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Wick rotation and the positivity of energy in quantum field theory: We propose a new axiom system for unitary quantum field theories on curved
space-time backgrounds, by postulating that the partition function and the
correlators extend analytically to a certain domain of complex-valued metrics.
Ordinary Riemannian metrics are contained in the allowable domain, while
Lorentzian metrics lie on its boundary. | hep-th |
An extended standard model and its Higgs geometry from the matrix model: We find a simple brane configuration in the IKKT matrix model which resembles
the standard model at low energies, with a second Higgs doublet and
right-handed neutrinos. The electroweak sector is realized geometrically in
terms of two minimal fuzzy ellipsoids, which can be interpreted in terms of
four point-branes in the extra dimensions. The electroweak Higgs connects these
branes and is an indispensable part of the geometry. Fermionic would-be zero
modes arise at the intersections with two larger branes, leading precisely to
the correct chiral matter fields at low energy, along with right-handed
neutrinos which can acquire a Majorana mass due to a Higgs singlet. The larger
branes give rise to $SU(3)_c$, extended by $U(1)_B$ and another $U(1)$ which
are anomalous at low energies and expected to disappear. At higher energies,
mirror fermions and additional fields arise, completing the full ${\cal N}=4$
supersymmetry. The brane configuration is a solution of the model, assuming a
suitable effective potential and a non-linear stabilization of the singlet
Higgs. The basic results can be carried over to ${\cal N}=4$ $SU(N)$
super-Yang-Mills on ordinary Minkowski space with sufficiently large $N$. | hep-th |
Casimir Torque in Inhomogeneous Dielectric Plates: In this work, we consider a torque caused by the well known quantum
mechanical Casimir effect arising from quantized field fluctuations between
plates with inhomogeneous, sharply discontinuous, dielectric properties. While
the Casimir effect is a relatively well understood phenomenon, systems
resulting in lateral or rotational forces are far less developed; to our
knowledge, a theoretical study of discontinuous dielectric variants of such
systems has not been attempted. We utilize a Proximity Force Approximation in
conjunction with the Lifshitz dielectric formula to perform theoretical
analyses of resultant torques in systems with bisected and quadrisected
dielectric regions. We also develop a high precision Monte Carlo type numerical
integrator to approximate our derived expressions. Our calculations of an
energy density linear with the alignment angle result in a constant torque and
have implications in NEMS (nano electromechanical systems) and MEMS (micro
electromechanical systems), including a postulated nanoscale oscillating drive
mechanism powered by quantum field interactions. | hep-th |
One-Loop Effective Action on the Four-Ball: This paper applies $\zeta$-function regularization to evaluate the 1-loop
effective action for scalar field theories and Euclidean Maxwell theory in the
presence of boundaries. After a comparison of two techniques developed in the
recent literature, vacuum Maxwell theory is studied and the contribution of all
perturbative modes to $\zeta'(0)$ is derived: transverse, longitudinal and
normal modes of the electromagnetic potential, jointly with ghost modes. The
analysis is performed on imposing magnetic boundary conditions, when the
Faddeev-Popov Euclidean action contains the particular gauge-averaging term
which leads to a complete decoupling of all perturbative modes. It is shown
that there is no cancellation of the contributions to $\zeta'(0)$ resulting
from longitudinal, normal and ghost modes. | hep-th |
Anisotropic Dyonic Black Brane and its Effects on Hydrodynamics: We construct $SL(2,R)$ invariant in anisotropic medium, with a dual
anisotropic charged black hole geometry in massive gravity. We show how to
obtain $SL(2,R)$ elements in terms of new degrees of freedom for
Electromagnetic configuration, and construct the general expressions for
conductivity with $SL(2,R)$ invariant. The holographic conductivities can be
calculated using horizon data in an external magnetic field, and we show the
numerical results using the linear response theory. | hep-th |
$N=2$ Super Yang-Mills and Subgroups of $SL(2,Z)$: We discuss $SL(2,Z)$ subgroups appropriate for the study of $N=2$ Super
Yang-Mills with $N_f=2n$ flavors. Hyperelliptic curves describing such theories
should have coefficients that are modular forms of these subgroups. In
particular, uniqueness arguments are sufficient to construct the $SU(3)$ curve,
up to two numerical constants, which can be fixed by making some assumptions
about strong coupling behavior. We also discuss the situation for higher
groups. We also include a derivation of the closed form $\beta$-function for
the $SU(2)$ and $SU(3)$ theories without matter, and the massless theories with
