are ultra-light axion-like
particles, while axions associated to blow-up modes can naturally play the role
of the QCD axion. Hence, the number of type IIB flux vacua with a closed string
QCD axion with an intermediate scale decay constant and a natural value of the
misalignment angle is only logarithmically suppressed. In a recent paper we
found that this correlates also with a logarithmic distribution of the
supersymmetry breaking scale, providing the intriguing indication that most, if
not all, of the phenomenologically interesting quantities in the string
landscape might feature a logarithmic distribution. | Classical Open String Integrability: We present a simple procedure to construct non-local conserved charges for
classical open strings on coset spaces. This is done by including suitable
reflection matrices on the classical transfer matrix. The reflection matrices
must obey certain conditions for the charges to be conserved and in involution.
We then study bosonic open strings on $AdS_5\times S^5$. We consider boundary
conditions corresponding to Giant Gravitons on $S^5$, $AdS_4\times S^2$
D5-branes and $AdS_5 \times S^3$ D7-branes. We find that we can construct the
conserved charges for the full bosonic string on a Maximal Giant Graviton or a
D7-brane. For the D5-brane, we find that this is possible only in a SU(2)
sub-sector of the open string. Moreover, the charges can not be constructed at
all for non-maximal Giant Gravitons. We discuss the interpretation of these
results in terms of the dual gauge theory spin chains. |
Bosonic near-CFT$_1$ models from Fock-space fluxes: Near-AdS$_2$ dynamics arise ubiquitously near the horizon of near-extremal
black holes. The Sachdev-Ye-Kitaev (SYK) model -- a $p$-local model of fermions
-- is the first microscopic model that realizes the dual near-CFT$_1$ dynamics.
However, a bosonic near-CFT$_1$ model has remained elusive in the $p$-local
approach because such constructions generally suffer from unwanted orderings at
low temperatures. Recently, it was pointed out that such near-CFT$_1$ dynamics
can quite generally arise if we place a large amount of random fluxes in a
many-body Fock space and $p$-locality is not essential. We will use this
insight to construct a collection of bosonic near-CFT$_1$ models with a
conserved charge. One class of models we wish to highlight are based on
canonical bosons with conserved occupation numbers. We further argue that such
bosonic models do not suffer from energetic instablities or unwanted
low-temperature orderings. Furthermore, canonical bosons allow the number
densities to be arbitrarily large, which is impossible in quibt- or
fermion-based constructions. This creates a larger variety of scaling regimes
for the thermodynamics. For comparison we also consider a second class of
charge-conserving models which are based on qubits. The thermodynamic scalings
(with respect to conserved charges) of these models are very similar to those
of the double-scaled complex SYK model but are free of certain singularities
the latter suffers from, even though both are solved by chord diagrams. We also
show the level statistics for both models are described by random matrix theory
universality down to very low energy. | The Sub-Leading Scattering Waveform from Amplitudes: We compute the next-to-leading order term in the scattering waveform of
uncharged black holes in classical general relativity and of half-BPS black
holes in $\mathcal{N}=8$ supergravity. We propose criteria, generalizing
explicit calculations at next-to-leading order, for determining the terms in
amplitudes that contribute to local observables. For general relativity, we
construct the relevant classical integrand through generalized unitarity in two
distinct ways, (1) in a heavy-particle effective theory and (2) in general
relativity minimally-coupled to scalar fields. With a suitable prescription for
the matter propagator in the former, we find agreement between the two methods,
thus demonstrating the absence of interference of quantum and
classically-singular contributions. The classical $\mathcal{N}=8$ integrand for
massive scalar fields is constructed through dimensional reduction of the known
five-point one-loop integrand. Our calculation exhibits novel features compared
to conservative calculations and inclusive observables, such as the appearance
of master integrals with intersecting matter lines and the appearance of a
classical infrared divergence whose absence from classical observables requires
a suitable definition of the retarded time. |
Theta dependence of the vacuum energy in the SU(3) gauge theory from the
lattice: We report on a precise computation of the topological charge distribution in
the SU(3) Yang--Mills theory. It is carried out on the lattice with high
statistics Monte Carlo simulations by employing the definition of the
topological charge suggested by Neuberger's fermions. We observe significant
deviations from a Gaussian distribution. Our results disfavour the theta
behaviour of the vacuum energy predicted by instanton models, while they are
compatible with the expectation from the large Nc expansion. | Universal properties of thermal and electrical conductivity of gauge
theory plasmas from holography: We propose that for conformal field theories admitting gravity duals, the
thermal conductivity is fixed by the central charges in a universal manner.
Though we do not have a proof as yet, we have checked our proposal against
several examples. This proposal, if correct, allows us to express electrical
conductivity in terms of thermodynamical quantities even in the presence of
chemical potential. |
G3-homogeneous gravitational instantons: We provide an exhaustive classification of self-dual four-dimensional
gravitational instantons foliated with three-dimensional homogeneous spaces,
i.e. homogeneous self-dual metrics on four-dimensional Euclidean spaces
admitting a Bianchi simply transitive isometry group. The classification
pattern is based on the algebra homomorphisms relating the Bianchi group and
the duality group SO(3). New and general solutions are found for Bianchi III. | Logarithmic enhancements in conformal perturbation theory and their real
time interpretation: We study various corrections of correlation functions to leading order in
conformal perturbation theory, both on the cylinder and on the plane. Many
problems on the cylinder are mathematically equivalent to those in the plane if
we give the perturbations a position dependent scaling profile. The integrals
to be done are then similar to the study of correlation functions with one
additional insertion at the center of the profile. We will be primarily
interested in the divergence structure of these corrections when computed in
dimensional regularization. In particular, we show that the logarithmic
divergences (enhancements) that show up in the plane under these circumstances
can be understood in terms of resonant behavior in time dependent perturbation
theory, for a transition between states that is induced by an oscillatory
perturbation on the cylinder. |
On supersymmetric E11 exceptional field theory: We construct an infinite system of non-linear duality equations, including
fermions, that are invariant under global E11 and gauge invariant under
generalised diffeomorphisms upon the imposition of a suitable section
constraint. We use finite-dimensional fermionic representations of the
R-symmetry E11 to describe the fermionic contributions to the duality
equations. These duality equations reduce to the known equations of E8
exceptional field theory or eleven-dimensional supergravity for appropriate
(partial) solutions of the section constraint. Of key importance in the
construction is an indecomposable representation of E11 that entails extra
non-dynamical fields beyond those predicted by E11 alone, generalising the
known constrained p-forms of exceptional field theories. The construction
hinges on the tensor hierarchy algebra extension of E11, both for the bosonic
theory and its supersymmetric extension. | Charged black rings in supergravity with a single non-zero gauge field: General charged black ring solution with two angular momenta, a charge and a
dipole charge is found by the inverse scattering method. The solution is
presented in a relatively concise form in which its symmetries are manifest.
The regularity conditions are found and the physical characteristics of the
regular solution are expressed via its parameters. |
Scattering in Mass-Deformed N>=4 Chern-Simons Models: We investigate the scattering matrix in mass-deformed N>=4 Chern-Simons
models including as special cases the BLG and ABJM theories of multiple M2
branes. Curiously the structure of this scattering matrix in three spacetime
dimensions is equivalent to (a) the two-dimensional worldsheet matrix found in
the context of AdS/CFT integrability and (b) the R-matrix of the
one-dimensional Hubbard model. The underlying reason is that all three models
are based on an extension of the psu(2|2) superalgebra which constrains the
matrix completely. We also compute scattering amplitudes in one-loop field
theory and find perfect agreement with scattering unitarity. | The Holographic Ward identity: Examples from 2+1 gravity: In the AdS/CFT correspondence the boundary Ward identities are encoded in the
bulk constraints. We study the three-dimensional version of this result using
the Chern-Simons formulation of gravity. Due the metric boundary conditions the
conformal identities cannot be derived in a straightforward way from the chiral
ones. We pay special attention to this case and find the necessary
modifications to the chiral currents in order to find the two Virasoro
operators. The supersymmetric Ward identities are studied as well. |
Comments on Large N Matrix Model: The large N Matrix model is studied with attention to the quantum
fluctuations around a given diagonal background. Feynman rules are explicitly
derived and their relation to those in usual Yang-Mills theory is discussed.
Background D-instanton configuration is naturally identified as a
discretization of momentum space of a corresponding QFT. The structure of large
N divergence is also studied on the analogy of UV divergences in QFT. | Instantons, Symmetries and Anomalies in Five Dimensions: All five-dimensional non-abelian gauge theories have a $U(1)_I$ global
symmetry associated with instantonic particles. We describe an obstruction to
coupling $U(1)_I$ to a classical background gauge field that occurs whenever
the theory has a one-form center symmetry. This is a finite-order mixed 't
Hooft anomaly between the two symmetries. We also show that a similar
obstruction takes place in gauge theories with fundamental matter by studying
twisted bundles for the ordinary flavor symmetry. We explore some general
dynamical properties of the candidate phases implied by the anomaly. Finally,
we apply our results to supersymmetric gauge theories in five dimensions and
analyze the symmetry enhancement patterns occurring at their conjectured RG
fixed points. |
The Super-Liouville-Equation on the Half-Line: A recursive formula for an infinity of integrals of motion for the
super-Liouville theory is derived. The integrable boundary interactions for
this theory and the super-Toda theory based on the affine superalgebra $B^{(1)}
(0,1)$ are computed. In the first case the boundary interactions are
unambiguously determined by supersymmetry, whilst in the latter case there are
free parameters. | Vacuum Energy as the Origin of the Gravitational Constant: We develop a geometro-dynamical approach to the cosmological constant problem
(CCP) by invoking a geometry induced by the energy-momentum tensor of vacuum,
matter and radiation. The construction, which utilizes the dual role of the
metric tensor that it structures both the spacetime manifold and
energy-momentum tensor of the vacuum, gives rise to a framework in which the
vacuum energy induced by matter and radiation, instead of gravitating,
facilitates the generation of the gravitational constant. The non-vacuum
sources comprising matter and radiation gravitate normally. At the level of
classical gravitation, the mechanism deadens the CCP yet quantum gravitational
effects, if can be strong in de Sitter space, can keep it existent. |
A-D-E Polynomial and Rogers--Ramanujan Identities: We conjecture polynomial identities which imply Rogers--Ramanujan type
identities for branching functions associated with the cosets $({\cal
G}^{(1)})_{\ell-1}\otimes ({\cal G}^{(1)})_{1} / ({\cal G}^{(1)})_{\ell}$, with
${\cal G}$=A$_{n-1}$ \mbox{$(\ell\geq 2)$}, D$_{n-1}$ $(\ell\geq 2)$,
E$_{6,7,8}$ $(\ell=2)$. In support of our conjectures we establish the correct
behaviour under level-rank duality for $\cal G$=A$_{n-1}$ and show that the
A-D-E Rogers--Ramanujan identities have the expected $q\to 1^{-}$ asymptotics
in terms of dilogarithm identities. Possible generalizations to arbitrary
cosets are also discussed briefly. | Analytic Scattering Amplitudes for QCD: By analytically continuing QCD scattering amplitudes through specific
complexified momenta, one can study and learn about the nature and the
consequences of factorization and unitarity. In some cases, when coupled with
the largest time equation and gauge invariance requirement, this approach leads
to recursion relations, which greatly simplify the construction of multi-gluon
scattering amplitudes. The setting for this discussion is in the space-cone
gauge. |
Fluid-gravity correspondence in the scalar-tensor theory of gravity:
(in)equivalence of Einstein and Jordan frames: The duality of gravitational dynamics (projected on a null hypersurface) and
of fluid dynamics is investigated for the scalar tensor (ST) theory of gravity.
The description of ST gravity, in both Einstein and Jordan frames, is analyzed
from fluid-gravity viewpoint. In the Einstein frame the dynamical equation for
the metric leads to the Damour-Navier-Stokes (DNS) equation with an external
forcing term, coming from the scalar field in ST gravity. In the Jordan frame
the situation is more subtle. We observe that finding the DNS equation in this
frame can lead to two pictures. In one picture, the usual DNS equation is
modified by a Coriolis-like force term, which originates completely from the
presence of a non-minimally coupled scalar field ($\phi$) on the gravity side.
Moreover, the identified fluid variables are no longer conformally equivalent
with those in the Einstein frame. However, this picture is consistent with the
saturation of Kovtun-Son-Starinets (KSS) bound. In the other picture, we find
the standard DNS equation (i.e. without the Coriolis-like force), with the
fluid variables conformally equivalent with those in Einstein frame. But, the
second picture, may not agree with the KSS bound for some values of $\phi$. We
conclude by rewriting the Raychaudhuri equation and the tidal force equation in
terms of the relevant parameters to demonstrate how the expansion scalar and
the shear-tensor evolve in the spacetime. Although, the area law of entropy is
broken in ST gravity, we show that the rewritten form of Raychaudhuri's
equation correctly results in the generalized second law of black hole
thermodynamics. | Lorentz and CPT Violating Chern-Simons Term in the Formulation of
Functional Integral: We show that in the functional integral formalism the (finite) coefficient of
the induced, Lorentz- and CPT-violating Chern-Simons term, arising from the
Lorentz- and CPT-violating fermion sector, is undetermined. |
Real-Time dynamics and phase separation in a holographic first order
phase transition: We study the fully nonlinear time evolution of a holographic system
possessing a first order phase transition. The initial state is chosen in the
spinodal region of the phase diagram, and includes an inhomogeneous
perturbation in one of the field theory directions. The final state of the time
evolution shows a clear phase separation in the form of domain formation. The
results indicate the existence of a very rich class of inhomogeneous black hole
solutions. | Aspects of warped braneworld models: We review various key issues in connection with the warped braneworld models
which provide us with new insights and explanations of physical phenomena
through interesting geometrical features of such extra dimensional theories.
Starting from the original Randall-Sundrum two brane models, we have discussed
the stability, hierarchy and other important issues in connection with such
braneworld. The role of higher derivative terms in the bulk for modulus
stabilization has been explained. Implications of the existence of various bulk
fields have been discussed and it has been shown how a warped braneworld model
can explain the invisibility of all antisymmetric bulk tensor fields on our
brane. We have also generalised the model for more than one warped dimensions
in the form of a multiply warped spacetime. It is shown that such model can
offer an explanation to the mass hierarchy among the standard model fermions
and the localization of fermions on the standard model brane with a definite
chirality. |
SU(N) transitions in M-theory on Calabi-Yau fourfolds and background
fluxes: We study M-theory on a Calabi-Yau fourfold with a smooth surface $S$ of
$A_{N-1}$ singularities. The resulting three-dimensional theory has a
$\mathcal{N}=2$ $SU(N)$ gauge theory sector, which we obtain from a twisted
dimensional reduction of a seven-dimensional $\mathcal{N}=1$ $SU(N)$ gauge
theory on the surface $S$. A variant of the Vafa-Witten equations governs the
moduli space of the gauge theory, which, for a trivial $SU(N)$ principal bundle
over $S$, admits a Coulomb and a Higgs branch. In M-theory these two gauge
theory branches arise from a resolution and a deformation to smooth Calabi-Yau
fourfolds, respectively. We find that the deformed Calabi-Yau fourfold
associated to the Higgs branch requires for consistency a non-trivial four-form
background flux in M-theory. The flat directions of the flux-induced
superpotential are in agreement with the gauge theory prediction for the moduli
space of the Higgs branch. We illustrate our findings with explicit examples
that realize the Coulomb and Higgs phase transition in Calabi-Yau fourfolds
embedded in weighted projective spaces. We generalize and enlarge this class of
examples to Calabi-Yau fourfolds embedded in toric varieties with an $A_{N-1}$
singularity in codimension two. | On 2D gauge theories in Jackiw-Teitelboim gravity: The low-energy behavior of near-extremal black holes can be understood from
the near-horizon AdS_2 region. In turn, this region is effectively described by
using Jackiw-Teitelboim gravity coupled to Yang-Mills theory through the
two-dimensional metric and the dilaton field. We show that such a
two-dimensional model of gravity coupled to gauge fields is soluble for an
arbitrary choice of gauge group and gauge couplings. Specifically, we determine
the partition function of the theory on two-dimensional surfaces of arbitrary
genus and with an arbitrary number of boundaries. When solely focusing on the
contribution from surfaces with disk topology, we show that the gravitational
gauge theory is described by the Schwarzian theory coupled to a particle moving
on the gauge group manifold. When considering the contribution from all genera,
we show that the theory is described by a particular double-scaled matrix
integral, where the elements of the matrix are functions that map the gauge
group manifold to complex or real numbers. Finally, we compute the expectation
value of various diffeomorphism invariant observables in the gravitational
gauge theory and find their exact boundary description. |
Canonical and symplectic analysis for three dimensional gravity without
dynamics: In this paper a detailed Hamiltonian analysis of three-dimensional gravity
without dynamics proposed by V. Hussain is performed. We report the complete
structure of the constraints and the Dirac brackets are explicitly computed. In
addition, the Faddeev-Jackiw symplectic approach is developed; we report the
complete set of Faddeev-Jackiw constraints and the generalized brackets, then
we show that the Dirac and the generalized Faddeev-Jackiw brackets coincide to
each other. Finally, the similarities and advantages between Faddeev-Jackiw and
Dirac's formalism are briefly discussed. | Persistent Superconductor Currents in Holographic Lattices: We consider a persistent superconductor current along the direction with no
translational symmetry in a holographic gravity model. Incorporating a lattice
structure into the model, we numerically construct novel solutions of hairy
charged stationary black brane with momentum/rotation along the latticed
direction. The lattice structure prevents the horizon from rotating, and the
total momentum is only carried by matter fields outside the black brane
horizon. This is consistent with the black hole rigidity theorem, and suggests
that in dual field theory with lattices, superconductor currents are made up by
"composite" fields, rather than "fractionalized" degrees of freedom. We also
show that our solutions are consistent with the superfluid hydrodynamics. |
The interface of noncommutative geometry and physics: The progress of noncommutative geometry has been crucially influenced, from
the beginning, by quantum physics: we review this development in recent years.