$N_f=n$. | hep-th |
HS in flat spacetime. The effective action method: This is the first paper in a series of three dealing with HS theories in flat
spacetime. It is divided in three parts. The first part is an elaboration on
the method of effective action, initiated in a previous paper. We study the
properties of correlators of currents in the free fermion coupled to external
higher spin (HS) potentials, and develop techniques for their explicit
calculation. In particular we show how they can be calculated via ordinary
Feynman diagram techniques. We also introduce the concept of {\it curved}
$L_\infty$ algebra and show how it can be realized in the context of the
fermion model. In part II we compare the results of the scalar model and those
of the fermion model (coupled to HS fields). We show that the HS field
formulation coming from the scalar model is the `square' of the one ensuing
from the fermion model. Finally, in part III, we analyze the possible
obstructions that one may meet in constructing the effective action: these are
the analogs of anomalies in ordinary gauge theories. We provide explicit and
compact formulas of the latter. | hep-th |
Supersymmetry Breaking and the Cosmological Constant: I review three attempts to explain the small value of the cosmological
constant, and their connection to SUSY breaking. They are The String Landscape,
Supersymmetric Large Extra Dimensions (SLED), and the Holographic Space-time
Formalism invented by Fischler and myself. | hep-th |
AdS Black Holes with a Bouncing Interior: We construct planar black hole solutions of AdS gravity minimally coupled to
a scalar field with an even, super-exponential potential. We show that the
evolution of the black hole interior exhibits an infinite sequence of Kasner
epochs, as the scalar field rolls back and forth in its potential. We obtain an
analytic expression for the `bounces' between each Kasner epoch and also give
an explicit formula for the times and strengths of the bounces at late interior
times, thereby fully characterizing the interior evolution. In this way we show
that the interior geometry approaches the Schwarzschild singularity at late
times, even as the scalar field is driven higher up its potential with each
bounce. | hep-th |
SDiff(2) Toda equation -- hierarchy, $τ$ function, and symmetries: A continuum limit of the Toda lattice field theory, called the SDiff(2) Toda
equation, is shown to have a Lax formalism and an infinite hierarchy of higher
flows. The Lax formalism is very similar to the case of the self-dual vacuum
Einstein equation and its hyper-K\"ahler version, however now based upon a
symplectic structure and the group SDiff(2) of area preserving diffeomorphisms
on a cylinder $S^1 \times \R$. An analogue of the Toda lattice tau function is
introduced. The existence of hidden SDiff(2) symmetries are derived from a
Riemann-Hilbert problem in the SDiff(2) group. Symmetries of the tau function
turn out to have commutator anomalies, hence give a representation of a central
extension of the SDiff(2) algebra. | hep-th |
Field-theoretic Methods in Strongly-Coupled Models of General Gauge
Mediation: An often-exploited feature of the operator product expansion (OPE) is that it
incorporates a splitting of ultraviolet and infrared physics. In this paper we
use this feature of the OPE to perform simple, approximate computations of soft
masses in gauge-mediated supersymmetry breaking. The approximation amounts to
truncating the OPEs for hidden-sector current-current operator products. Our
method yields visible-sector superpartner spectra in terms of vacuum
expectation values of a few hidden-sector IR elementary fields. We manage to
obtain reasonable approximations to soft masses, even when the hidden sector is
strongly coupled. We demonstrate our techniques in several examples, including
a new framework where supersymmetry-breaking arises both from a hidden sector
and dynamically. | hep-th |
Towards the description of anisotropic plasma at strong coupling: We initiate a study of anisotropic plasma at strong coupling using the
AdS/CFT correspondence. We construct an exact dual geometry which represents a
static uniform but anisotropic system and find, that although it is singular,
it allows for a notion of `incoming' boundary conditions. We study small
fluctuations around this background and find that the dispersion relation
depends crucially on the direction of the wave-vector relative to the shape of
the anisotropy reminiscent of similar behaviour at weak coupling. We do not
find explicit instabilities to the considered order but only a huge difference
in the damping behaviour. | hep-th |
On the "scattering law" for Kasner parameters appearing in asymptotics
of an exact S-brane solution: A multidimensional cosmological model with scalar and form fields [1-4] is
studied. An exact S-brane solution (either electric or magnetic) in a model
with l scalar fields and one antisymmetric form of rank m > 1 is considered.
This solution is defined on a product manifold containing n Ricci-flat factor
spaces M_1, ..., M_n. In the case when the kinetic term for scalar fields is
positive definite we singled out a special solution governed by the function
cosh. It is shown that this special solution has Kasner-like asymptotics in the
limits \tau \to + 0 and \tau \to + \infty, where \tau is a synchronous time
variable. A relation between two sets of Kasner parameters \alpha_{\infty} and
\alpha_0 is found. This relation, named as ``scattering law'' (SL) formula, is
coinciding with the ``collision law'' (CL) formula obtained previously in [5]
in a context of a billiard description of S-brane solutions near the
singularity. A geometric sense of SL formula is clarified: it is shown that SL
transformation is a map of a ``shadow'' part of the Kasner sphere S^{N-2} (N =
n+l) onto ``illuminated'' part. This map is just a (generalized) inversion with
respect to a point v located outside the Kasner sphere S^{N-2}. The shadow and
illuminated parts of the Kasner sphere are defined with respect to a point-like
source of light located at v. Explicit formulae for SL transformations
corresponding to SM2- and SM5-brane solutions in 11-dimensional supergravity
are presented. | hep-th |
Noncommutative quantum mechanics as a constrained system: It is shown that quantum mechanics on noncommutative spaces (NQM) can be
obtained by the canonical quantization of some underlying second class
constrained system formulated in extended configuration space. It leads, in
particular, to an intriguing possibility of quantization in terms of the
initial (noncommutative) variables. Two different formulations are discissed.
The first one is appropriate for at most quadratic potential. The
noncommutativity parameter and rank of matrix of the constraint brackets depend
on the potential. It explains appearance of two phases of the resulting NQM.
The second formulation is appropriate for an arbitrary potential. In both cases
the corresponding Lagrangian action is presented and quantized, which leads to
quantum mechanics with ordinary product replaced by the Moyal product. | hep-th |
Area Operators in Holographic Quantum Gravity: We argue that the holographic formula relating entanglement entropy and the
area of a minimal surface is the key to define the area of surfaces in the
(emergent) spacetime from the dual theory on the boundary. So we promote the
entropy/area relation to operators to define the "area" observable in a
holographic formulation of quantum gravity, then we find a suitable geometric
representation for the states, and show that the Ryu-Takayanagi proposal is
recovered in the approximation of semi-classical gravity. Finally, we discuss
this picture in the example of a AdS-Black hole. | hep-th |
The NSVZ beta-function in supersymmetric theories with different
regularizations and renormalization prescriptions: We briefly review the calculations of quantum corrections related with the
exact NSVZ $\beta$-function in ${\cal N}=1$ supersymmetric theories, paying
especial attention to the scheme dependence of the results. It is explained,
how the NSVZ relation is obtained for the renormalization group functions
defined in terms of the bare coupling constant if a theory is regularized by
higher derivatives. Also we describe, how to construct a special
renormalization prescription which gives the NSVZ relation for the
renormalization group functions defined in terms of the renormalized coupling
constant exactly in all orders for Abelian supersymmetric theories, regularized
by higher derivatives. The scheme dependence of the NSVZ $\beta$-function (for
the renormalization group functions defined in terms of the renormalized
coupling constant) is discussed in the non-Abelian case. It is shown that in
this case the NSVZ $\beta$-function leads to a certain scheme-independent
equality. | hep-th |
Semiclassical circular strings in AdS_5 and "long" gauge field strength
operators: We consider circular strings rotating with equal spins S_1=S_2=S in two
orthogonal planes in AdS_5 and suggest that they may be dual to "long" gauge
theory operators built out of self-dual components of gauge field strength. As
was found in hep-th/0404187, the one-loop anomalous dimensions of the such
gauge-theory operators are described by an anti-ferromagnetic XXX_1 spin chain
and scale linearly with length L>>1. We find that in the case of rigid rotating
string both the classical energy E_0 and the 1-loop string correction E_1
depend linearly on the spin S (within the stability region of the solution).