The Standard Model, with its central role for the Dirac operator, led to
several formulations culminating in the concept of a real spectral triple.
String theory then came into contact with NCG, leading to an emphasis on
Moyal-like algebras and formulations of quantum field theory on noncommutative
spaces. Hopf algebras have yielded an unexpected link between the
noncommutative geometry of foliations and perturbative quantum field theory.
The quest for a suitable foundation of quantum gravity continues to promote
fruitful ideas, among them the spectral action principle and the search for a
better understanding of "noncommutative spaces". | A One Loop Problem of the Matrix Big Bang Model: We compute the one-loop effective action of two D0-branes in the matrix model
for a cosmological background, and find vanishing static potential. However,
there is a non-vanishing $v^2$ term not predicted in a supergravity
calculation. This term is complex and signals an instability of the two
D0-brane system, it may also indicate that the matrix model is incorrect. |
Renormalization group improvement of the effective potential in massive
$φ^4$ theory: Using the method of renormalization group, we improve the two-loop effective
potential of the massive $\phi^4$ theory to obtain the next-next-to-leading
logarithm correction in the $\bar{MS}$ scheme. Our result well reproduces the
next-next-to-leading logarithm parts of the ordinary loop expansion result
known up to the four-loop order. | F-theory Family Unification: We propose a new geometric mechanism for naturally realizing unparallel three
families of flavors in string theory, using the framework of F-theory. We
consider a set of coalesced local 7-branes of a particular Kodaira singularity
type and allow some of the branes to bend and separate from the rest, so that
they meet only at an intersection point. Such a local configuration can
preserve supersymmetry. Its matter spectrum is investigated by studying string
junctions near the intersection, and shown to coincide, after an orbifold
projection, with that of a supersymmetric coset sigma model whose target space
is a homogeneous Kahler manifold associated with a corresponding painted Dynkin
diagram. In particular, if one starts from the E7 singularity, one obtains the
E7/(SU(5)xU(1)^3) model yielding precisely three generations with an unparallel
family structure. Possible applications to string phenomenology are also
discussed. |
Cosmological perturbations in $k$-essence model: Subhorizon approximation is often used in cosmological perturbation theory.
In this paper, however, it is shown that the subhorizon approximation is not
always a good approximation at least in case of $k$-essence model. We also show
that the sound speed given by $k$-essence model exerts a huge influence on the
time evolution of the matter density perturbation, and the future observations
could clarify the differences between the $\Lambda$CDM model and $k$-essence
model. | Observable Quantum Loop Effects in the Sky: Expanding on [1], we analyze in detail the single field chaotic inflationary
models plus a cosine modulation term, augmented by a light scalar field with
inflaton dependent oscillatory mass term. We work out in detail the Feynman
diagrams and compute one, two and in general estimate higher loop two and three
point functions in the in-in formulation. We explicitly establish how the
oscillatory mass term can amplify one-loop effects to dominate over the tree as
well as the higher loop contributions. The power spectrum of curvature
perturbations of this model is hence enhanced compared to the simple single
field chaotic model. As a consequence, one can suppress the tensor to scalar
ratio r and have a different expression for scalar spectral tilt and the
running of the tilt, opening the way to reconcile chaotic models with convex
potential and the Planck data. As in monodromy inflation models, we also have a
cosine modulation in the spectral tilt. We also analyze the bispectrum, which
can be dominated by the amplified one-loop effects, yielding a new shape in
non-Gassuianty. We discuss the bounds on parameter space from all available CMB
observables and possible implications for reheating. |
A supersymmetric holographic dual of a fractional topological insulator: We construct a supersymmetric generalization of the holographic dual of a
fractional topological insulator found in \cite{HoyosBadajoz:2010ac}. This is
accomplished by introducing a nontrivial gauge field on the world volume of the
probe D7 brane. The BPS equations are derived from the $\kappa$-symmetry
transformation of the probe brane. The BPS equations are shown to reduce to two
first oder nonlinear partial differential equations. Solutions of the BPS
equations correspond to a probe brane configuration which preserves four of the
thirty-two supersymmetries of the $AdS_5\times S^5$ background. Solutions of
the BPS equations which correspond to a holographic fractional topological
insulator are obtained numerically. | Late-time correlation functions in dS$_3$/CFT$_2$ correspondence: We compute the late-time correlation functions on three-dimensional de Sitter
spacetime for a higher-spin gravity theory. For this, we elaborate on the
formulation to obtain the wave functional of universe from a dual conformal
field theory, which is used to compute the late-time correlation functions. We
argue that the relation to direct bulk Feynman diagram computations in the
in-in formulation. We furthermore provide a precise prescription to construct a
higher-spin dS$_3$ holography as an analytic continuation of
Gaberdiel-Gopakumar duality for AdS$_3$. Part of results here were already
reported in an earlier letter. We explain the details of their derivations and
extend the analysis to more generic cases in this paper. Previously, we have
examined two- and three-point functions and a simple four-point correlator at
the leading order in Newton constant. Here we also evaluate more complicated
four-point correlators. Finally, we study late-time correlators in an
alternative limit of dS$_3$/CFT$_2$ with critical level coset, such as,
two-point correlator on conical defect geometry. We also examine one-loop
corrections to two-point correlator on dS$_3$. |
Superconducting and Spinning Non-Abelian Flux Tubes: We find new non-Abelian flux tube solutions in a model of $N_f$ scalar fields
in the fundamental representation of SU(N)xU(1) with $N \leq N_f$ (the
``extended non-Abelian Higgs model''), and study their main properties. Among
the solutions there are spinning strings as well as superconducting ones. The
solutions exist only in a non trivial domain of the parameter space defined by
the ratio between the SU(N) and U(1) coupling constants, the scalar
self-interaction coupling constants, the magnetic fluxes (Abelian as well as
non-Abelian) and the ``twist parameter'' which is a non-trivial relative phase
of the Higgs fields. | Reduction of Toda Lattice Hierarchy to Generalized KdV Hierarchies and
Two-Matrix Model: Toda lattice hierarchy and the associated matrix formulation of the
$2M$-boson KP hierarchies provide a framework for the Drinfeld-Sokolov
reduction scheme realized through Hamiltonian action within the second KP
Poisson bracket. By working with free currents, which abelianize the second KP
Hamiltonian structure, we are able to obtain an unified formalism for the
reduced $SL(M+1,M-k)$-KdV hierarchies interpolating between the ordinary KP and
KdV hierarchies. The corresponding Lax operators are given as superdeterminants
of graded $SL (M+1,M-k)$ matrices in the diagonal gauge and we describe their
bracket structure and field content. In particular, we provide explicit
free-field representations of the associated $W(M,M-k)$ Poisson bracket
algebras generalizing the familiar nonlinear $W_{M+1}$-algebra. Discrete
B\"{a}cklund transformations for $SL(M+1,M-k)$-KdV are generated naturally from
lattice translations in the underlying Toda-like hierarchy. As an application
we demonstrate the equivalence of the two-matrix string model to the $SL
(M+1,1)$-KdV hierarchy. |
Liouville Theory, AdS$_2$ String, and Three-Point Functions: This is a write-up of the lectures given in Young Researchers Integrability
School 2017. The main goal is to explain the connection between the ODE/IM
correspondence and the classical integrability of strings in AdS. As a warm up,
we first discuss the classical three-point function of the Liouville theory.
The starting point is the well-known fact that the classical solutions to the
Liouville equation can be constructed by solving a Schrodinger-like
differential equation. We then convert it into a set of functional equations
using a method similar to the ODE/IM correspondence. The classical three-point
functions can be computed directly from these functional equations, and the
result matches with the classical limit of the celebrated DOZZ formula. We then
discuss the semi-classical three-point function of strings in AdS2 and show
that one can apply a similar idea by making use of the classical integrability
of the string sigma model on AdS2. The result is given in terms of the
"massive" generalization of Gamma functions, which show up also in string
theory on pp-wave backgrounds and the twistorial generalization of topological
string. | Hawking-like radiation as tunneling from the apparent horizon in a FRW
Universe: We study Hawking-like radiation in a Friedmann-Robertson-Walker (FRW)
universe using the quasi-classical WKB/tunneling method which pictures this
process as a "tunneling" of particles from behind the apparent horizon. The
correct temperature of the Hawking-like radiation from the FRW spacetime is
obtained using a canonical invariant tunneling amplitude. In contrast to the
usual quantum mechanical WKB/tunneling problem where the tunneling amplitude
has only a spatial contribution, we find that the tunneling amplitude for FRW
spacetime (i.e. the imaginary part of the action) has both spatial and temporal
contributions. In addition we study back reaction and energy conservation of
the radiated particles and find that the tunneling probability and change in
entropy, ${\cal S}$ are related by the relationship: $\Gamma\propto\exp[-\Delta
{\cal S}]$ which differs from the standard result $\Gamma\propto\exp[\Delta
{\cal S}]$. By regarding the whole FRW universe as an isolated adiabatic system
the change in the total entropy is zero. Then splitting the entropy between
interior and exterior parts of the horizon ($\Delta {\cal S}_{total}=\Delta
{\cal S}_{int} + \Delta {\cal S}_{ext}=0$), we can explain the origin of the
minus sign difference with the usual result: our $\Delta {\cal S}$ is for the
interior region while the standard result from black hole physics is for the
exterior region. |
Interactions in Intersecting Brane Models: We discuss tree level three and four point scattering amplitudes in type II
string models with matter fields localized at the intersections of D-brane
wrapping cycles. Using conformal field theory techniques we calculate the four
fermion amplitudes. These give "contact" interactions that can lead to flavour
changing effects. We show how in the field theory limit the amplitudes can be
interpreted as the exchange of Kaluza-Klein excitations, string oscillator
states and stretched heavy string modes. | Dualities from dualities: the sequential deconfinement technique: It is an interesting question whether a given infra-red duality between
quantum field theories can be explained in terms of other more elementary
dualities. For example recently it has been shown that mirror dualities can be
obtained by iterative applications of Seiberg-like dualities. In this paper we
continue this line of investigation focusing on theories with tensor matter. In
such cases one can apply the idea of deconfinement, which consists of trading
the tensor matter for extra gauge nodes by means of a suitable elementary
duality. This gives an auxiliary dual frame which can then be manipulated with
further dualizations, in an iterative procedure eventually yielding an
interesting dual description of the original theory. The sequential
deconfinement technique has avatars in different areas of mathematical physics,
such as the study of hypergeometric and elliptic hypergeometric integral
identities or of $2d$ free field correlators. We discuss various examples in
the context $4d$ $\mathcal{N}=1$ supersymmetric theories, which are related to
elliptic hypergeometric integrals. These include a new self-duality involving a
quiver theory which exhibits a non-trivial global symmetry enhancement to
$E_6$. |
On 2d TQFTs whose values are holomorphic symplectic varieties: For simple and simply-connected complex algebraic group G, we conjecture the
existence of a functor eta_G from the category of 2-bordisms to the category of
holomorphic symplectic varieties with Hamiltonian action, such that gluing of
boundaries corresponds to the holomorphic symplectic quotient with respect to
the diagonal action of G. We describe various properties of eta_G obtained via
string-theoretic analysis. Mathematicians are urged to construct eta_G
rigorously. | Crystal Manyfold Universes in AdS Space: We derive crystal braneworld solutions, comprising of intersecting families
of parallel $n+2$-branes in a $4+n$-dimensional $AdS$ space. Each family
consists of alternating positive and negative tension branes. In the simplest
case of exactly orthogonal families, there arise different crystals with
unbroken 4D Poincare invariance on the intersections, where our world can
reside. A crystal can be finite along some direction, either because that
direction is compact, or because it ends on a segment of $AdS$ bulk, or
infinite, where the branes continue forever. If the crystal is interlaced by
connected 3-branes directed both along the intersections and orthogonal to
them, it can be viewed as an example of a Manyfold universe proposed recently
by Arkani-Hamed, Dimopoulos, Dvali and the author. There are new ways for
generating hierarchies, since the bulk volume of the crystal and the lattice
spacing affect the 4D Planck mass. The low energy physics is sensitive to the
boundary conditions in the bulk, and has to satisfy the same constraints
discussed in the Manyfold universe. Phenomenological considerations favor
either finite crystals, or crystals which are infinite but have broken
translational invariance in the bulk. The most distinctive signature of the
bulk structure is that the bulk gravitons are Bloch waves, with a band
spectrum, which we explicitly construct in the case of a 5-dimensional theory. |
Supersymmetric and Kappa-invariant Coincident D0-Branes: We propose a generic supersymmetric and kappa-invariant action for describing
coincident D0-branes with non-abelian matter fields on their worldline. The
action is shown to be in agreement with the Matrix Theory limit of the
ND0-brane effective action. | On loop corrections to integrable $2D$ sigma model backgrounds: We study regularization scheme dependence of $\beta$-function for sigma
models with two-dimensional target space. Working within four-loop
approximation, we conjecture the scheme in which the $\beta$-function retains
only two tensor structures up to certain terms containing $\zeta_3$. Using this
scheme, we provide explicit solutions to RG flow equation corresponding to
Yang-Baxter- and $\lambda$-deformed $SU(2)/U(1)$ sigma models, for which these
terms disappear. |
Particles with anomalous magnetic moment in external e.m. fields: the
proper time formulation: In this paper we evaluate the expression for the Green function of a
pseudo-classical spinning particle interacting with constant electromagnetic
external fields by taking into account the anomalous magnetic and electric
moments of the particle. The spin degrees of freedom are described in terms of
Grassmann variables and the evolution operator is obtained through the
Fock-Schwinger proper time method. | Grand Unified Brane World Scenario: We present a field theoretical model unifying grand unified theory (GUT) and
brane world scenario. As a concrete example, we consider $SU(5)$ GUT in 4+1
dimensions where our 3+1 dimensional spacetime spontaneously arises on five
domain walls. A field-dependent gauge kinetic term is used to localize massless
non-Abelian gauge fields on the domain walls and to assure the charge
universality of matter fields. We find the domain walls with the symmetry
breaking $SU(5)\to SU(3)\times SU(2)\times U(1)$ as a global minimum and all
the undesirable moduli are stabilized with the mass scale of $M_{\rm GUT}$.
Profiles of massless Standard Model particles are determined as a consequence
of wall dynamics. The proton decay can be exponentially suppressed. |
Geometry of Topological Defects of Two-dimensional Sigma Models: A topological defect separating a pair of two-dimensional CFTs is a
codimension one interface along which all components of the stress-energy
tensor glue continuously. We study topological defects of the bosonic, (0,1)-
and (0,2)-supersymmetric sigma models in two dimensions. We find a geometric
classification of such defects closely analogous to that of A-branes of
symplectic manifolds, with the role of symplectic form played instead by a
neutral signature metric. Alternatively, we find a compact description in terms
of a generalized metric on the product of the targets. In the (0,1) case, we
describe the target space geometry of a bundle in which the fermions along the
defect take values. In the (0,2) case, we describe the defects as being
simultaneously A-branes and B-branes. | Unitary Extension of Exotic Massive 3D Gravity from Bi-gravity: We obtain a new 3D gravity model from two copies of parity-odd
Einstein-Cartan theories. Using Hamiltonian analysis, we demonstrate that the
only local degrees of freedom are two massive spin-2 modes. Unitarity of the
model in anti-de Sitter and Minkowski backgrounds can be satisfied for vast
choices of the parameters without fine-tuning. The recent "exotic massive 3D
gravity" model arises as a limiting case of the new model. We also show that
there exist trajectories on the parameter space of the new model which cross
the boundary between unitary and non-unitary regions. At the crossing point,
one massive graviton decouples resulting in a unitary model with just one bulk
degree of freedom but two positive central charges at odds with the usual
expectation that the critical model has at least one vanishing central charge.