This supports the relation between the rigid rotating string and the
gauge-theory operator corresponding to the maximal-spin (ferromagnetic) state
of the XXX_1 spin chain. The energy of more general rotating and pulsating
strings also happens to scale linearly with both the spin and the oscillation
number. Such solutions should be dual to other lower-spin states of the spin
chain, with the anti-ferromagnetic ground state presumably corresponding to the
string pulsating in two planes with no rotation. | hep-th |
From black holes to flux throats: polarization can resolve the
singularity: Supersymmetry-breaking is a key ingredient for string theory models to be
phenomenologically viable. We review the strong analogy in the physics and the
methods used for describing non-supersymmetric flux vacua and
non-supersymmetric black holes in string theory. We also show how the polarized
state could be the key to describing a well-behaved back-reaction of
anti-branes in flux backgrounds, shedding a new light on a recent debate in the
literature. | hep-th |
Derivative Expansion of the Effective Action for Massless Scalar
Electrodynamics in Arbitrary Gauge: It is shown how operator regularization can be used to obtain an expansion of
the effective action in powers of derivatives of the background field. This is
applied to massless scalar electrodynamics to find the one-loop corrections to
the kinetic terms associated with both the scalar and vector fields in
arbitrary gauge. This allows us to examine the radiatively induced masses
arising in this model. | hep-th |
On Brane-Antibrane Forces: In this note, we will discuss two aspects of brane-antibrane forces. In one
aspect, we generalize the force calculation of D0-${\bar {\rm D}}$0 of Banks
and Susskind to Dp-${\bar {\rm D}}p$ for $1\le p \leq 8$. In particular, we
find that the force is also divergent for p = 1 while for the other cases ($p
\ge 2$) the forces are in general finite when $Z \to 0^+$, where $Z =
\frac{Y^2}{2\pi^2\alpha'} - 1$ with Y, the brane-antibrane separation. However,
the forces are divergent for all cases when Z < 0, signalling the occurrence of
open string tachyon condensation in this regime. The other deals with the
puzzling static nature of the supergravity brane-antibrane configurations. We
will show that the force on a brane probe due to a brane-antibrane background
vanishes when the probe is placed at the location of the coincident
brane-antibranes, thereby providing a direct evidence for the existence of
general static brane-antibrane configuration in the supergravity approximation. | hep-th |
Background Independent Field Quantization with Sequences of
Gravity-Coupled Approximants II: Metric Fluctuations: We apply the new quantization scheme outlined in Phys. Rev. D102 (2020)
125001 to explore the influence which quantum vacuum fluctuations of the
spacetime metric exert on the universes of Quantum Einstein Gravity, which is
regarded an effective theory here. The scheme promotes the principle of
Background Independence to the level of the regularized precursors of a quantum
field theory ("approximants") and severely constrains admissible regularization
schemes. Without any tuning of parameters, we find that the zero point
oscillations of linear gravitons on maximally symmetric spacetimes do not
create the commonly expected cosmological constant problem of a cutoff-size
curvature. On the contrary, metric fluctuations are found to reduce positive
curvatures to arbitrarily tiny and ultimately vanishing values when the cutoff
is lifted. This suggests that flat space could be the distinguished groundstate
of pure quantum gravity. Our results contradict traditional beliefs founded
upon background-dependent calculations whose validity must be called into
question therefore. | hep-th |
Complex linear superfields, Supercurrents and Supergravities: We present expressions for the supercurrents generated by a generic
$4D,~\mathcal{N}=1$ theory of complex linear superfield $\Sigma$. We verify
that these expressions satisfy the appropriate superspace conservation
equations. Furthermore, we discuss the component projection in order to derive
expressions for the energy-momentum tensor, the supersymmetry current and the
R-symmetry current when available. In addition, we discuss aspects of the
coupling of the theory to supergravity. Specifically, we present a
straightforward method to select the appropriate formulations of supergravity
that one must use in order to do the coupling. This procedure is controlled by
a superfield X originating from the Super-Poincar\'{e} invariance of the
theory. We apply these results to examples of theories with higher derivative