Given the fact that a suitable non-relativistic version of bi-gravity has been
used as an effective theory for gapped spin-2 fractional quantum Hall states,
our model may have interesting applications in condensed matter physics. |
Higher spin wormholes from modular bootstrap: We investigate the connection between spacetime wormholes and ensemble
averaging in the context of higher spin AdS$_3$/CFT$_2$. Using techniques from
modular bootstrap combined with some holographic inputs, we evaluate the
partition function of a Euclidean wormhole in AdS$_3$ higher spin gravity. The
fixed spin sectors of the dual CFT$_2$ exhibit features that starkly go beyond
conventional random matrix ensembles: power-law ramps in the spectral form
factor and potentials with a double-well/crest underlying the level statistics. | Open string fluctuations in AdS_5xS^5 and operators with large R-charge: A semiclassical string description is given for correlators of Wilson loops
with local operators in N=4 SYM theory in the regime when operators carry
parametrically large R-charge. The OPE coefficients of the circular Wilson loop
in chiral primary operators are computed to all orders in the alpha' expansion
in AdS_5xS^5 string theory. The results agree with field-theory predictions. |
Effective string description of confining flux tubes: We review the current knowledge about the theoretical foundations of the
effective string theory for confining flux tubes and the comparison of the
predictions to pure gauge lattice data. A concise presentation of the effective
string theory is provided, incorporating recent developments. We summarize the
predictions for the spectrum and the profile/width of the flux tube and their
comparison to lattice data. The review closes with a short summary of open
questions for future research. | Nonanalyticity and On-Shell Factorization of Inflation Correlators at
All Loop Orders: The dynamics of quantum fields during cosmic inflation can be probed via
their late-time boundary correlators. The analytic structure of these boundary
correlators contains rich physical information of bulk dynamics, and is also
closely related to cosmological collider observables. In this work, we study a
particular type of nonanalytic behavior, called nonlocal signals, for inflation
correlators with massive exchanges at arbitrary loop orders. We propose a
signal-detection algorithm to identify all possible sources of nonlocal signals
in an arbitrary loop graph, and prove that the algorithm is exhaustive. We then
present several versions of the on-shell factorization theorem for the leading
nonlocal signal in graphs with arbitrary number of loops, and provide the
explicit analytical expression for the leading nonlocal signal. We also
generalize the nonlocal-signal cutting rule to arbitrary loop graphs. Finally,
we provide many explicit examples to demonstrate the use of our results,
including an n-loop melon graph and a variety of 2-loop graphs. |
On the Addition of Quantum Matrices: We introduce an addition law for the usual quantum matrices $A(R)$ by means
of a coaddition $\underline{\Delta} t=t\otimes 1+1\otimes t$. It supplements
the usual comultiplication $\Delta t=t\otimes t$ and together they obey a
codistributivity condition. The coaddition does not form a usual Hopf algebra
but a braided one. The same remarks apply for rectangular $m\times n$ quantum
matrices. As an application, we construct left-invariant vector fields on
$A(R)$ and other quantum spaces. They close in the form of a braided Lie
algebra. As another application, the wave-functions in the lattice
approximation of Kac-Moody algebras and other lattice fields can be added and
functionally differentiated. | Supersymmetric Black Holes: The effective action of $N=2$, $d=4$ supergravity is shown to acquire no
quantum corrections in background metrics admitting super-covariantly constant
spinors. In particular, these metrics include the Robinson-Bertotti metric
(product of two 2-dimensional spaces of constant curvature) with all 8
supersymmetries unbroken. Another example is a set of arbitrary number of
extreme Reissner-Nordstr\"om black holes. These black holes break 4 of 8
supersymmetries, leaving the other 4 unbroken.
We have found manifestly supersymmetric black holes, which are non-trivial
solutions of the flatness condition $\cd^{2} = 0$ of the corresponding
(shortened) superspace. Their bosonic part describes a set of extreme
Reissner-Nordstr\"om black holes. The super black hole solutions are exact even
when all quantum supergravity corrections are taken into account. |
Spacetimes for λ-deformations: We examine a recently proposed class of integrable deformations to
two-dimensional conformal field theories. These {\lambda}-deformations
interpolate between a WZW model and the non-Abelian T-dual of a Principal
Chiral Model on a group G or, between a G/H gauged WZW model and the
non-Abelian T-dual of the geometric coset G/H.
{\lambda}-deformations have been conjectured to represent quantum group
q-deformations for the case where the deformation parameter is a root of unity.
In this work we show how such deformations can be given an embedding as full
string backgrounds whose target spaces satisfy the equations of type-II
supergravity. One illustrative example is a deformation of the Sl(2,R)/U(1)
black-hole CFT. A further example interpolates between the $\frac{SU(2)\times
SU(2)}{SU(2)}\times\frac{SL(2,R)\times SL(2,R)}{SL(2,R)} \times U(1)^4$ gauged
WZW model and the non-Abelian T-dual of $AdS_3\times S^3\times T^4$ supported
with Ramond flux. | Newton-Cartan (super)gravity as a non-relativistic limit: We define a procedure that, starting from a relativistic theory of
supergravity, leads to a consistent, non-relativistic version thereof. As a
first application we use this limiting procedure to show how the Newton-Cartan
formulation of non-relativistic gravity can be obtained from general
relativity. Then we apply it in a supersymmetric case and derive a novel,
non-relativistic, off-shell formulation of three-dimensional Newton-Cartan
supergravity. |
Complexity in the presence of a boundary: The effects of a boundary on the circuit complexity are studied in two
dimensional theories. The analysis is performed in the holographic realization
of a conformal field theory with a boundary by employing different proposals
for the dual of the complexity, including the "Complexity = Volume" (CV) and
"Complexity = Action" (CA) prescriptions, and in the harmonic chain with
Dirichlet boundary conditions. In all the cases considered except for CA, the
boundary introduces a subleading logarithmic divergence in the expansion of the
complexity as the UV cutoff vanishes. Holographic subregion complexity is also
explored in the CV case, finding that it can change discontinuously under
continuous variations of the configuration of the subregion. | The Barton Expansion and the Path Integral Approach in Thermal Field
Theory: It has been shown how on-shell forward scattering amplitudes (the ``Barton
expansion'') and quantum mechanical path integral (QMPI) can both be used to
compute temperature dependent effects in thermal field theory. We demonstrate
the equivalence of these two approaches and then apply the QMPI to compute the
high temperature expansion for the four-point function in QED, obtaining
results consistent with those previously obtained from the Barton expansion. |
Weakly coupled conformal manifolds in 4d: We classify ${\cal N}=1$ gauge theories with simple gauge groups in four
dimensions which possess a conformal manifold passing through weak coupling. A
very rich variety of models is found once one allows for arbitrary
representations under the gauge group. For each such model we detail the
dimension of the conformal manifold, the conformal anomalies, and the global
symmetry preserved on a generic locus of the manifold. We also identify, at
least some, sub-loci of the conformal manifolds preserving more symmetry than
the generic locus. Several examples of applications of the classification are
discussed. In particular we consider a conformal triality such that one of the
triality frames is a $USp(6)$ gauge theory with six fields in the two index
traceless antisymmetric representation. We discuss an IR dual of a conformal
$Spin(5)$ gauge theory with two chiral superfields in the vector representation
and one in the fourteen dimensional representation. Finally, an extension of
the conformal manifold of ${\cal N}=2$ class ${\cal S}$ theories by conformally
gauging symmetries corresponding to maximal punctures with the addition of two
adjoint chiral superfields is commented upon. | A Note on Large N Thermal Free Energy in Supersymmetric Chern-Simons
Vector Models: We compute the exact effective action for \cN=3 U(N)_k and \cN=4,6
U(N)_k\times U(N')_{-k} Chern-Simons theories with minimal matter content in
the 't Hooft vector model limit under which N and k go to infinity holding N/k,
N' fixed. We also extend this calculation to \cN=4,6 mass deformed case. We
show those large N effective actions except mass-deformed \cN=6 case precisely
reduce to that of \cN=2 U(N)_k Chern-Simons theory with one fundamental chiral
field up to overall multiple factor. By using this result we argue the thermal
free energy and self-duality of the \cN=3,4,6 Chern-Simons theories including
the \cN=4 mass term reduce to those of the \cN=2 case under the limit. |
Axial anomaly of QED in a strong magnetic field and noncommutative
anomaly: The Adler-Bell-Jackiw (ABJ) anomaly of a 3+1 dimensional QED is calculated in
the presence of a strong magnetic field. It is shown that in the regime with
the lowest Landau level (LLL) dominance a dimensional reduction from D=4 to D=2
dimensions occurs in the longitudinal sector of the low energy effective field
theory. In the chiral limit, the resulting anomaly is therefore comparable with
the axial anomaly of a two dimensional massless Schwinger model. It is further
shown that the U(1) axial anomaly of QED in a strong magnetic field is closely
related to the ``nonplanar'' axial anomaly of a conventional noncommutative
QED. | Some Properties of the Calogero-Sutherland Model with Reflections: We prove that the Calogero-Sutherland Model with reflections (the BC_N model)
possesses a property of duality relating the eigenfunctions of two Hamiltonians
with different coupling constants. We obtain a generating function for their
polynomial eigenfunctions, the generalized Jacobi polynomials. The symmetry of
the wave-functions for certain particular cases (associated to the root systems
of the classical Lie groups B_N, C_N and D_N) is also discussed. |
Superradiance in a ghost-free scalar theory: We study superradiance effect in the ghost-free theory. We consider a
scattering of a ghost-free scalar massless field on a rotating cylinder. We
assume that cylinder is thin and empty inside, so that its interaction with the
field is described by a delta-like potential. This potential besides the real
factor, describing its height, contains also imaginary part, responsible for
the absorption of the field. By calculating the scattering amplitude we
obtained the amplification coefficient both in the local and non-local
(ghost-free) models and demonstrated that in the both cases it is greater than
1 when the standard superradiance condition is satisfied. We also demonstrated
that dependence of the amplification coefficient on the frequency of the scalar
field wave may be essentially modified in the non-local case. | Microscopic Theory of Black Hole Superradiance: We study how black hole superradiance appears in string microscopic models of
rotating black holes. In order to disentangle superradiance from
finite-temperature effects, we consider an extremal, rotating D1-D5-P black
hole that has an ergosphere and is not supersymmetric. We explain how the
microscopic dual accounts for the superradiant ergosphere of this black hole.
The bound 0< omega < m Omega_H on superradiant mode frequencies is argued to be
a consequence of Fermi-Dirac statistics for the spin-carrying degrees of
freedom in the dual CFT. We also compute the superradiant emission rates from
both sides of the correspondence, and show their agreement. |
Space-Time Foam Effects on Particle Interactions and the GZK Cutoff: Modelling space-time foam using a non-critical Liouville-string model for the
quantum fluctuations of D branes with recoil, we discuss the issues of momentum
and energy conservation in particle propagation and interactions. We argue that
momentum should be conserved exactly during propagation and on the average
during interactions, but that energy is conserved only on the average during
propagation and is in general not conserved during particle interactions,
because of changes in the background metric. We discuss the possible
modification of the GZK cutoff on high-energy cosmic rays, in the light of this
energy non-conservation as well as the possible modification of the usual
relativistic momentum-energy relation. | On the modular operator of mutli-component regions in chiral CFT: We introduce a new approach to find the Tomita-Takesaki modular flow for
multi-component regions in general chiral conformal field theory. Our method is
based on locality and analyticity of primary fields as well as the so-called
Kubo-Martin-Schwinger (KMS) condition. These features can be used to transform
the problem to a Riemann-Hilbert problem on a covering of the complex plane cut
along the regions, which is equivalent to an integral equation for the matrix
elements of the modular Hamiltonian. Examples are considered. |
Orbital Inflation: inflating along an angular isometry of field space: The simplicity of the CMB data, so well described by single-field inflation,
raises the question whether there might be an equally simple multi-field
realization consistent with the observations. We explore the idea that an
approximate 'angular' shift symmetry in field space (an isometry) protects the
dynamics of coupled inflationary perturbations. This idea relates to the recent
observation that multi-field inflation mimics the predictions of single-field
inflation, if the inflaton is efficiently and constantly coupled to a second
massless degree of freedom (the isocurvature perturbation). In multi-field
inflation, the inflationary trajectory is in general not aligned with the
gradient of the potential. As a corollary the potential does not reflect the
symmetries of perturbations. We propose a new method to reconstruct
simultaneously a two-field action and an inflationary trajectory which proceeds
along an `angular' direction of field space, with a constant radius of
curvature, and that has a controlled mass of `radial' isocurvature
perturbations (entropy mass). We dub this `Orbital Inflation'. In this set-up
the Hubble parameter determines the behavior of both the background and the
perturbations. First, Orbital Inflation provides a playground for quasi-single
field inflation. Second, the exquisite analytical control of these models
allows us to exactly solve the phenomenology of Orbital Inflation with a small
entropy mass and a small radius of curvature, a regime not previously explored.
The predictions are single-field-like, although the consistency relations are
violated. Moreover, the value of the entropy mass dictates how the inflationary
predictions fan out in the ($n_s$, $r$) plane. Depending on the size of the
self interactions of the isocurvature perturbations, the non-Gaussianity
parameter $f_{NL}$ can range from slow-roll suppressed to $\mathcal{O}(\text{a
few})$. | Deconfinement phase transition in a magnetic field in 2+1 dimensions
from holographic models: Using two different models from holographic quantum chromodynamics (QCD) we
study the deconfinement phase transition in $2+1$ dimensions in the presence of
a magnetic field. Working in 2+1 dimensions lead us to {\sl exact} solutions on
the magnetic field, in contrast with the case of 3+1 dimensions where the
solutions on the magnetic field are perturbative. As our main result we predict
a critical magnetic field $B_c$ where the deconfinement critical temperature
vanishes. For weak fields meaning $B<B_c$ we find that the critical temperature
decreases with increasing magnetic field indicating an inverse magnetic
catalysis (IMC). On the other hand, for strong magnetic fields $B>B_c$ we find
that the critical temperature raises with growing field showing a magnetic
catalysis (MC). These results for IMC and MC are in agreement with the
literature. |
Black hole energy extraction via stationary scalar clouds: We study scalar field configurations around Kerr black holes with a
time-independent energy-momentum tensor. These stationary `scalar clouds',
confined near the black hole (BH) by their own mass or a mirror at fixed
radius, exist at the threshold for energy extraction via superradiance.
Motivated by the electromagnetic Blandford-Znajek (BZ) mechanism, we explore
whether scalar clouds could serve as a proxy for the force-free magnetosphere
in the BZ process. We find that a stationary energy-extracting scalar cloud
solution exists when the reflecting mirror is replaced by a semi-permeable
surface which allows the cloud to radiate some energy to infinity while
maintaining self-sustained superradiance. The radial energy flux displays the
same behaviour for rapidly rotating holes as magnetohydrodynamic simulations
predict for the BZ mechanism. | Hard Thermal Loops, Quark-Gluon Plasma Response, and T=0 Topology: I outline various derivations of the non-Abelian Kubo equation, which governs
the response of a quark-gluon plasma to hard thermal perturbations. In the
static case, it is proven that gauge theories do not support hard thermal
solitons. Explicit solutions are constructed within an SU(2) Ansatz and they
are shown to support the general result. The time-dependent problem, i.e.,
non-Abelian plasma waves, has not been completely solved. We express and
motivate the hope that the intimate relations linking the gauge-invariance
condition for hard thermal loops to the equation of motion for T=0, topological
Chern-Simons theory may yield new insight into this field. |
From the Komar Mass and Entropic Force Scenarios to the Einstein Field
Equations on the Ads Brane: By bearing the Komar's definition for the mass, together with the entropic
origin of gravity in mind, we find the Einstein field equations in
$(n+1$)-dimensional spacetime. Then, by reflecting the ($4+1$)-dimensional
Einstein equations on the ($3+1$)-hypersurface, we get the Einstein equations
onto the $3$-brane. The corresponding energy conditions are also addressed.
Since the higher dimensional considerations modify the Einstein field equations
in the ($3+1$)-dimensions and thus the energy-momentum tensor, we get a
relation for the Komar mass on the brane. In addition, the strongness of this
relation compared with existing definition for the Komar mass on the brane is
addressed. | Boost modes for a massive fermion field: We have shown that Wightman function of a free quantum field generates any
complete set of solutions of relativistic wave equations. Using this approach
we have constructed the complete set of solutions to 2d Dirac equation
consisting of eigenfunctions of the generator of Lorentz rotations (boost
operator). It is shown that at the surface of the light cone the boost modes
for a fermion field contain $\delta$-function of a complex argument. Due to the
presence of such singularity exclusion even of a single mode with an arbitrary
value of the boost quantum number makes the set of boost modes incomplete. |
Interaction and modular invariance of strings on curved manifolds: We review and present new results for a string moving on an $SU(1,1)$ group
manifold. We discuss two classes of theories which use discrete
representations. For these theories the representations forbidden by unitarity
decouple and, in addition, one can construct modular invariant partition
functions. The partion functions do, however, contain divergencies due to the
time-like direction of the $SU(1,1)$ manifold. The two classes of theories have
the corresponding central charges $c=9,6,5,9/2,\ldots$ and
$c=9,15,21,27,\ldots$. Subtracting two from the latter series of central
charges we get the Gervais-Neveu series $c-2=7,13,19,25$. This suggests a
relationship between the $SU(1,1)$ string and the Liouville theory, similar to
the one found in the $c=1$ string. Modular invariance is also demonstrated for
the principal continous representations. Furthermore, we present new results
for the Euclidean coset $SU(1,1)/U(1)$. The same two classes of theories will
be possible here and will have central charges $c=8,5,4,\dots$ and
$c=8,14,20,26,\ldots$, where the latter class includes the critical 2d black
hole. The partition functions for the coset theory are convergent.(Talk
presented by S.H. at the 16'th Johns Hopkins' Workshop, G\"oteborg, Sweden,
June 8-10, 1992) | Comments on the double cone wormhole: In this paper we revisit the double cone wormhole introduced by Saad, Shenker
and Stanford (SSS), which was shown to reproduce the ramp in the spectral form
factor. As a first approximation we can say that this solution computes
$\textrm{Tr}[e^{-iKT}]$, a trace of the "evolution" operator that generates
Schwarzschild time translations on the two sided wormhole geometry. This point
of view leads to a simple way to compute the normalization factor of the
wormhole. When we have bulk matter fields, SSS suggested using a modified
evolution $\tilde K$ which involves a slightly complex geometry, so that we are
really computing $\textrm{Tr}[e^{-i\tilde{K}T}]$. We argue that, for general
black holes, the spectrum of $\tilde K$ is given by quasinormal mode
frequencies. We explain that this reproduces various features that were
previously predicted from the spectral form factor on hydrodynamics grounds. We
also give a general algebraic construction of the modified boost in terms of
operators constructed from half sided modular inclusions. For the special case
of JT gravity, we work out the backreaction of matter on the geometry of the
double cone and find that it deforms the geometry in an undesirable direction.
We finally give some comments on the possible physical interpretation of
$\tilde K$. |
(2+1) Dimensional Black Hole and (1+1) Dimensional Quantum Gravity: In the Chern-Simons gauge theory formulation of the spinning (2+1)
dimensional black hole, we may treat the horizon and the spatial infinity as
boundaries. We obtain the actions induced on both boundaries, applying the
Faddeev and Shatashvili procedure. The action induced on the boundary of the
horizon is precisely the gauged $SL(2,R)/U(1)$ Wess-Zumino-Witten (WZW) model,
which has been studied previously in connection with a Lorentz signature black
hole in (1+1) dimensions. The action induced on the boundary of spatial
infinity is also found to be a gauged $SL(2,R)$ WZW model, which is equivalent
to the Liouville model, the covariant action for the (1+1) dimensional quantum
gravity. Thus, the (2+1) dimensional black hole is intimately related to the
quantum gravity in (1+1) dimensions. | Holographic duals of 3d S-fold CFTs: We construct non-geometric AdS$_4$ solutions of IIB string theory where the
fields in overlapping patches are glued by elements of the S-duality group. We
obtain them by suitable quotients of compact and non-compact geometric
solutions. The quotient procedure suggests CFT duals as quiver theories with
links involving the so-called $T[U(N)]$ theory. We test the validity of the
non-geometric solutions (and of our proposed holographic duality) by computing
the three-sphere partition function $Z$ of the CFTs. A first class of solutions
is obtained by an S-duality quotient of Janus-type non-compact solutions and is
dual to 3d $\mathcal{N}=4$ SCFTs; for these we manage to compute $Z$ of the
dual CFT at finite $N$, and it agrees perfectly with the supergravity result in
the large $N$ limit. A second class has five-branes, it is obtained by a
M\"obius-like S-quotient of ordinary compact solutions and is dual to 3d
$\mathcal{N}=3$ SCFTs. For these, $Z$ agrees with the supergravity result if
one chooses the limit carefully so that the effect of the fivebranes does not
backreact on the entire geometry. Other limits suggest the existence of IIA
duals. |
The Graviton Propagator with a Non-Conserved External Generating Source: A novel general expression is obtained for the graviton propagator from
Lagrangian field theory by taking into account the necessary fact that in the
functional differential approach of quantum field theory, in order to generate
non-linearities in gravitation and interactions with matter, the external
source $T_{\mu\nu}$, coupled to the gravitational field, should \textit{a
priori} not be conserved $\partial^\mu T_{\mu\nu}\neq 0$, so variations with
respect to its ten components may be varied \textit{independently}. The
resulting propagator is the one which arises in the functional approach and
does \textit{not} coincide with the corresponding time-ordered product of two
fields and it includes so-called Schwinger terms. The quantization is carried
out in a gauge corresponding to physical states with two polarization states to
ensure positivity in quantum applications. | Non-Equilibrium Dynamics of Phase Transitions: From the Early Universe
to Chiral Condensates: In this brief review we introduce the methods of quantum field theory out of
equilibrium and study the non-equilibrium aspects of phase transitions.
Specifically we critically study the picture of the ``slow-roll'' phase
transition in the new inflationary models, we show that the instabilities that
are the hallmark of the phase transition, that is the formation of correlated
domains, dramatically change this picture. We analyze in detail the dynamics of
phase separation in strongly supercooled phase transitions in Minkowski space.
We argue that this is typically the situation in weakly coupled scalar
theories. The effective evolution equations for the expectation value and the
fluctuations of an inflaton field in a FRW cosmology are derived both in the
loop expansion and in a self-consistent non-perturbative scheme. Finally we use
these non-equilibrium techniques and concepts to study the influence of quantum
and thermal fluctuations on the dynamics of a proposed mechanism for the
formation of disoriented chiral condensates during a rapid phase transition out
of equilibrium. This last topic may prove to be experimentally relevant at
present accelerator energies. To appear in the Proceedings of the `2nd.
Journ\'ee Cosmologie', Observatoire de Paris, 2-4, June 1994. H J de Vega and
N. S\'anchez, Editors, World Scientific. |
Consistent inflationary cosmology from quadratic gravity with dynamical
torsion: The idea of gauge theories of gravity predicts that there should exist not
only the massless graviton but also massive particles carrying the
gravitational force. We study the cosmology in a quadratic gravity with
dynamical torsion where gravity may be interpreted as a gauge force associated
with the Poincar\'{e} group. In addition to the massless spin-2 graviton, the
model contains four non-ghost massive particle species: a couple of spin-0, a
spin-1 and a spin-2. Supposing the restoration of the local Weyl invariance in
the UV limit and the parity invariance, we find the most general minisuperspace
action describing a homogeneous and isotropic universe with a flat spatial
geometry. We then transform the minisuperspace action to a quasi-Einstein frame
in which the field space is a hyperboloid and the field potential is a
combination of those of a Starobinsky-like inflation and a natural inflation.
Remarkably, thanks to the multi-field dynamics, the Starobinsky-like
inflationary trajectory can be realized even if the initial condition is away
from the top of the Starobinsky-like potential. We also study linear tensor
perturbations and find qualitatively different features than the Starobinsky
inflation, spontaneous parity violation and mixing of the massless and massive
spin-2 modes, which might reveal the underlying nature of gravity through
inflationary observables. | Managing $γ_5$ in Dimensional Regularization II: the Trace with
more $γ_5$: In the present paper we evaluate the anomaly for the abelian axial current in
a non abelian chiral gauge theory, by using dimensional regularization. This
amount to formulate a procedure for managing traces with more than one
$\gamma_5$. \par The suggested procedure obeys Lorentz covariance and
cyclicity, at variance with previous approaches (e.g. the celebrated 't Hooft
and Veltman's where Lorentz is violated) \par The result of the present paper
is a further step forward in the program initiated by a previous work on the
traces involving a single $\gamma_5$. The final goal is an unconstrained
definition of $\gamma_5$ in dimensional regularization. Here, in the evaluation
of the anomaly, we profit of the axial current conservation equation, when
radiative corrections are neglected. This kind of tool is not always exploited
in field theories with $\gamma_5$, e.g. in the use of dimensional
regularization of infrared and collinear divergences. |
Non-critical superstrings: a comparison between continuum and discrete
approaches: We review the relation between the matrix model and Liouville approaches to
two-dimensional gravity as elaborated by Moore, Seiberg and Staudacher. Then,
based on the supersymmetric Liouville formulation and the discrete eigenvalue
model proposed by Alvarez-Gaum\'e, Itoyama, Ma\~nes and Zadra, we extend the
previous relation to the supersymmetric case. The minisuperspace approximation
for the supersymmetric case is formulated, and the corresponding wave equation
is found. | Polyakov conjecture on the supertorus: We prove the Polyakov conjecture on the supertorus $(ST_2)$: we dermine an
iterative solution at any order of the superconformal Ward identity and we show
that this solution is resumed by the Wess-Zumino-Polyakov (WZP) action that
describes the $(1,0)$ 2D-supergravity. The resolution of the superBeltrami
equation for the Wess-Zumino (WZ) field is done by using on the one hand the
Cauchy kernel defined on $ST_2$ and on the other hand, the formalism developed
to get the general solution on the supercomplex plane. Hence, we determine the
n-points Green functions from the (WZP) action expressed in terms of the (WZ)
field. |
Structure in Supersymmetric Yang-Mills Theory: We show that requiring sixteen supersymmetries in quantum mechanical gauge
theory implies the existence of a web of constrained interactions. Contrary to
conventional wisdom, these constraints extend to arbitrary orders in the
momentum expansion. | The screening Horndeski cosmologies: We present a systematic analysis of homogeneous and isotropic cosmologies in
a particular Horndeski model with Galileon shift symmetry, containing also a
$\Lambda$-term and a matter. The model, sometimes called Fab Five, admits a
rich spectrum of solutions. Some of them describe the standard late time
cosmological dynamic dominated by the $\Lambda$-term and matter, while at the
early times the universe expands with a constant Hubble rate determined by the
value of the scalar kinetic coupling. For other solutions the $\Lambda$-term
and matter are screened at all times but there are nevertheless the early and
late accelerating phases. The model also admits bounces, as well as peculiar
solutions describing "the emergence of time". Most of these solutions contain
ghosts in the scalar and tensor sectors. However, a careful analysis reveals
three different branches of ghost-free solutions, all showing a late time
acceleration phase. We analyze the dynamical stability of these solutions and
find that all of them are stable in the future, since all their perturbations
stay bounded at late times. However, they all turn out to be unstable in the
past, as their perturbations grow violently when one approaches the initial
spacetime singularity. We therefore conclude that the model has no viable
solutions describing the whole of the cosmological history, although it may
describe the current acceleration phase. We also check that the flat space
solution is ghost-free in the model, but it may acquire ghost in more general
versions of the Horndeski theory. |
Holographic baby universes: an observable story: We formulate the baby universe construction rigorously by giving a primordial
role to the algebra of observables of quantum gravity rather than the Hilbert
space. Utilizing diffeomorphism invariance, we study baby universe creation and
annihilation via change in topology. We then construct the algebra of boundary
observables for holographic theories and show that it enhances to contain an
'extra' Abelian tensor factor to describe the bulk in the quantum regime; via
the gravitational path integral we realize this extra tensor factor, at the
level of the Hilbert space, in the context of the GNS representation. We
reformulate the necessary assumptions for the "baby universe hypothesis" using
the GNS representation. When the baby universe hypothesis is satisfied, we
demonstrate that the "miraculous cancellations" in the corresponding
gravitational path integral have a natural explanation in terms of the
character theory of Abelian $C^\ast$-algebras. We find the necessary and
sufficient mathematical condition for the baby universe hypothesis to hold, and
transcribe it into sufficient physical conditions. We find that they are
incompatible with a baby universe formation that is influenced by any bulk
process from the AdS/CFT correspondence. We illustrate our construction by
applying it to two settings, which leads to a re-interpretion of some
topological models of gravity, and to draw an analogy with the topological
vacua of gauge theory. | Extra-Natural Inflation (De)constructed: Extra-natural inflation is (de)constructed. Explicit models are compared with
cosmological observations. The models successfully achieve trans-Planckian
inflaton field excursions. |
Tensionless Tales of Compactification: We study circle compactifications of tensionless bosonic string theory, both
at the classical and the quantum level. The physical state condition for
different representations of BMS$_3$, the worldsheet residual gauge symmetry
for tensionless strings, admits three inequivalent quantum vacua. We obtain the
compactified mass spectrum in each of these vacua using canonical quantization
and explicate their properties. | Duality and hidden dimensions: Using a global superalgebra with 32 fermionic and 528 bosonic charges, many
features of p-brane dualities and hidden dimensions are discussed. |
Heavy quark potential with dynamical flavors: a first order transition: We study the static potential between external quark-antiquark pairs in a
strongly coupled gauge theory with a large number of colors and massive
dynamical flavors, using a dual string description. When the constituent mass
of the dynamical quarks is set below a certain critical value, we find a first
order phase transition between a linear and a Coulomb-like regime. Above the
critical mass the two phases are smoothly connected. We also study the
dependence on the theory parameters of the quark-antiquark separation at which
the static configuration decays into specific static-dynamical mesons. | Holographic Complexity in Vaidya Spacetimes I: We examine holographic complexity in time-dependent Vaidya spacetimes with
both the complexity$=$volume (CV) and complexity$=$action (CA) proposals. We
focus on the evolution of the holographic complexity for a thin shell of null
fluid, which collapses into empty AdS space and forms a (one-sided) black hole.
In order to apply the CA approach, we introduce an action principle for the
null fluid which sources the Vaidya geometries, and we carefully examine the
contribution of the null shell to the action. Further, we find that adding a
particular counterterm on the null boundaries of the Wheeler-DeWitt patch is
essential if the gravitational action is to properly describe the complexity of
the boundary state. For both the CV proposal and the CA proposal (with the
extra boundary counterterm), the late time limit of the growth rate of the
holographic complexity for the one-sided black hole is precisely the same as
that found for an eternal black hole. |
Schwinger Pair Production in Pulsed Electric Fields: We numerically investigate the temporal behavior and the structure of
longitudinal momentum spectrum and the field polarity effect on pair production
in pulsed electric fields in scalar quantum electrodynamics (QED). Using the
evolution operator expressed in terms of the particle and antiparticle
operators, we find the exact quantum states under the influence of electric
pulses and measure the number of pairs of the Minkowski particle and
antiparticle. The number of pairs, depending on the configuration of electric
pulses, exhibits rich structures in the longitudinal momentum spectrum and
undergoes diverse dynamical behaviors at the onset of the interaction but
always either converges to a momentum-dependent constant or oscillates around a
momentum-dependent time average after the completion of fields. | Generalized Kähler Geometry and current algebras in $SU(2)\times U(1)$
N=2 superconformal WZW model: We examine the Generalized K$\ddot{a}$hler Geometry of quantum N=2
superconformal WZW model on $SU(2)\times U(1)$ and relate the right-moving and
left-moving Kac-Moody superalgebra currents to the Generalized K$\ddot{a}$hler
Geometry data of the group manifold using Hamiltonian formalism. |
Magnetic Monopoles, Bogomol'nyi Bound and SL(2,Z) Invariance in String
Theory: We show that in heterotic string theory compactified on a six dimensional
torus, the lower bound (Bogomol'nyi bound) on the dyon mass is invariant under
the SL(2,Z) transformation that interchanges strong and weak coupling limits of
the theory. Elementary string excitations are also shown to satisfy this lower
bound. Finally, we identify specific monopole solutions that are related via
the strong-weak coupling duality transformation to some of the elementary
particles saturating the Bogomol'nyi bound, and these monopoles are shown to
have the same mass and degeneracy of states as the corresponding elementary
particles. | A Cheap Alternative to the Lattice?: We show how to perform accurate, nonperturbative and controlled calculations
in quantum field theory in d dimensions. We use the Truncated Conformal Space
Approach (TCSA), a Hamiltonian method which exploits the conformal structure of
the UV fixed point. The theory is regulated in the IR by putting it on a sphere
of a large finite radius. The QFT Hamiltonian is expressed as a matrix in the
Hilbert space of CFT states. After restricting ourselves to energies below a
certain UV cutoff, an approximation to the spectrum is obtained by numerical
diagonalization of the resulting finite-dimensional matrix. The cutoff
dependence of the results can be computed and efficiently reduced via a
renormalization procedure. We work out the details of the method for the phi^4
theory in d dimensions with d not necessarily integer. A numerical analysis is
then performed for the specific case d = 2.5, a value chosen in the range where
UV divergences are absent. By going from weak to intermediate to strong
coupling, we are able to observe the symmetry-preserving, symmetry-breaking,
and conformal phases of the theory, and perform rough measurements of masses
and critical exponents. As a byproduct of our investigations we find that both
the free and the interacting theories in non integral d are not unitary, which
however does not seem to cause much effect at low energies. |
A Note on the Stability of Quantum Supermembranes: We re-examine the question of the stability of quantum supermembranes. In the
past, the instability of supermembranes was established by using a regulator,
i.e. approximating the membrane by SU(N) super Yang-Mills theory and letting $N
\rightarrow \infty$. In this paper, we (a) show that the instability persists
even if we directly examine the continuum theory (b) give heuristic arguments
that even a theory of unstable membranes at the Planck length may still be
compatible with experiment (c) resolve a certain puzzling discrepancy between
earlier works on the stability of supermembranes. Presented at the 2nd
International Sakharov Conference in Moscow, May 1996. | Uniqueness theorem for charged rotating black holes in five-dimensional
minimal supergravity: We show a uniqueness theorem for charged rotating black holes in the bosonic
sector of five-dimensional minimal supergravity. More precisely, under the
assumptions of the existence of two commuting axial isometries and spherical
topology of horizon cross-sections, we prove that an asymptotically flat,
stationary charged rotating black hole with finite temperature in
five-dimensional Einstein-Maxwell-Chern-Simons theory is uniquely characterized
by the mass, charge, and two independent angular momenta and therefore is
described by the five-dimensional Cvetic-Youm solution with equal charges. We
also discuss a generalization of our uniqueness theorem for spherical black
holes to the case of black rings. |
ADE Little String Theory on a Riemann Surface (and Triality): We initiate the study of (2,0) little string theory of ADE type using its
definition in terms of IIB string compactified on an ADE singularity. As one
application, we derive a 5d ADE quiver gauge theory that describes the little
string compactified on a sphere with three full punctures, at low energies. As
a second application, we show the partition function of this theory equals the
3-point conformal block of ADE Toda CFT, q-deformed. To establish this, we
generalize the A_n triality of \cite{AHS} to all ADE Lie algebras; IIB string
perspective is crucial for this as well. | Gravitational instantons and anomalous chiral symmetry breaking: We study anomalous chiral symmetry breaking in two-flavour QCD induced by
gravitational and QCD-instantons within asymptotically safe gravity within the
functional renormalisation group approach. Similarly to QCD-instantons,
gravitational ones, associated to a K3-surface connected by a wormhole-like
throat in flat spacetime, generate contributions to the 't~Hooft coupling
proportional to $\exp(-1/g_N)$ with the dimensionless Newton coupling $g_N$.