terms. | hep-th |
Some Properties of Open - String Theories: Open-string theories may be related to suitable models of oriented closed
strings. The resulting construction of ``open descendants'' is illustrated in a
few simple cases that exhibit some of its key features. | hep-th |
A Deformation of Sasakian Structure in the Presence of Torsion and
Supergravity Solutions: We discuss a deformation of Sasakian structure in the presence of totally
skew-symmetric torsion by introducing odd dimensional manifolds whose metric
cones are K\"ahler with torsion. It is shown that such a geometry inherits
similar properties to those of Sasakian geometry. As an example of them, we
present an explicit expression of local metrics and see how Sasakian structure
is deformed by the presence of torsion. We also demonstrate that our example of
the metrics admits the existence of hidden symmetries described by non-trivial
odd-rank generalized closed conformal Killing-Yano tensors. Furthermore, using
these metrics as an {\it ansatz}, we construct exact solutions in five
dimensional minimal (un-)gauged supergravity and eleven dimensional
supergravity. Finally, we discuss the global structures of the solutions and
obtain regular metrics on compact manifolds in five dimensions, which give
natural generalizations of Sasaki--Einstein manifolds $Y^{p,q}$ and
$L^{a,b,c}$. We also discuss regular metrics on non-compact manifolds in eleven
dimensions. | hep-th |
One-loop divergences in the Galileon model: The investigation of UV divergences is a relevant step in better
understanding of a new theory. In this work the one-loop divergences in the
free field sector are obtained for the popular Galileons model. The
calculations are performed by the generalized Schwinger-DeWitt technique and
also by means of Feynman diagrams. The first method can be directly generalized
to curved space, but here we deal only with the flat-space limit. We show that
the UV completion of the theory includes the $\pi \Box^4\pi$ term. According to
our previous analysis in the case of quantum gravity, this means that the
theory can be modified to become superrenormalizable, but then its physical
spectrum includes two massive ghosts and one massive scalar with positive
kinetic energy. The effective approach in this theory can be perfectly
successful, exactly as in the higher derivative quantum gravity, and in this
case the non-renormalization theorem for Galileons remains valid in the
low-energy region. | hep-th |
Orbifold instantons, moment maps and Yang-Mills theory with sources: We revisit the problem of constructing instantons on ADE orbifolds R^4/\Gamma
and point out some subtle relations with the complex structure on the orbifold.
We consider generalized instanton equations on R^4/\Gamma which are BPS
equations for the Yang-Mills equations with an external current. The relation
between level sets of the moment maps in the hyper-Kaehler quotient
construction of the instanton moduli space and sources in the Yang-Mills
equations is discussed. We describe two types of spherically-symmetric
\Gamma-equivariant connections on complex V-bundles over R^4/\Gamma which are
tailored to the way in which the orbifold group acts on the fibres. Some
explicit abelian and nonabelian SU(2)-invariant solutions to the nstanton
equations on the orbifold are worked out. | hep-th |
A Variational Perturbation Approach to One-Point Functions in QFT: In this paper, we develop a variational perturbation (VP) scheme for
calculating vacuum expectation values (VEVs) of local fields in quantum field
theories. For a comparatively general scalar field model, the VEV of a
comparatively general local field is expanded and truncated at second order in
the VP scheme. The resultant truncated expressions (we call Gaussian smearing
formulae) consist mainly of Gaussian transforms of the local-field function,
the model-potential function and their derivatives, and so can be used to skip
calculations on path integrals in a concrete theory. As an application, the VP
expansion series of the VEV of a local exponential field in the sine- and
sinh-Gordon field theories is truncated and derived up to second order
equivalently by directly performing the VP scheme, by finishing ordinary
integrations in the Gaussian smearing formulae, and by borrowing Feynman
diagrammatic technique, respectively. Furthermore, the one-order VP results of
the VEV in the two-dimensional sine- and sinh-Gordon field theories are
numerically calculated and compared with the exact results conjectured by
Lukyanov, Zamolodchikov $et al.$, or with the one-order perturbative results