Hence, in the asymptotically safe gravity scenario with a non-vanishing fixed
point coupling $g_N^*$, the induced 't Hooft coupling is finite at the Planck
scale, and its size depends on the chosen UV-completion. Within this scenario
the gravitational effects on anomalous $U(1)_A$-breaking at the Planck scale
may survive at low energy scales. In turn, fermion masses of the order of the
Planck scale cannot be present. This constrains the allowed asymptotically safe
UV-completion of the Gravity-QCD system. We map-out the parameter regime that
is compatible with the existence of light fermions in the low-energy regime. |
Noncommutative Kaluza-Klein Theory: Efforts have been made recently to reformulate traditional Kaluza-Klein
theory by using a generalized definition of a higher-dimensional extended
space-time. Both electromagnetism and gravity have been studied in this
context. We review some of the models which have been proposed, with a special
effort to keep the mathematical formalism to a very minimum. | Cosmological density perturbations from conformal scalar field: infrared
properties and statistical anisotropy: We consider a scenario in which primordial scalar perturbations are generated
when complex conformal scalar field rolls down its negative quartic potential.
Initially, these are the perturbations of the phase of this field; they are
converted into the adiabatic perturbations at a later stage. A potentially
dangerous feature of this scenario is the existence of perturbations in the
radial field direction, which have red power spectrum. We show, however, that
to the linear order in the small parameter - the quartic self-coupling - the
infrared effects are completely harmless, as they can be absorbed into field
redefinition. We then evaluate the statistical anisotropy inherent in the model
due to the existence of the long-ranged radial perturbations. To the linear
order in the quartic self-coupling the statistical anisotropy is free of the
infrared effects. The latter show up at the quadratic order in the
self-coupling and result in the mild (logarithmic) enhancement of the
corresponding contribution to the statistical anisotropy. The resulting
statistical anisotropy is a combination of a larger term which, however, decays
as momentum increases, and a smaller term which is independent of momentum. |
Origin of the Pure Spinor and Green-Schwarz Formalisms: The pure spinor formalism for the superstring was recently obtained by
gauge-fixing a purely bosonic classical action involving a twistor-like
constraint $\partial x^m (\gamma_m\lambda)_\alpha =0$ where $\lambda^\alpha$ is
a d=10 pure spinor. This twistor-like constraint replaces the usual Virasoro
constraint $\partial x^m \partial x_m =0$, and the Green-Schwarz fermionic
spacetime spinor variables $\theta^\alpha$ arise as Faddeev-Popov ghosts for
this constraint.
In this paper, the purely bosonic classical action is simplified by replacing
the classical d=10 pure spinor $\lambda^\alpha$ with a d=10 projective pure
spinor. The pure spinor and Green-Schwarz formalisms for the superparticle and
superstring are then obtained as different gauge-fixings of this purely bosonic
classical action, and the Green-Schwarz kappa symmetry is directly related to
the pure spinor BRST symmetry. Since a d=10 projective pure spinor
parameterizes ${{SO(10)}\over{U(5)}}$, this action can be interpreted as a
standard $\hat c=5$ topological action where one integrates over the
${{SO(10)}\over{U(5)}}$ choice of complex structure. Finally, a purely bosonic
action for the d=11 supermembrane is proposed which reduces upon
double-dimensional reduction to the purely bosonic action for the d=10 Type IIA
superstring. | Particle level screening of scalar forces in 1+1 dimensions: We investigate how non-linear scalar field theories respond to point sources.
Taking the symmetron as a specific example of such a theory, we solve the
non-linear equation of motion in one spatial dimension for (i) an isolated
point source and (ii) two identical point sources with arbitrary separation. We
find that the mass of a single point source can be screened by the symmetron
field, provided that its mass is above a critical value. We find that two point
sources behave as independent, isolated sources when the separation between
them is large, but, when their separation is smaller than the symmetron's
Compton wavelength, they behave much like a single point source with the same
total mass. Finally, we explore closely related behavior in a toy Higgs-Yukawa
model, and find indications that the maximum fermion mass that can be generated
consistently via a Yukawa coupling to the Higgs in 1+1 dimensions is roughly
the mass of the Higgs itself, with potentially intriguing implications for the
hierarchy problem. |
A note on the two point function on the boundary of AdS spacetime: We calculate by a new way the two point function on the boundary of AdS
spacetime in 1+2 dimensions for the massless conformal real scalar field. The
result agrees with the answer provided by the Boundary-limit Holography and
Witten recipe. This is done in Poincar\'{e} coordinates. The basic ingredients
of this new method are conformal techniques, quantum fields defined on a half
of Minkowski spacetime and a limit inspired by the Boundary-limit Holography.
We also show that a state in AdS, the global vacuum, in three dimensions
induces a state on the conformal boundary of AdS spacetime, which in turn
induces a state on the BTZ black hole. On the other hand the same state in AdS
induces a state on the BTZ black hole which in turn induces a state on its
conformal boundary. The two ways of getting the state on the conformal boundary
of the BTZ black hole coincide for the massless conformal real scalar field. We
point out that the normalizable modes in the AdS/CFT correspondence for the BTZ
black hole give a similar contribution as the non-normalizable modes used in
the Witten prescription. We also give some clues on why the Witten and the
Boundary-limit Holography prescription coincide. | Construction of a non-standard quantum field theory through a
generalized Heisenberg algebra: We construct a Heisenberg-like algebra for the one dimensional quantum free
Klein-Gordon equation defined on the interval of the real line of length $L$.
Using the realization of the ladder operators of this type Heisenberg algebra
in terms of physical operators we build a 3+1 dimensional free quantum field
theory based on this algebra. We introduce fields written in terms of the
ladder operators of this type Heisenberg algebra and a free quantum Hamiltonian
in terms of these fields. The mass spectrum of the physical excitations of this
quantum field theory are given by $\sqrt{n^2 \pi^2/L^2+m_q^2}$, where $n=
1,2,...$ denotes the level of the particle with mass $m_q$ in an infinite
square-well potential of width $L$. |
On the Universality of the Chern-Simons Diffusion Rate: We prove the universality of the Chern-Simons diffusion rate - a crucial
observable for the chiral magnetic effect - in a large class of planar strongly
correlated gauge theories with dual string description. When the effects of
anomalies are suppressed, the diffusion rate is simply given in terms of
temperature, entropy density and gauge coupling, with a universal numerical
coefficient. We show that this result holds, in fact, for all the top-down
holographic models where the calculation has been performed in the past, even
in presence of magnetic fields and anisotropy. We also extend the check to
further well known models for which the same computation was lacking. Finally
we point out some subtleties related to the definition of the Chern-Simons
diffusion rate in the presence of anomalies. In this case, the usual definition
of the rate - a late time limit of the imaginary part of the retarded
correlator of the topological charge density - would give an exactly vanishing
result, due to its relation with a non-conserved charge correlator. We confirm
this observation by explicit holographic computations on generic isotropic
black hole backgrounds. Nevertheless, a non-trivial Chern-Simons relaxation
time can in principle be extracted from a quasi-normal mode calculation. | Wavefunctions for a Class of Branes in Three-space: Wavefunctions are proposed for a class of Lagrangian branes in three
complex-dimensional space. The branes are asymptotic to Legendrian surfaces of
genus g. The expansion of these wavefunctions in appropriate coordinates
conjecturally encodes all-genus open Gromov-Witten invariants, i.e. the free
energy of the topological open string.
This paper is written in physics language, but tries to welcome
mathematicians. Most results stem from joint mathematical works with Linhui
Shen and David Treumann. |
Holographic superconductors with Weyl corrections: A quick review on the analytical aspects of holographic superconductors (HSC)
with Weyl corrections has been presented. Mainly we focus on matching method
and variations approaches. Different types of such HSC have been investigated,
s-wave, p-wave and St\'{u}ckelberg ones. We also review the fundamental
construction of a p-wave type , in which the non-Abelian gauge field is coupled
to the Weyl tensor. The results are compared from numerics to analytical
results. | Exact analytic expressions of real tensor eigenvalue distributions of
Gaussian tensor model for small $N$: We obtain exact analytic expressions of real tensor eigenvalue/vector
distributions of real symmetric order-three tensors with Gaussian distributions
for $N\leq 8$. This is achieved by explicitly computing the partition function
of a zero-dimensional boson-fermion system with four-interactions. The
distributions are expressed by combinations of polynomial, exponential and
error functions as results of feasible complicated bosonic integrals which
appear after fermionic integrations. By extrapolating the expressions and also
using a previous result, we guess a large-$N$ expression. The expressions are
compared with Monte Carlo simulations, and precise and good agreement are
obtained with the exact and the large-$N$ expressions, respectively.
Understanding the feasibility of the integration is left for future study,
which would provide a general-$N$ analytic formula. |
The Generalized Uncertainty Principle and Quantum Gravity Phenomenology: In this article we examine a Generalized Uncertainty Principle which differs
from the Heisenberg Uncertainty Principle by terms linear and quadratic in
particle momenta, as proposed by the authors in an earlier paper. We show that
this affects all Hamiltonians, and in particular those which describe low
energy experiments. We discuss possible observational consequences. Further, we
also show that this indicates that space may be discrete at the fundamental
level. | Loop Equations in Abelian Gauge Theories: The equations obeyed by the vacuum expectation value of the Wilson loop of
Abelian gauge theories are considered from the point of view of the loop-space.
An approximative scheme for studying these loop-equations for lattice Maxwell
theory is presented. The approximation leads to a partial difference equation
in the area and length variables of the loop, and certain physically motivated
ansatz is seen to reproduce the mean field results from a geometrical
perspective. |
Eigenvalue instantons in the spectral form factor of random matrix model: We study the late time plateau behavior of the spectral form factor in the
Gaussian Unitary Ensemble (GUE) random matrix model. The time derivative of the
spectral form factor in the plateau regime is not strictly zero, but non-zero
due to a non-perturbative correction in the $1/N$ expansion. We argue that such
a non-perturbative correction comes from the eigenvalue instanton of random
matrix model and we explicitly compute the instanton correction as a function
of time. | Looking At The Cosmological Constant From Infinite--Volume Bulk: I briefly review the arguments why the braneworld models with infinite-volume
extra dimensions could solve the cosmological constant problem, evading
Weinberg's no-go theorem. Then I discuss in detail the established properties
of these models, as well as the features which should be studied further in
order to conclude whether these models can truly solve the problem. This
article is dedicated to the memory of Ian Kogan. |
Light-cone gauge Hamiltonian for AdS_4 x CP^3 superstring: It is developed the phase-space formulation for the Type IIA superstring on
the AdS_4 x CP^3 background in the kappa-symmetry light-cone gauge for which
the light-like directions are taken from the D=3 Minkowski boundary of AdS_4.
After fixing bosonic light-cone gauge the superstring Hamiltonian is expressed
as a function of the transverse physical variables and in the quadratic
approximation corresponds to the light-cone gauge-fixed IIA superstring in flat
space. | Quantum Phases of $4d$ $SU(N)$ $\mathcal{N}=4$ SYM: It is argued that $4d$ $SU(N)$ $\mathcal{N}=4$ SYM has an accumulation line
of zero-temperature topologically ordered phases. Each of these phases
corresponds to $N$ bound states charged under electromagnetic
$\mathbb{Z}^{(1)}_N$ one-form symmetries. Each of the $N$ bound states is made
of two Dyonic flux components each of them extended over a two dimensional
surface. They are localized at the fixed loci of a rotational action, and are
argued to correspond to conformal blocks (or primaries) of an $SU(N)_1$ WZNW
model on a two-torus. |
Order 1/N^2 test of the Maldacena conjecture: Cancellation of the
one-loop Weyl anomaly: We test the Maldacena conjecture for type IIB String Theory/ N=4 Yang-Mills
by calculating the one-loop corrections in the bulk theory to the Weyl anomaly
of the boundary CFT when the latter is coupled to a Ricci-flat metric. The
contributions cancel within each supermultiplet, in agreement with the
conjecture. | Schwinger Effect in Near-extremal Charged Black Holes in High Dimensions: We study the Schwinger effect in near-extremal nonrotating black holes in an
arbitrary $D(\geq 4)$-dimensional asymptotically flat and (A)dS space. Using
the near-horizon geometry $\mathrm{AdS}_2 \times \mathrm{S}^{D-2}$ of
near-extremal black holes with Myers-Perry metric, we find a universal
expression of the emission formula for charges that is a multiplication of the
Schwinger effects in an $\mathrm{AdS}_2$ space and in a two-dimensional Rindler
space. The effective temperature of an accelerated charge for the Schwinger
effect is determined by the radii of the effective $\mathrm{AdS}_2$ space and
$\mathrm{S}^{D-2}$ as well as the mass, charge, angular momentum of the charge
and the radius of the (A)dS space. The Schwinger effect in the asymptotically
flat space is more efficient and persistent for a wide range of large black
holes for dimensions higher than four. The AdS (dS) boundary enhances
(suppresses) the Schwinger effect than the asymptotically flat space. The
Schwinger effect persists for a wide range of black holes in the AdS space and
has an upper bound in the dS space. |
Exact results for corner contributions to the entanglement entropy and
Renyi entropies of free bosons and fermions in 3d: In the presence of a sharp corner in the boundary of the entanglement region,
the entanglement entropy (EE) and Renyi entropies for 3d CFTs have a
logarithmic term whose coefficient, the corner function, is scheme-independent.
In the limit where the corner becomes smooth, the corner function vanishes
quadratically with coefficient $\sigma$ for the EE and $\sigma_n$ for the Renyi
entropies. For a free real scalar and a free Dirac fermion, we evaluate
analytically the integral expressions of Casini, Huerta, and Leitao to derive
exact results for $\sigma$ and $\sigma_n$ for all $n=2,3,\dots$. The results
for $\sigma$ agree with a recent universality conjecture of Bueno, Myers, and
Witczak-Krempa that $\sigma/C_T = \pi^2/24$ in all 3d CFTs, where $C_T$ is the
central charge. For the Renyi entropies, the ratios $\sigma_n/C_T$ do not
indicate similar universality. However, in the limit $n \to \infty$, the
asymptotic values satisfy a simple relationship and equal $1/(4\pi^2)$ times
the asymptotic values of the free energy of free scalars/fermions on the
$n$-covered 3-sphere. | Ward identity for loop level soft photon theorem for massless QED
coupled to gravity: Strominger and his collaborators pioneered the study of equivalence between
soft theorems and asymptotic conservation laws. We study this equivalence in
the context of loop level subleading soft photon theorem for massless scalar
QED in presence of dynamical gravity. Motivated by Campiglia and Laddha
\cite{1903.09133}, we show that the Sahoo-Sen soft photon theorem
\cite{1808.03288} for loop amplitudes is equivalent to an asymptotic
conservation law. This asymptotic charge is directly related to the dressing of
fields due to long range forces exclusively present in four spacetime
dimensions. In presence of gravity, the new feature is that soft photons also
acquire a dressing due to long range gravitational force and this dressing
contributes to the asymptotic charge. |
State of a particle pair produced by the Schwinger effect is not
necessarily a maximally entangled Bell state: We analyze the spins of a Schwinger particle pair in a spatially uniform but
time dependent electric field. The particle pair's spins are in the maximally
entangled Bell state only if the particles' momenta are parallel to the
electric field. However if transverse momentum is present, the spins are not in
the maximally entangled Bell state. The reason is that the pair is created by
the external field, which also carries angular momentum, and the particle pair
can take away some of this external angular momentum. | Celestial Liouville Theory for Yang-Mills Amplitudes: We consider Yang-Mills theory with the coupling constant and theta angle
determined by the vacuum expectation values of a dynamical (complex) dilaton
field. We discuss the tree-level N-gluon MHV scattering amplitudes in the
presence of a nontrivial background dilaton field and construct the
corresponding celestial amplitudes by taking Mellin transforms with respect to
the lightcone energies. In this way, we obtain two-dimensional CFT correlators
of primary fields on the celestial sphere. We show that the celestial
Yang-Mills amplitudes evaluated in the presence of a spherical dilaton
shockwave are given by the correlation functions of primary field operators
factorized into the holomorphic current operators times the "light" Liouville
operators. They are evaluated in the semiclassical limit of Liouville theory
(the limit of infinite central charge) and are determined by the classical
Liouville field describing metrics on the celestial sphere. |
Vafa-Witten theorem and Lee-Yang singularities: We prove the analyticity of the finite volume QCD partition function for
complex values of the theta-vacuum parameter. The absence of singularities
different from Lee-Yang zeros only permits ^ cusp singularities in the vacuum
energy density and never v cusps. This fact together with the Vafa-Witten
diamagnetic inequality implies the vanishing of the density of Lee-Yang zeros
at theta=0 and has an important consequence: the absence of a first order phase
transition at theta=0. The result provides a key missing link in the
Vafa-Witten proof of parity symmetry conservation in vector-like gauge theories
and follows from renormalizability, unitarity, positivity and existence of BPS
bounds. Generalizations of this theorem to other physical systems are also
discussed, with particular interest focused on the non-linear CPn sigma model. | Laplacians on discrete and quantum geometries: We extend discrete calculus for arbitrary ($p$-form) fields on embedded
lattices to abstract discrete geometries based on combinatorial complexes. We
then provide a general definition of discrete Laplacian using both the primal
cellular complex and its combinatorial dual. The precise implementation of
geometric volume factors is not unique and, comparing the definition with a
circumcentric and a barycentric dual, we argue that the latter is, in general,
more appropriate because it induces a Laplacian with more desirable properties.
We give the expression of the discrete Laplacian in several different sets of
geometric variables, suitable for computations in different quantum gravity
formalisms. Furthermore, we investigate the possibility of transforming from
position to momentum space for scalar fields, thus setting the stage for the
calculation of heat kernel and spectral dimension in discrete quantum
geometries. |
Quantum Distillation of Hilbert Spaces, Semi-classics and Anomaly
Matching: A symmetry-twisted boundary condition of the path integral provides a
suitable framework for the semi-classical analysis of nonperturbative quantum
field theories (QFTs), and we reinterpret it from the viewpoint of the Hilbert
space. An appropriate twist with the unbroken symmetry can potentially produce
huge cancellations among excited states in the state-sum, without affecting the
ground states; we call this effect "quantum distillation". Quantum distillation
can provide the underlying mechanism for adiabatic continuity, by preventing a
phase transition under $S^1$ compactification. We revisit this point via the 't
Hooft anomaly matching condition when it constrains the vacuum structure of the
theory on $\mathbb{R}^d$ and upon compactification. We show that there is a
precise relation between the persistence of the anomaly upon compactification,
the Hilbert space quantum distillation, and the semi-classical analysis of the
corresponding symmetry-twisted path integrals. We motivate quantum distillation
in quantum mechanical examples, and then study its non-trivial action in QFT,
with the example of the 2D Grassmannian sigma model $\mathrm{Gr}(N,M)$. We also
discuss the connection of quantum distillation with large-$N$ volume
independence and flavor-momentum transmutation. | On strong coupling in nonrelativistic general covariant theory of
gravity: We study the strong coupling problem in the Horava-Melby-Thompson setup of
the Horava-Lifshitz gravity with an arbitrary coupling constant $\lambda$,
generalized recently by da Silva, where $\lambda$ describes the deviation of
the theory in the infrared from general relativity that has $\lambda_{GR} = 1$.
We find that a scalar field in the Minkowski background becomes strong coupling
for processes with energy higher than $\Lambda_{\omega} [\equiv
(M_{pl}/c_1)^{3/2} M_{pl}|\lambda - 1|^{5/4}]$, where generically $c_1 \ll
M_{pl}$. However, this problem can be cured by introducing a new energy scale
$M_{*}$, so that $M_{*} < \Lambda_{\omega}$, where $M_{*}$ denotes the
suppression energy of high order derivative terms of the theory. |
Comments on Holographic Entanglement Entropy and RG Flows: Using holographic entanglement entropy for strip geometry, we construct a
candidate for a c-function in arbitrary dimensions. For holographic theories
dual to Einstein gravity, this c-function is shown to decrease monotonically
along RG flows. A sufficient condition required for this monotonic flow is that
the stress tensor of the matter fields driving the holographic RG flow must
satisfy the null energy condition over the holographic surface used to
calculate the entanglement entropy. In the case where the bulk theory is
described by Gauss-Bonnet gravity, the latter condition alone is not sufficient
to establish the monotonic flow of the c-function. We also observe that for
certain holographic RG flows, the entanglement entropy undergoes a 'phase
transition' as the size of the system grows and as a result, evolution of the
c-function may exhibit a discontinuous drop. | Trivializing and Orbifolding the Conifold's Base: The conifold is a cone over the space T^11, which is known to be
topologically S^2xS^3. The coordinates used in the literature describe a
sphere-bundle which can be proven to be topologically trivializable. We provide
an explicit trivialization of this bundle, with simultaneous global coordinates
for both spheres. Using this trivialization we are able to describe the
topology of the base of several infinite families of chiral and non-chiral
orbifolds of the conifold. We demonstrate that in each case the 2nd Betti
number of the base matches the number of independent ranks in the dual quiver
gauge theory. |
Pulsating strings with mixed three-form flux: Circular strings pulsating in $AdS_3 \times S^3 \times T^4$ with mixed R-R
and NS-NS three-form fluxes can be described by an integrable deformation of
the one-dimensional Neumann-Rosochatius mechanical model. In this article we
find a general class of pulsating solutions to this integrable system that can
be expressed in terms of elliptic functions. In the limit of strings moving in
$AdS_{3}$ with pure NS-NS three-form flux, where the action reduces to the
$SL(2,\mathbb{R})$ WZW model, we find agreement with the analysis of the
classical solutions of the system performed using spectral flow by Maldacena
and Ooguri. We use our elliptic solutions in $AdS_{3}$ to extend the dispersion
relation beyond the limit of pure NS-NS flux. | General Covariance Constraints on Cosmological Correlators: We study the extent to which diffeomorphism invariance restricts the
properties of the primordial perturbations in single scalar field models. We
derive a set of identities that constrain the connected correlators of the
cosmological perturbations, as well as the one-particle-irreducible vertices of
the theory in any gauge. These identities are the analogues of Slavnov-Taylor
identities in gauge theories, and follow essentially from diffeomorphism
invariance alone. Yet because quantization requires diffeomorphism invariance
to be broken, they not only reflect invariance under diffeomorphisms, but also
how the latter has been broken by gauge fixing terms. In order to not lose the
symmetry altogether, we cannot simply set some fields to zero, as is usually
done in cosmological perturbation theory, but need to decouple them smoothly
and make sure that they do not contribute to cosmological correlators in the
decoupling limit. We use these identities to derive a set of consistency
relations between bispectra and power spectra of cosmological perturbations in
different gauges. Without additional assumptions, these consistency relations
just seem to reflect the redundancy implied by diffeomorphisms. But when
combined with analyticity, in a formulation of the theory in which auxiliary
fields have been integrated out, we recover novel and previously derived
relations that follow from invariance under both time and spatial
diffeomorphisms. |
An Orientifold from F Theory: The massless spectrum of an orientifold of the IIB string theory is computed
and shown to be identical to F theory on the Calabi-Yau threefold with
$h_{11}=51$ and $h_{21}=3$. Target space duality is also considered in this
model. | Vertex Operators for the Supermembrane and Background Field Matrix
Theory: We derive the vertex operators that are expected to govern the emission of
the massless d=11 supermultiplet from the supermembrane in the light cone
gauge. Our results immediately imply the linear coupling of matrix theory to an
arbitrary supergravity background to all orders in anticommuting coordinates.
Finally we address the definition of n-point tree level and one-loop scattering
amplitudes. The resulting 3-point tree level amplitudes turn out to agree with
d=11 supergravity and are completely fixed by supersymmetry and the existence
of a normalizable ground state. |
Consistent actions for massive particles interacting with
electromagnetism and gravity: Consistent interactions with electromagnetism and gravity for mass $m$
particles of any spin are obtained. This is done by finding interactions which
preserve the covariantized massive gauge symmetry present in recently
constructed massive particle actions. This gauge principle is sufficient for
finding consistent completions of minimal as well as non-minimal couplings of
any type. For spins $s\geq 3/2$, consistency requires infinitely many
interaction terms in the action, including arbitrarily high order derivatives
of electromagnetic and gravitational curvatures, with correspondingly high
powers of $1/m$. These interactions may be formally resummed and expressed in
terms of non-local operators. The inherent non-locality is a manifestation of
the known causality problems present in interacting massive particles with spin
$s\geq 3/2$. | QFT Entanglement Entropy, 2D Fermion and Gauge Fields: Entanglement and the R\'enyi entropies for Dirac fermions on 2 dimensional
torus in the presence of chemical potential, current source, and topological
Wilson loop are unified in a single framework by exhausting all the ingredients
of the electromagnetic vertex operators of $\mathbb{Z}_n$ orbifold conformal
field theory. We employ different normalizations for different topological
sectors to organize various topological phase transitions in the context of
entanglement entropy. Pictorial representations for the topological transitions
are given for the $n=2$ R\'enyi entropy.
Our analytic computations reveal numerous novelties and provide resolutions
for existing issues. We have settled to provide non-singular entanglement
entropies that are also continuous across the topological sectors.
Surprisingly, in infinite space, these entropies become exact and depend only
on the Wilson loop. On a circle, we resolve to find the entropies subtly depend
on the chemical potential at zero temperature, which is useful for probing the
ground state energy levels of quantum systems. |
3d N=1 effective supergravity and F-theory from M-theory on fourfolds: We consider 3d N=1 M-theory compactifications on Calabi-Yau fourfolds, and
the effective 3d theory of light modes obtained by reduction from eleven
dimensions. We study in detail the mass spectrum at the vacuum and, by
decoupling the massive multiplets, we derive the effective 3d N=1 theory in the
large-volume limit up to quartic fermion terms. We show that in general it is
an ungauged N=1 supergravity of the form expected from 3d supersymmetry. In
particular the massless bosonic fields consist of the volume modulus and the
axions originating from the eleven-dimensional three-form, while the
moduli-space metric is locally isometric to hyperbolic space. We consider the
F-theory interpretation of the 3d N=1 M-theory vacua in the light of the
F-theory effective action approach. We show that these vacua generally have
F-theory duals with circle fluxes, thus breaking 4d Poincar\'e invariance. | Non-uniqueness, Counterrotation, and Negative Horizon Mass of
Einstein-Maxwell-Chern-Simons Black Holes: Stationary black holes in 5-dimensional Einstein-Maxwell-Chern-Simons theory
possess surprising properties. When considering the Chern-Simons coefficient
$\lambda$ as a parameter, two critical values of $\lambda$ appear: the
supergravity value $\lambda_{\rm SG}=1$, and the value $\lambda=2$. At
$\lambda=1$, supersymmetric black holes with vanishing horizon angular
velocity, but finite angular momentum exist. As $\lambda$ increases beyond
$\lambda_{\rm SG}$ a rotational instability arises, and counterrotating black
holes appear, whose horizon rotates in the opposite sense to the angular
momentum. Thus supersymmetry is associated with the borderline between
stability and instability. At $\lambda=2$ rotating black holes with vanishing
angular momentum emerge. Beyond $\lambda=2$ black holes may possess a negative
horizon mass, while their total mass is positive. Charged rotating black holes
with vanishing gyromagnetic ratio appear, and black holes are no longer
uniquely characterized by their global charges. |
Closed universes in two dimensional gravity: We study closed universes in simple models of two dimensional gravity, such
as Jackiw-Teiteilboim (JT) gravity coupled to matter, and a toy topological
model that captures the key features of the former. We find there is a stark
contrast, as well as some connections, between the perturbative and
non-perturbative aspects of the theory. We find rich semi-classical physics.
However, when non-perturbative effects are included there is a unique closed
universe state in each theory. We discuss possible meanings and interpretations
of this observation. | Electromagnetic Force on a Brane: A fundamental assumption in the theory of brane world is that all matter and
radiation are confined on the four-dimensional brane and only gravitons can
propagate in the five-dimensional bulk spacetime. The brane world theory did
not provide an explanation for the existence of electromagnetic fields and the
origin of the electromagnetic field equation. In this paper, we propose a model
for explaining the existence of electromagnetic fields on a brane and deriving
the electromagnetic field equation. Similar to the case in Kaluza-Klein theory,
we find that electromagnetic fields and the electromagnetic field equation can
be derived from the five-dimensional Einstein field equation. However, the
derived electromagnetic field equation differs from the Maxwell equation by
containing a term with the electromagnetic potential vector coupled to the
spacetime curvature tensor. So it can be considered as generalization of the
Maxwell equation in a curved spacetime. The gravitational field equation on the
brane is also derived with the stress-energy tensor for electromagnetic fields
explicitly included and the Weyl tensor term explicitly expressed with matter
fields and their derivatives in the direction of the extra-dimension. The model
proposed in the paper can be regarded as unification of electromagnetic and
gravitational interactions in the framework of brane world theory. |
Spin Observables and Path Integrals: We discuss the formulation of spin observables associated to a
non-relativistic spinning particles in terms of grassmanian differential
operators. We use as configuration space variables for the pseudo-classical
description of this system the positions $x$ and a Grassmanian vector
$\vec\epsilon$. We consider an explicit discretization procedure to obtain the
quantum amplitudes as path integrals in this superspace. We compute the quantum
action necessary for this description including an explicit expression for the
boundary terms. Finally we shown how for simple examples, the path integral may
be performed in the semi-classical approximation, leading to the correct
quantum propagator. | Quantization of the tachyonic field: A consistent quantization scheme for imaginary-mass field is proposed. It is
related to an appriopriate choice of the synchronization procedure (definition
of time), which guarantee an absolute causality. In that formulation a possible
existence of field exctitations (tachyons) distinguish an inertial frame
(tachyon privileged frame of reference) via spontaneous breaking of the so
called synchronization group. |
The joy of factorization at large $N$: five-dimensional indices and AdS
black holes: We discuss the large $N$ factorization properties of five-dimensional
supersymmetric partition functions for CFT with a holographic dual. We consider
partition functions on manifolds of the form $\mathcal{M}= \mathcal{M}_3 \times
S^2_\epsilon$, where $\epsilon$ is an equivariant parameter for rotation. We
show that, when $\mathcal{M}_3$ is a squashed three-sphere, the large $N$
partition functions can be obtained by gluing elementary blocks associated with
simple physical quantities. The same is true for various observables of the
theories on $\mathcal{M}_3=\Sigma_\mathfrak{g} \times S^1$, where
$\Sigma_\mathfrak{g}$ is a Riemann surface of genus $\mathfrak{g}$, and, with a
natural assumption on the form of the saddle point, also for the partition
function, corresponding to either the topologically twisted index or a mixed
one. This generalizes results in three and four dimensions and correctly
reproduces the entropy of known black objects in AdS$_6 \times_{w} S^4$ and
AdS$_7\times S^4$. We also provide the supersymmetric background and explicitly
perform localization for the mixed index on $\Sigma_\mathfrak{g} \times S^1
\times S^2_\epsilon$, filling a gap in the literature. | New Supersymmetric String Compactifications: We describe a new class of supersymmetric string compactifications to 4d
Minkowski space. These solutions involve type II strings propagating on
(orientifolds of) non Calabi-Yau spaces in the presence of background NS and RR
fluxes. The simplest examples have descriptions as cosets, generalizing the
three-dimensional nilmanifold. They can also be thought of as twisted tori. We
derive a formula for the (super)potential governing the light fields, which is
generated by the fluxes and certain ``twists'' in the geometry. Detailed
consideration of an example also gives strong evidence that in some cases,
these exotic geometries are related by smooth transitions to standard
Calabi-Yau or G2 compactifications of M-theory. |
3 Dimensional N=8 Supersymmetric Field Theory Revisited: Inspired by ideas regarding Hermitian NxN matrix fields obeying a
non-associative algebra, 3-dimensional N=8 SUSic field theories are proposed to
on-shell represent subalgebras of OSp(8|2) and OSp(8|4) groups of SUSY
transformations. They are theories of 8 scalar and 8 spinor fields with Yukawa,
quartic and sextic self-interactions. The actions as their R-symmetry exhibit
only SO(7) or SO(4)xSO(4) subgroups of full SO(8) automorphisms. It is argued
that the number of degrees of freedom scale like N^{3/2}. There also exists an
extra S_N permutation symmetry group. | Exact Tachyon Condensation on Noncommutative Torus: We construct the exact noncommutative solutions on tori. This gives an exact
description of tachyon condensation on bosonic D-branes, non-BPS D-branes and
brane-antibrane systems. We obtain various bound states of D-branes after the
tachyon condensation. Our results show that these solutions can be generated by
applying the gauge Morita equivalence between the constant curvature projective
modules. We argue that there is a general framework of the noncommutative
geometry based on the notion of Morita equivalence which underlies this
specific example. |
Discrete spacetime symmetries and particle mixing in non-Hermitian
scalar quantum field theories: We discuss second quantization, discrete symmetry transformations and inner
products in free non-Hermitian scalar quantum field theories with PT symmetry,
focusing on a prototype model of two complex scalar fields with anti-Hermitian
mass mixing. Whereas the definition of the inner product is unique for theories
described by Hermitian Hamiltonians, its formulation is not unique for
non-Hermitian Hamiltonians. Energy eigenstates are not orthogonal with respect
to the conventional Dirac inner product, so we must consider additional
discrete transformations to define a positive-definite norm. We clarify the
relationship between canonical-conjugate operators and introduce the additional
discrete symmetry C', previously introduced for quantum-mechanical systems, and
show that the C'PT inner product does yield a positive-definite norm, and hence
is appropriate for defining the Fock space in non-Hermitian models with PT
symmetry in terms of energy eigenstates. We also discuss similarity
transformations between PT-symmetric non-Hermitian scalar quantum field
theories and Hermitian theories, showing that they would require modification
in the presence of interactions. As an illustration of our discussion, we
compare particle mixing in a Hermitian theory and in the corresponding
non-Hermitian model with PT symmetry, showing how the latter maintains
unitarity and exhibits mixing between scalar and pseudoscalar bosons. | Using nanokelvin quantum thermometry to detect timelike Unruh effect in
a Bose-Einstein condensate: It is found that the Unruh effect can not only arise out of the entanglement
between two sets of modes spanning the left and right Rindler wedges, but also
between modes spanning the future and past light cones. Furthermore, an
inertial Unruh-DeWitt detector along a spacetime trajectory in one of these
cones may exhibit the same thermal response to the vacuum as that of an
accelerated detector confined in the Rindler wedge. This feature thus could be
an alternative candidate to verify the ``Unruh effect", termed as the timelike
Unruh effect correspondingly. In this paper we propose to detect the timelike
Unruh effect by using an impurity immersed in a Bose-Einstein condensate (BEC).
The impurity acts as the detector which interacts with the density fluctuations
in the condensate, working as an effective quantum field. Following the
paradigm of the emerging field of quantum thermometry, we combine quantum
parameter estimation theory with the theory of open quantum systems to realize
a nondemolition Unruh temperature measurement in the nanokelvin (nK) regime.