obtained by Poghossian. The comparisons provide a strong support to the
conjectured exact formulae and illustrate non-perturbability of the VP scheme. | hep-th |
On Asymptotic Symmetries of 3d Extended Supergravities: We study asymptotic symmetry algebras for classes of three dimensional
supergravities with and without cosmological constant. In the first part we
generalise some of the non-Dirichlet boundary conditions of $AdS_3$ gravity to
extended supergravity theories, and compute their asymptotic symmetries. In
particular, we show that the boundary conditions proposed to holographically
describe the chiral induced gravity and Liouville gravity do admit extension to
the supergravity contexts with appropriate superalgebras as their asymptotic
symmetry algebras. In the second part we consider generalisation of the 3d
$BMS$ computation to extended supergravities without cosmological constant, and
show that their asymptotic symmetry algebras provide examples of nonlinear
extended superalgebras containing the $BMS_3$ algebra. | hep-th |
Manifestations of Space-Time Multidimensionality in Scattering of Scalar
Particles: We analyze a possibility of experimental detection of the contribution of the
Kaluza-Klein tower of heavy particles to scattering cross-section in a
six-dimensional scalar model with two dimensions being compactified to the
torus with the radii $R$. It is shown that there is a noticeable effect even
for the energies of colliding particles below $R^{-1}$ which may be observed in
future collider experiments if $R^{-1}$ is of the order of $1 TeV$. | hep-th |
Black Holes at Exp-time: Classical GR governs the evolution of black holes for a long time, but at
some exponentially large time it must break down. The breakdown, and what comes
after it, is not well understood. In this paper I'll discuss the problem using
concepts drawn from complexity geometry. In particular the geometric concept of
cut locus plays a key role. | hep-th |
The M-theory Archipelago: We combine supersymmetric localization results and the numerical conformal
bootstrap technique to study the 3d maximally supersymmetric (${\cal N} = 8$)
CFT on $N$ coincident M2-branes (the $U(N)_k \times U(N)_{-k}$ ABJM theory at
Chern-Simons level $k=1$). In particular, we perform a mixed correlator
bootstrap study of the superconformal primaries of the stress tensor multiplet
and of the next possible lowest-dimension half-BPS multiplet that is allowed by
3d ${\cal N} = 8$ superconformal symmetry. Of all known 3d ${\cal N} = 8$
SCFTs, the $k=1$ ABJM theory is the only one that contains both types of
multiplets in its operator spectrum. By imposing the values of the short OPE
coefficients that can be computed exactly using supersymmetric localization, we
are able to derive precise islands in the space of semi-short OPE coefficients
for an infinite number of such coefficients. We find that these islands
decrease in size with increasing $N$. More generally, we also analyze 3d ${\cal
N} = 8$ SCFT that contain both aforementioned multiplets in their operator
spectra without inputing any additional information that is specific to ABJM
theory. For such theories, we compute upper and lower bounds on the semi-short
OPE coefficients as well as upper bounds on the scaling dimension of the lowest
unprotected scalar operator. These latter bounds are more constraining than the
analogous bounds previously derived from a single correlator bootstrap of the
stress tensor multiplet. This leads us to conjecture that the $U(N)_2 \times
U(N+1)_{-2}$ ABJ theory, and not the $k=1$ ABJM theory, saturates the single
correlator bounds. | hep-th |
Anomaly-induced edge currents in hydrodynamics with parity anomaly: In this paper, we discuss relativistic hydrodynamics for a massless Dirac
fermion in $(2+1)$ dimensions, which has the parity anomaly -- a global 't
Hooft anomaly between $\mathrm{U}(1)$ and parity symmetries. We investigate how
hydrodynamics implements the party anomaly, particularly focusing on the
transport phenomena at the boundary. Based on the parity anomaly matching and
the second law of local thermodynamics, we find $\mathrm{U}(1)$ and entropy
currents localized at the boundary as well as the bulk anomalous current with
vanishing divergence. These edge currents are similar to the
$(1+1)$-dimensional chiral transports, but the coefficients are given by half
of theirs. We also generalize our discussion to more general anomalies among
multiple $\mathrm{U}(1)$ symmetries and single $\mathbb{Z}_2$ symmetry. | hep-th |
Aspects of three-dimensional C-metric: In this work, we present an extensive analysis of the thermodynamics and
holographic properties of three-dimensional C-metrics in the FG gauge, where we
find that the free energy is equal to the Euclidean on-shell action with a
generic conformal factor. For the black hole solutions we find that Smarr
relation and the first law of thermodynamics can be formulated when the
contributions of the boundary entropy are considered . We also compute
holographic entanglement entropy following the AdS/BCFT formalism. By comparing
the free energies of different bulk solutions with a fixed flat torus boundary
geometry, we find that a specific type of accelerating black hole is dominant
in the high temperature regime. | hep-th |
Time-dependent AdS/CFT Duality II: Holographic Reconstruction of Bulk
Metric and Possible Resolution of Singularity: We continue the studies of our earlier proposal for an AdS/CFT correspondence
for time-dependent supergravity backgrounds. We note that by performing a
suitable change of variables, the dual super Yang-Mills theory lives on a flat
base space, and the time-dependence of the supergravity background is entirely
encoded in the time-dependent couplings (gauge and axionic) and their
supersymmetric completion. This form of the SYM allows a detailed perturbative
analysis to be performed. In particular the one-loop Wilsonian effective action
of the boundary SYM theory is computed. By using the holographic UV/IR
relation, we propose a way to extract the bulk metric from the Wilsonian
effective action; and we find that the bulk metric of our supergravity
solutions can be reproduced precisely. While the bulk geometry can have various
singularities such as geodesic incompleteness, gauge theory quantum effects can
introduce higher derivative corrections in the effective action which can serve
as a way to resolve the singularities. | hep-th |
Temperature, Topology and Quantum Fields: This thesis uses Path Integrals and Green's Functions to study Gravity,
Quantum Field Theory and Statistical Mechanics, particularly with respect to:
finite temperature quantum systems of different spin in gravitational fields;
finite temperature interacting quantum systems in perturbative regime;
self-interacting fermi models in non-trivial space-time of different
dimensions; non-linear quantum models at finite temperatures in a background
curved space-time; 3-D topological field models in non-trivial space-time and
at finite temperatures; thermal quantum systems in a background curved
space-time. Results include: Non-Equivalence of Inertial and Gravitational
Mass. | hep-th |
Jet suppression in non-conformal plasma using AdS/CFT: In this paper, we study suppression of light quark in strongly coupled
non-conformal plasmas using the AdS/CFT correspondence. The well-known falling
string profile in the bulk is considered as light quark moving through the
plasma. The maximum distance which string with energy E can travel before
falling through the horizon is interpreted as thermalization distance of light
quark in the hot-strongly coupled plasma. Our numerical results show that the
thermalization distance of light quark increases by increasing deviation from
conformal invariance. The relation between this distance and the energy of
quark and the temperature of the plasma is analyzed numerically. The jet
quenching parameter is also calculated in the non-conformal backgrounds and it
is found that the jet quenching parameter is generally decreased by increasing
the non-conformality. Our results are compared with the results of N = 4 SYM
theory and also some available experimental data. | hep-th |
Nambu and the Ising Model: In 2021, to mark the occasion of 2021 was Y\^oichir\^o Nambu's birth
centenary, we engaged in writing a historical/scientific description of his
most incisive papers. Nambu was the humblest genius we have known, and we
expected to find some of his great but forgotten insights. We found one,
written in 1947: ``A Note on the Eigenvalue Problem in Crystal Statistics",
where he formulates and solves the $(N\times N)$ Ising model in a
$2N$-dimensional Hilbert space | hep-th |
Caustics in Self-gravitating N-body systems and Cosmological Large Scale
Structures: In this paper we demonstrate the generation of gravitational caustics that
appear due to the geodesic focusing in a self-gravitating N-body system. The
gravitational caustics are space regions where the density of particles is
higher than the average density in the surrounding space. It is suggested that
the intrinsic mechanism of caustics generation is responsible for the formation
of the cosmological Large Scale Structure that consists of matter
concentrations in the form of galaxies, galactic clusters, filaments, and vast
regions devoid of galaxies.