Our results demonstrate that the timelike Unruh effect can be probed using a
stationary two-level impurity with time-dependent energy gap immersed in a BEC
within current technologies. |
Kac-Moody Extensions of 3-Algebras and M2-branes: We study the 3-algebraic structure involved in the recently shown M2-branes
worldvolume gauge theories. We first extend an arbitrary finite dimensional
3-algebra into an infinite dimensional 3-algebra by adding a mode number to
each generator. A unique central charge in the algebra of gauge transformations
appears naturally in this extension. We present an infinite dimensional
extended 3-algebra with a general metric and also a different extension with a
Lorentzian metric. We then study ordinary finite dimensional 3-algebras with
different signatures of the metric, focusing on the cases with a negative
eigenvalue and the cases with a zero eigenvalue. In the latter cases we present
a new algebra, whose corresponding theory is a decoupled abelian gauge theory
together with a free theory with global gauge symmetry, and there is no
negative kinetic term from this algebra. | Decomposing Instantons in Two Dimensions: We study BPS string-like solutions in the 3+1 dimensional gauged CP(1)
non-linear sigma model. The same analysis can be applied to study instantons in
2 euclidean dimensions. We use the moduli matrix approach to construct
analytically the moduli space and and solve numerically the BPS equations. We
identify two topologically inequivalent type of magnetic vortices, which we
call S and N vortices. Moreover we discuss their relation to "lump-string"
solutions present in the un-gauged case. In particular, we describe how a lump
is split into a couple of component S-N vortices after gauging. We extend this
analysis to the case of the extended Abelian Higgs model with two flavors,
which is known to admit semi-local vortices. When we gauge the relative phase
between fields, semi-local vortices are also split into component vortices. We
discuss interesting applications of this simple set-up. First, gauging of
non-linear sigma models reveals a "partonic" nature of instantons in 1+1
dimensions, an idea long studied also in connection with four dimensional
instantons. Second, weak gauging provides for an interesting regularization of
the metric of semi-local vortices which preserves supersymmetry and does not
lift the moduli space of the string. |
Expansion of tree amplitudes for EM and other theories: The expansions of tree-level amplitudes for one theory into amplitudes for
another theory, which have been studied in various recent literatures, exhibit
hidden connections between different theories that are invisible in traditional
Lagrangian formulism of quantum field theory. In this paper, the general
expansion of tree EM (Einstein-Maxwell) amplitudes into KK basis of tree YM
(Yang-Mills) amplitudes have been derived by applying the method based on
differential operators. The obtained coefficients are shared by the expansion
of tree $\phi^4$ amplitudes into tree BS (bi-adjoint scalar) amplitudes, the
expansion of tree sYMS (special Yang-Mills-scalar) amplitudes into tree BS
amplitudes, as well the expansion of tree DBI (Dirac-Born-Infeld) amplitudes
into tree special extended DBI amplitudes. | The Mass Operator in the Light-Cone Representation: I argue that for the case of fermions with nonzero bare mass there is a term
in the matter density operator in the light-cone representation which has been
omitted from previous calculations. The new term provides agreement with
previous results in the equal-time representation for mass perturbation theory
in the massive Schwinger model. For the DLCQ case the physics of the new term
can be represented by an effective operator which acts in the DLCQ subspace,
but the form of the term might be hard to guess and I do not know how to
determine its coefficient from symmetry considerations. |
Two-field Kähler moduli inflation on large volume moduli stabilization: In this paper we present a two-field inflation model, which distinguishes
itself with a non-canonical kinetic lagrangian and comes from the large volume
approach to the moduli stabilization in flux compactification of type IIB
superstring on a Calabi-Yau orientifold of $h^{(1,2)} > h^{(1,1)}\geq 4$. The
K\"ahler moduli are classified as volume modulus, heavy moduli and two light
moduli. The axion-dilaton, complex structure moduli and all heavy K\"ahler
moduli including the volume modulus are frozen by nonperturbatively corrected
flux superpotential and the $\alpha^\prime$-corrected K\"ahler potential in the
large volume limit. The minimum of the scalar potential at which the heavy
moduli are stabilized provides the dominant potential energy for the survived
light K\"ahler moduli. We consider a simplified case where the axionic
components in the light K\"ahler moduli are further stabilized at the potential
minimum and only the geometrical components are taken as the scalar fields to
drive an assisted-like inflation. For a certain range of moduli stabilization
parameters and inflation initial conditions, we obtain a nearly flat power
spectrum of the curvature perturbation, with $n_s\approx 0.96$ at Hubble-exit,
and an inflationary energy scale of $3 \times 10^{14}$ GeV. In our model,
significant correlation exists between the curvature and isocurvature
perturbations on super-Hubble scales so that at the end of inflation a great
deal of the curvature power spectrum originates from this correlation. | Supersymmetric webs of D3/D5-branes in supergravity: We study webs of D3- and D5-branes in type IIB supergravity. These webs
preserve at least 8 supercharges. By solving the Killing spinor equations we
determine the form of supergravity solutions for the system. We then turn to
the sub-class of the intersecting D3/D5 brane system and elucidate some of its
features. |
Field-Dependent BRST-antiBRST Lagrangian Transformations: We continue our study of finite BRST-antiBRST transformations for general
gauge theories in Lagrangian formalism, initiated in [arXiv:1405.0790[hep-th]
and arXiv:1406.0179[hep-th]], with a doublet $\lambda_{a}$, $a=1,2$, of
anticommuting Grassmann parameters and prove the correctness of the explicit
Jacobian in the partition function announced in [arXiv:1406.0179[hep-th]],
which corresponds to a change of variables with functionally-dependent
parameters $\lambda_{a}=U_{a}\Lambda$ induced by a finite Bosonic functional
$\Lambda(\phi,\pi,\lambda)$ and by the anticommuting generators $U_{a}$ of
BRST-antiBRST transformations in the space of fields $\phi$ and auxiliary
variables $\pi^{a},\lambda$. We obtain a Ward identity depending on the
field-dependent parameters $\lambda_{a}$ and study the problem of gauge
dependence, including the case of Yang--Mills theories. We examine a
formulation with BRST-antiBRST symmetry breaking terms, additively introduced
to the quantum action constructed by the Sp(2)-covariant Lagrangian rules,
obtain the Ward identity and investigate the gauge-independence of the
corresponding generating functional of Green's functions. A formulation with
BRST symmetry breaking terms is developed. It is argued that the gauge
independence of the above generating functionals is fulfilled in the BRST and
BRST-antiBRST settings. These concepts are applied to the average effective
action in Yang--Mills theories within the functional renormalization group
approach. | Argyres-Douglas matter and S-duality: Part II: We study S-duality of Argyres-Douglas theories obtained by compactification
of 6d (2,0) theories of ADE type on a sphere with irregular punctures. The
weakly coupled descriptions are given by the degeneration limit of auxiliary
Riemann sphere with marked points, among which three punctured sphere
represents isolated superconformal theories. We also discuss twisted irregular
punctures and their S-duality. |
On the Form Factors of Relevant Operators and their Cluster Property: We compute the Form Factors of the relevant scaling operators in a class of
integrable models without internal symmetries by exploiting their cluster
properties. Their identification is established by computing the corresponding
anomalous dimensions by means of Delfino--Simonetti--Cardy sum--rule and
further confirmed by comparing some universal ratios of the nearby
non--integrable quantum field theories with their independent numerical
determination. | M-theory resolution of four-dimensional cosmological singularities via
U-duality: We consider cosmological solutions of string and M-theory compactified to
four dimensions by giving a general prescription to construct four-dimensional
modular cosmologies with two commuting Killing vectors from vacuum solutions.
By lifting these solutions to higher dimensions we analyze the existence of
cosmological singularities and find that, in the case of non-closed
Friedmann-Robertson-Walker universes, singularities can be removed from the
higher-dimensional model when only one of the extra dimensions is time-varying.
By studying the moduli space of compactifications of M-theory resulting in
homogeneous cosmologies in four dimensions we show that U-duality
transformations map singular cosmologies into non-singular ones. |
Underlying gauge symmetries of second-class constraints systems: Gauge-invariant systems in unconstrained configuration and phase spaces,
equivalent to second-class constraints systems upon a gauge-fixing, are
discussed. A mathematical pendulum on an $n-1$-dimensional sphere $S^{n-1}$ as
an example of a mechanical second-class constraints system and the O(n)
non-linear sigma model as an example of a field theory under second-class
constraints are discussed in details and quantized using the existence of
underlying dilatation gauge symmetry and by solving the constraint equations
explicitly. The underlying gauge symmetries involve, in general, velocity
dependent gauge transformations and new auxiliary variables in extended
configuration space. Systems under second-class holonomic constraints have
gauge-invariant counterparts within original configuration and phase spaces.
The Dirac's supplementary conditions for wave functions of first-class
constraints systems are formulated in terms of the Wigner functions which
admit, as we show, a broad set of physically equivalent supplementary
conditions. Their concrete form depends on the manner the Wigner functions are
extrapolated from the constraint submanifolds into the whole phase space. | Brane Induced Gravity, its Ghost and the Cosmological Constant Problem: "Brane Induced Gravity" is regarded as a promising framework for addressing
the cosmological constant problem, but it also suffers from a ghost instability
for parameter values that make it phenomenologically viable. We carry out a
detailed analysis of codimension > 2 models employing gauge invariant variables
in a flat background approximation. It is argued that using instead a curved
background sourced by the brane would not resolve the ghost issue, unless a
very specific condition is satisfied (if satisfiable at all). As for other
properties of the model, from an explicit analysis of the 4-dimensional
graviton propagator we extract a mass, a decay width and a momentum dependent
modification of the gravitational coupling for the spin 2 mode. In the flat
space approximation, the mass of the problematic spin 0 ghost is instrumental
in filtering out a brane cosmological constant. The mass replaces a background
curvature that would have had the same function. The optical theorem is used to
demonstrate the suppression of graviton leakage into the uncompactified bulk.
Then, we derive the 4-dimensional effective action for gravity and show that
general covariance is spontaneously broken by the bulk-brane setup. This
provides a natural realization of the gravitational Higgs mechanism. We also
show that the addition of extrinsic curvature dependent terms has no bearing on
linearized brane gravity. |
Fixing the Dilaton with Asymptotically Expensive Physics?: We propose a general mechanism for stabilizing the dilaton against runaway to
weak coupling. The method is based on features of the effective superpotential
which arise for supersymmetric gauge theories which are not asymptotically
free. Consideration of the 2PI effective action for bilinear operators of
matter and gauge superfields allows one to overcome the obstacles to
constructing a nonvanishing superpotential. | Modular bootstrap for D4-D2-D0 indices on compact Calabi-Yau threefolds: We investigate the modularity constraints on the generating series
$h_r(\tau)$ of BPS indices counting D4-D2-D0 bound states with fixed D4-brane
charge $r$ in type IIA string theory compactified on complete intersection
Calabi-Yau threefolds with $b_2 = 1$. For unit D4-brane, $h_1$ transforms as a
(vector-valued) modular form under the action of $SL(2,Z)$ and thus is
completely determined by its polar terms. We propose an Ansatz for these terms
in terms of rank 1 Donaldson-Thomas invariants, which incorporates
contributions from a single D6-anti-D6 pair. Using an explicit overcomplete
basis of the relevant space of weakly holomorphic modular forms (valid for any
$r$), we find that for 10 of the 13 allowed threefolds, the Ansatz leads to a
solution for $h_1$ with integer Fourier coefficients, thereby predicting an
infinite series of DT invariants.For $r > 1$, $h_r$ is mock modular and
determined by its polar part together with its shadow. Restricting to $r = 2$,
we use the generating series of Hurwitz class numbers to construct a series
$h^{an}_2$ with exactly the same modular anomaly as $h_2$, so that the
difference $h_{2}-h^{an}_2$ is an ordinary modular form fixed by its polar
terms. For lack of a satisfactory Ansatz, we leave the determination of these
polar terms as an open problem. |
S-matrix for magnons in the D1-D5 system: We show that integrability and symmetries of the near horizon geometry of the
D1-D5 system determine the S-matrix for the scattering of magnons with
polarizations in AdS3 $\times$ S3 completely up to a phase. Using
semi-classical methods we evaluate the phase to the leading and to the one-loop
approximation in the strong coupling expansion. We then show that the phase
obeys the unitarity constraint implied by the crossing relations to the
one-loop order. We also verify that the dispersion relation obeyed by these
magnons is one-loop exact at strong coupling which is consistent with their BPS
nature. | Manifest calculation and the finiteness of the superstring Feynman
diagrams: The multi-loop amplitudes for the closed, oriented superstring are
represented by finite dimensional integrals of explicit functions calculated
through the super-Schottky group parameters and interaction vertex coordinates
on the supermanifold. The integration region is proposed to be consistent with
the group of the local symmetries of the amplitude and with the unitarity
equations. It is shown that, besides the SL(2) group, super-Schottky group and
modular one, the total group of the local symmetries includes an isomorphism
between sets of the forming group transformations, the period matrix to be the
same. The singular integration configurations are studied. The calculation of
the integrals over the above configurations is developed preserving all the
local symmetries of the amplitude, the amplitudes being free from divergences.
The nullification of the 0-, 1-, 2- and 3-point amplitudes of massless states
is verified. Vanishing the amplitudes for a longitudinal gauge boson is argued. |
Quantum corrections to vortex masses and energies: We study the 2+1 dimensional abelian Higgs model defined on a spatial torus
at critical self-coupling. We propose a method to compute the quantum
contribution to the mass of the ANO vortex and to multi-vortex energies. The
one-loop quantum correction to multi-vortex energies is computed analytically
at the critical value of the torus area (Bradlow limit). For other values of
the area one can set up an expansion around this critical area (Bradlow
parameter expansion). The method is explained and the next-to-leading term
explicitly evaluated. To this order, the resulting energies depend on the torus
periods, but not on the vortex positions. | Finite Pseudo-Riemannian Spectral Triples and The Standard Model: Starting from the formulation of pseudo-Riemannian generalisation of real
spectral triples we develop the data of geometries over finite-dimensional
algebras with indefinite metric and their Riemannian parts. We then discuss the
Standard Model spectral triple in this formalism and interpret the physical
symmetry preserving the lepton number as a shadow of a finite pseudo-Riemannian
structure. |
To the cusp and back: Resurgent analysis for modular graph functions: Modular graph functions arise in the calculation of the low-energy expansion
of closed-string scattering amplitudes. For toroidal world-sheets, they are
${\rm SL}(2,\mathbb{Z})$-invariant functions of the torus complex structure
that have to be integrated over the moduli space of inequivalent tori. We use
methods from resurgent analysis to construct the non-perturbative corrections
arising when the argument of the modular graph function approaches the cusp on
this moduli space. ${\rm SL}(2,\mathbb{Z})$-invariance will in turn strongly
constrain the behaviour of the non-perturbative sector when expanded at the
origin of the moduli space. | Flavoured Large N Gauge Theory in an External Magnetic Field: We consider a D7-brane probe of AdS$_{5}\times S^5$ in the presence of pure
gauge $B$-field. In the dual gauge theory, the $B$-field couples to the
fundamental matter introduced by the D7-brane and acts as an external magnetic
field. The $B$-field supports a 6-form Ramond-Ramond potential on the D7-branes
world volume that breaks the supersymmetry and enables the dual gauge theory to
develop a non-zero fermionic condensate. We explore the dependence of the
fermionic condensate on the bare quark mass $m_{q}$ and show that at zero bare
quark mass a chiral symmetry is spontaneously broken. A study of the meson
spectrum reveals a coupling between the vector and scalar modes, and in the
limit of weak magnetic field we observe Zeeman splitting of the states. We also
observe the characteristic $\sqrt{m_{q}}$ dependence of the ground state
corresponding to the Goldstone boson of spontaneously broken chiral symmetry. |
Causal Dynamical Triangulations without Preferred Foliation: We introduce a generalized version of the Causal Dynamical Triangulations
(CDT) formulation of quantum gravity, in which the regularized, triangulated
path integral histories retain their causal properties, but do not have a
preferred proper-time foliation. An extensive numerical study of the associated
nonperturbative path integral in 2+1 dimensions shows that it can nevertheless
reproduce the emergence of an extended de Sitter universe on large scales, a
key feature of CDT quantum gravity. This suggests that the preferred foliation
normally used in CDT is not a crucial (albeit convenient) part of its
background structure. | Perturbative versus Non-perturbative QFT -- Lessons from the O(3) NLS
Model: The two-point functions of the energy-momentum tensor and the Noether current
are used to probe the O(3) nonlinear sigma model in an energy range below 10^4
in units of the mass gap $m$. We argue that the form factor approach, with the
form factor series trunctated at the 6-particle level, provides an almost exact
solution of the model in this energy range. The onset of the (2-loop)
perturbative regime is found to occur only at energies around $100m$. |
String Landscape and the Standard Model of Particle Physics: In this paper we describe ideas about the string landscape, and how to relate
it to the physics of the Standard Model of particle physics. First, we give a
short status report about heterotic string compactifications. Then we focus on
the statistics of D-brane models, on the problem of moduli stabilization, and
finally on some attempts to derive a probability wave function in moduli space,
which goes beyond the purely statistical count of string vacua. | Hawking Radiation from Kerr-Newman Black Hole and Tunneling Mechanism: We present the derivation of Hawking radiation by using the tunneling
mechanism in a rotating and charged black hole background. We show that the
4-dimensional Kerr-Newman metric, which has a spherically nonsymmetric
geometry, becomes an effectively 2-dimensional spherically symmetric metric by
using the technique of the dimensional reduction near the horizon. We can thus
readily apply the tunneling mechanism to the nonspherical Kerr and Kerr-Newman
metric. |
BPS jumping loci and special cycles: We study BPS jumping loci, or the subloci in moduli spaces of supersymmetric
string vacua where BPS states come into existence discontinuously. This
phenomenon is distinct from wall-crossing. We argue that these loci should be
thought of as special cycles in the sense of Noether-Lefschetz loci or special
Shimura subvarieties, which are indeed examples of BPS jumping loci for certain
string compactifications. We use the Hodge-elliptic genus as an informative
tool, suggesting that our work can be extended to understand the jumping
behavior of motivic Donaldson-Thomas invariants. | Quantum Analytic Langlands Correspondence: The analytic Langlands correspondence describes the solution to the spectral
problem for the quantised Hitchin Hamiltonians. It is related to the S-duality
of $\cal{N}=4$ super Yang-Mills theory. We propose a one-parameter deformation
of the Analytic Langlands Correspondence, and discuss its relations to quantum
field theory. The partition functions of the $H_3^+$ WZNW model are interpreted
as the wave-functions of a spherical vector in the quantisation of complex
Chern-Simons theory. Verlinde line operators generate a representation of two
copies of the quantised skein algebra on generalised partition functions. We
conjecture that this action generates a basis for the underlying Hilbert space,
and explain in which sense the resulting quantum theory represents a
deformation of the Analytic Langlands Correspondence. |
A Gravitino Distance Conjecture: We conjecture that in a consistent supergravity theory with non-vanishing
gravitino mass, the limit $m_{3/2}\rightarrow 0$ is at infinite distance. In
particular one can write $M_{\mathrm{tower}} \sim m_{3/2}^\delta$ so that as
the gravitino mass goes to zero, a tower of KK states as well as emergent
strings becomes tensionless. This conjecture may be motivated from the Weak
Gravity Conjecture as applied to strings and membranes and implies in turn the
AdS Distance Conjecture. We test this proposal in classical 4d type IIA
orientifold vacua in which one obtains a range of values $\tfrac13 \le \delta
\le 1$. The parameter $\delta$ is related to the scale decoupling exponent in
AdS vacua and to the $\alpha$ exponent in the Swampland Distance Conjecture for
the type IIA complex structure. We present a general analysis of the gravitino
mass in the limits of moduli space in terms of limiting Mixed Hodge Structures
and study in some detail the case of two-moduli F-theory settings. Moreover, we
obtain general lower bounds $\delta\, \geq \, \frac{1}{3}, \, \frac{1}{4}$ for
Calabi--Yau threefolds and fourfolds, respectively. The conjecture has
important phenomenological implications. In particular we argue that low-energy
supersymmetry of order 1 TeV is only obtained if there is a tower of KK states
at an intermediate scale, of order $10^8$ GeV. One also has an upper bound for
the Hubble constant upon inflation $H \lesssim m_{3/2}^\delta
M^{(1-\delta)}_{\text{P}}$. | Marginally Trapped Surfaces and AdS/CFT: It has been proposed that the areas of marginally trapped or anti-trapped
surfaces (also known as leaves of holographic screens) may encode some notion
of entropy. To connect this to AdS/CFT, we study the case of marginally trapped
surfaces anchored to an AdS boundary. We establish that such boundary-anchored
leaves lie between the causal and extremal surfaces defined by the anchor and
that they have area bounded below by that of the minimal extremal surface. This
suggests that the area of any leaf represents a coarse-grained von Neumann
entropy for the associated region of the dual CFT. We further demonstrate that
the leading area-divergence of a boundary-anchored marginally trapped surface
agrees with that for the associated extremal surface, though subleading
divergences generally differ. Finally, we generalize an argument of Bousso and
Engelhardt to show that holographic screens with all leaves anchored to the
same boundary set have leaf-areas that increase monotonically along the screen,
and we describe a construction through which this monotonicity can take the
more standard form of requiring entropy to increase with boundary time. This
construction is related to what one might call future causal holographic
information, which in such cases also provides an upper bound on the area of
the associated leaves. |
Constrained Spin Systems and KNdS Black Holes: Kerr-Newman de Sitter (KNdS) spacetimes have a rich thermodynamic structure
that involves multiple horizons, and so differs in key respects from
asymptotically flat or AdS black holes. In this paper, we show that certain
features of KNdS spacetimes can be reproduced by a constrained system of $N$
non-interacting spins in a magnetic field. Both the KNdS and spin systems have
bounded energy and entropy, a maximum of the entropy in the interior of the
energy range, and a symmetry that maps lower energy states to higher energy
states with the same entropy. Consequently, both systems have a temperature
that can be positive or negative, where the gravitational temperature is
defined analogously to that of the spins. We find that the number of spins $N$
corresponds to $1/\Lambda$ for black holes with very small charge $q$ and
rotation parameter $a$, and scales like $\sqrt{(a^2+q^2)/\Lambda}$ for larger
values of $a$ and $q$. By studying constrained spin systems, we provide insight
into the thermodynamics of KNdS spacetimes and its quantum mechanical
description. | Holographic Renormalization of 3D Minimal Massive Gravity: We study holographic renormalization of 3D minimal massive gravity using the
Chern-Simons-like formulation of the model. We explicitly present Gibbons-
Hawking term as well as all counterterms needed to make the action finite in
terms of dreibein and spin-connection. This can be used to find correlation
functions of stress tensor of holographic dual field theory. |
On gravity dual of a metastable vacuum in Klebanov-Strassler theory: We discuss a supergravity description of the metastable state that is created
by a stack of anti-D3-branes placed at the tip of the KS background. When the
number p of the anti-D3-branes is large g_s p >> 1 the characteristic curvature
of the corresponding gravity dual is large in stringy units and one may expect
the background to be regular everywhere. Starting from the distances of order R
~ (g_s p)^{1/4} away from the tip the new background can be well approximated
by a linear perturbation around KS. By applying the appropriate boundary
conditions in both IR and UV we found the lowest KK mode of the corresponding
linear perturbation. The solution we found contains VEVs of the SU(2)x SU(2)
invariant operators at the linear order in p. As a non-trivial check we
calculate the ADM mass which exactly matches the probe approximation. As a
byproduct we also found a gravity background dual to the KS theory deformed by
the operators W^2 and W^2\bar{W}^2 with small coefficients. | The structure of maximally supersymmetric Yang-Mills theory:
constraining higher-order corrections: We solve the superspace Bianchi identities for ten-dimensional supersymmetric
Yang-Mills theory without imposing any kind of constraints apart from the
standard conventional one. In this way we obtain a set of algebraic conditions
on certain fields which in the on-shell theory are constructed as composite
ones out of the physical fields. These conditions must hence be satisfied by
any kind of theory in ten dimensions invariant under supersymmetry and some,
abelian or non-abelian, gauge symmetry. Deformations of the ordinary SYM theory
(as well as the fields) are identified as elements of a certain spinorial
cohomology, giving control over field redefinitions and the distinction between
physically relevant higher-order corrections and those removable by field
redefinitions. The conditions derived severely constrain theories involving
F^2-level terms plus higher-order corrections, as for instance those derived
from open strings as effective gauge theories on D-branes. |
Nernst branes in gauged supergravity: We study static black brane solutions in the context of N = 2 U(1) gauged
supergravity in four dimensions. Using the formalism of first-order flow
equations, we construct novel extremal black brane solutions including examples
of Nernst branes, i.e. extremal black brane solutions with vanishing entropy
density. We also discuss a class of non-extremal generalizations which is
captured by the first-order formalism. | Axion electrodynamics: Green's functions, zero-point energy and optical
activity: Starting from the theory of Axion Electrodynamics, we work out the axionic
modifications to the electromagnetic Casimir energy using the Green's function,
both when the axion field is initially assumed purely time-dependent and when
the axion field configuration is a static domain wall. For the first case it
means that the oscillating axion background is taken to resemble an axion fluid
at rest in a conventional Casimir setup with two infinite parallel conducting
plates, while in the second case we evaluate the radiation pressure acting on
an axion domain wall. We extend previous theories in order to include finite
temperatures. Various applications are discussed. 1. We review the theory of
Axion Electrodynamics and particularly the energy-momentum conservation in a
linear dielectric and magnetic material. We treat this last aspect by extending
former results by Brevik and Chaichian (2022) and Patkos (2022). 2. Adopting
the model of the oscillating axion background we discuss the axion-induced
modifications to the Casimir force between two parallel plates by using a
Green's function approach. 3. We calculate the radiation pressure acting on an
axion domain wall at finite temperature T. Our results for an oscillating axion
field and a domain wall are also useful for condensed matter physics, where
"axionic topological insulators" interact with the electromagnetic field with a
Chern-Simons interaction, like the one in Axion Electrodynamics, and there are
experimental systems analogous to time-dependent axion fields and domain walls
as the ones showed by Jiang, Q. D., \& Wilczek, F. (2019) and Fukushima et al.
(2019). 4. We compare our results, where we assume time-dependent or
space-dependent axion configurations, with the discussion of the optical
activity of Axion Electrodynamics by Sikivie (2021) and Carrol et al. (1990). |
Non-Abelian aether-like term in four dimensions: The non-Abelian aether-like Lorentz-breaking term, involving triple and
quartic self-coupling vertices, is generated from the non-Abelian
generalization of the Lorentz-breaking extended QED including only a minimal
spinor-vector interaction. This term is shown explicitly to be finite and
non-ambiguous. | Universal shocks in random matrix theory: We link the appearance of universal kernels in random matrix ensembles to the
phenomenon of shock formation in some fluid dynamical equations. Such equations
are derived from Dyson's random walks after a proper rescaling of the time. In
the case of the Gaussian Unitary Ensemble, on which we focus in this letter, we
show that the orthogonal polynomials, and their Cauchy transforms, evolve
according to a viscid Burgers equation with an effective "spectral viscosity"
$\nu_s=1/2N$, where $N$ is the size of the matrices. We relate the edge of the
spectrum of eigenvalues to the shock that naturally appears in the Burgers
equation for appropriate initial conditions, thereby obtaining a new
perspective on universality. |
Compact QED3 with theta term and axionic confining strings: We discuss three dimensional compact QED with a theta term due to an axionic
field. The variational gauge invariant functional is considered and it is shown
that the ground state energy is independent of theta in a leading
approximation. The mass gap of the axionic field is found to be dependent upon
theta, the mass gap of the photon field and the scalar potential. The vacuum
expectation of the Wilson loop is shown to be independent of theta in a leading
approximation, to obey the area law and to lead to confinement. We also briefly
discuss the properties of axionic confining strings. | Supertranslations and Holographic Stress Tensor: It is well known in the context of four dimensional asymptotically flat
spacetimes that the leading order boundary metric must be conformal to unit de
Sitter metric when hyperbolic cutoffs are used. This situation is very
different from asymptotically AdS settings where one is allowed to choose an
arbitrary boundary metric. The closest one can come to changing the boundary
metric in the asymptotically flat context, while maintaining the group of
asymptotic symmetries to be Poincare, is to change the so-called
`supertranslation frame' \omega. The most studied choice corresponds to taking
\omega = 0. In this paper we study consequences of making alternative choices.
We perform this analysis in the covariant phase space approach as well as in
the holographic renormalization approach. We show that all choices for \omega
are allowed in the sense that the covariant phase space is well defined
irrespective of how we choose to fix supertranslations. The on-shell action and
the leading order boundary stress tensor are insensitive to the
supertranslation frame. The next to leading order boundary stress tensor
depends on the supertranslation frame but only in a way that the transformation
of angular momentum under translations continues to hold as in special
relativity. |
Quantization of U_q[so(2n+1)] with deformed para-Fermi operators: The observation that n pairs of para-Fermi (pF) operators generate the
universal enveloping algebra of the orthogonal Lie algebra so(2n+1) is used in
order to define deformed pF operators. It is shown that these operators are an
alternative to the Chevalley generators. On this background Uq[so(2n+1)] and
its "Cartan-Weyl" generators are written down entirely in terms of deformed pB
operators. | A gauge invariant formulation for the SU(N) non-linear sigma model in
2+1 dimensions: We derive a local, gauge invariant action for the SU(N) non-linear
sigma-model in 2+1 dimensions. In this setting, the model is defined in terms
of a self-interacting pseudo vector-field \theta_\mu, with values in the Lie
algebra of the group SU(N). Thanks to a non-trivially realized gauge
invariance, the model has the correct number of degrees of freedom: only one
polarization of \theta_\mu, like in the case of the familiar Yang-Mills theory
in 2+1 dimensions. Moreover, since \theta_\mu is a pseudo-vector, the physical
content corresponds to one massless pseudo-scalar field in the Lie algebra of
SU(N), as in the standard representation of the model. We show that the
dynamics of the physical polarization corresponds to that of the SU(N)
non-linear sigma model in the standard representation, and also construct the
corresponding BRST invariant gauge-fixed action. |
Kaluza-Klein Aspects of Noncommutative Geometry: Using some elementary methods from noncommutative geometry a structure is
given to a point of space-time which is different from and simpler than that
which would come from extra dimensions. The structure is described by a
supplementary factor in the algebra which in noncommutative geometry replaces
the algebra of functions. Using different examples of algebras it is shown that
the extra structure can be used to describe spin or isospin. | On the universal Representation of the Scattering Matrix of Affine Toda
Field Theory: By exploiting the properties of q-deformed Coxeter elements, the scattering
matrices of affine Toda field theories with real coupling constant related to
any dual pair of simple Lie algebras may be expressed in a completely generic
way. We discuss the governing equations for the existence of bound states, i.e.
the fusing rules, in terms of q-deformed Coxeter elements, twisted q-deformed
Coxeter elements and undeformed Coxeter elements. We establish the precise
relation between these different formulations and study their solutions. The
generalized S-matrix bootstrap equations are shown to be equivalent to the
fusing rules. The relation between different versions of fusing rules and
quantum conserved quantities, which result as nullvectors of a doubly
q-deformed Cartan like matrix, is presented. The properties of this matrix
together with the so-called combined bootstrap equations are utilised in order
to derive generic integral representations for the scattering matrix in terms
of quantities of either of the two dual algebras. We present extensive
case-by-case data, in particular on the orbits generated by the various Coxeter
elements. |
Supersymmetric AdS_3 solutions of type IIB supergravity: For every positively curved Kahler-Einstein manifold in four dimensions we
construct an infinite family of supersymmetric solutions of type IIB
supergravity. The solutions are warped products of AdS_3 with a compact
seven-dimensional manifold and have non-vanishing five-form flux. Via the
AdS/CFT correspondence, the solutions are dual to two-dimensional conformal
field theories with (2,0) supersymmetry. The corresponding central charges are
rational numbers. | Excitation basis for (3+1)d topological phases: We consider an exactly solvable model in 3+1 dimensions, based on a finite
group, which is a natural generalization of Kitaev's quantum double model. The
corresponding lattice Hamiltonian yields excitations located at
torus-boundaries. By cutting open the three-torus, we obtain a manifold bounded
by two tori which supports states satisfying a higher-dimensional version of
Ocneanu's tube algebra. This defines an algebraic structure extending the
Drinfel'd double. Its irreducible representations, labeled by two fluxes and
one charge, characterize the torus-excitations. The tensor product of such
representations is introduced in order to construct a basis for (3+1)d gauge
models which relies upon the fusion of the defect excitations. This basis is
defined on manifolds of the form $\Sigma \times \mathbb{S}_1$, with $\Sigma$ a
two-dimensional Riemann surface. As such, our construction is closely related
to dimensional reduction from (3+1)d to (2+1)d topological orders. |
Three-Charge Supertubes in a Rotating Black Hole Background: The low velocity scattering of a D0-F1 supertube in the background of a BMPV
black hole has been investigated in the moduli space approximation by Marolf
and Virmani. Here we extend the analysis to the case of the D0-D4-F1 supertube
of Bena and Kraus. We find that, similarly to the two-charge case, there is a
critical value of the supertube circumferential angular momentum; above this
value an adiabatic merger with the black hole cannot occur. By reconsidering
the calculation of supertube angular momentum in the transverse direction,
correspondence between the worldvolume and supergravity descriptions is
established. We also examine dynamical mergers and discuss their implications. | Euler top and freedom in supersymmetrization of one-dimensional
mechanics: Recently A.Galajinsky has suggested the N=1 supersymmetric extension of Euler
top and made a few interesting observations on its properties [arXiv:2111.06083
[hep-th]]. In this paper we use the formulation of the Euler top as a system on
complex projective plane, playing the role of phase space, i.e. as a
one-dimensional mechanical system.
Then we suggest the supersymmetrization scheme of the generic one-dimensional
systems with positive Hamiltonian which yields a priori integrable family of
N=2k supersymmetric Hamiltonians parameterized by N/2 arbitrary real functions. |
Black hole phase transitions via Bragg-Williams: We argue that a convenient way to analyze instabilities of black holes in AdS
space is via Bragg-Williams construction of a free energy function. Starting
with a pedagogical review of this construction in condensed matter systems and
also its implementation to Hawking-Page transition, we study instabilities
associated with hairy black holes and also with the $R$-charged black holes.
For the hairy black holes, an analysis of thermal quench is presented. | Island formula in Planck brane: Double holography offers a profound understanding of the island formula by
describing a gravitational system on AdS$_d$ coupled to a conformal field
theory on $\mathbb{R}^{1,d-1}$, dual to an AdS$_{d+1}$ spacetime with an
end-of-the-world (EOW) brane. In this work, we extend the proposal in [A.
Almheiri et al. JHEP 03 (2020) 149] by considering that the dual bulk spacetime
has two EOW branes: one with a gravitational system and the other with a
thermal bath. We demonstrate an equivalence between this proposal and the wedge
holographic theory. We examine it in both Anti-de Sitter gravity and de Sitter
gravity by calculating the entanglement entropy of the Hawking radiation.
Finally, we employ the doubly holographic model to verify the formula for the
entanglement entropy in a subregion within conformally flat spacetime. |
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