In our approach the dynamics of a self-gravitating N-body system is
formulated in terms of a geodesic flow on a curved Riemannian manifold of
dimension 3N equipped by the Maupertuis's metric. We investigate the sign of
the sectional curvatures that defines the stability of geodesic trajectories in
different parts of the phase space. The regions of negative sectional
curvatures are responsible for the exponential instability of geodesic
trajectories, deterministic chaos and relaxation phenomena of globular clusters
and galaxies, while the regions of positive sectional curvatures are
responsible for the gravitational geodesic focusing and generation of caustics.
By solving the Jacobi and the Raychaudhuri equations we estimated the
characteristic time scale of generation of gravitational caustics, calculated
the density contrast on the caustics and compared it with the density contrasts
generated by the Jeans-Bonnor-Lifshitz-Khalatnikov gravitational instability
and that of the spherical top-hat model of Gunn and Gott. | hep-th |
N=2 Superstrings with (1,2m) Spacetime Signature: We show that the $N=2$ superstring in $d=2D\ge6$ real dimensions, with
criticality achieved by including background charges in the two real time
directions, exhibits a ``coordinate-freezing'' phenomenon, whereby the momentum
in one of the two time directions is constrained to take a specific value for
each physical state. This effectively removes this time direction as a physical
coordinate, leaving the theory with $(1,d-2)$ real spacetime signature. Norm
calculations for low-lying physical states suggest that the theory is ghost
free. | hep-th |
Flows involving Lifshitz solutions: We construct gravity solutions describing renormalization group flows
relating relativistic and non-relativistic conformal theories. We work both in
a simple phenomenological theory with a massive vector field, and in an N=4,
d=6 gauged supergravity theory, which can be consistently embedded in string
theory. These flows offer some further insight into holography for Lifshitz
geometries: in particular, they enable us to give a description of the field
theory dual to the Lifshitz solutions in the latter theory. We also note that
some of the AdS and Lifshitz solutions in the N=4, d=6 gauged supergravity
theory are dynamically unstable. | hep-th |
Couplings for Compactifications: A general formula is obtained for Yukawa couplings in compactification on
\LGO{s} and corresponding \CY\ spaces. Up to the kinetic term normalizations,
this equates the classical Koszul ring structure with the \LGO\ chiral ring
structure and the true super\CFT\ ring structure. | hep-th |
Entanglement entropy in Galilean conformal field theories and flat
holography: We present the analytical calculation of entanglement entropy for a class of
two dimensional field theories governed by the symmetries of the Galilean
conformal algebra, thus providing a rare example of such an exact computation.
These field theories are the putative holographic duals to theories of gravity
in three-dimensional asymptotically flat spacetimes. We provide a check of our
field theory answers by an analysis of geodesics. We also exploit the
Chern-Simons formulation of three-dimensional gravity and adapt recent
proposals of calculating entanglement entropy by Wilson lines in this context
to find an independent confirmation of our results from holography. | hep-th |
An Étude on the Regularization and Renormalization of Divergences in
Primordial Observables: Many cosmological observables of interest derive from primordial vacuum
fluctuations evolved to late times. These observables represent statistical
draws from some underlying quantum or statistical field theoretic framework
where infinities arise and require regularization. After subtracting
divergences, renormalization conditions must be imposed by measurements or
observations at some scale, mindful of scheme and background dependence. We
review this process on backgrounds that transition from finite duration
inflation to radiation domination, and show how in spite of the ubiquity of
scaleless integrals, UV divergences can still be meaningfully extracted from
quantities that nominally vanish when dimensionally regularized. In this way,
one can contextualize calculations with hard cutoffs, distinguishing between UV
and IR scales corresponding to the beginning and end of inflation from UV and
IR scales corresponding the unknown completion of the theory and its
observables. This distinction has significance as observable quantities cannot
depend on the latter although they will certainly depend on the former. One can
also explicitly show the scheme independence of the coefficients of UV
divergent logarithms. Furthermore, certain IR divergences can be shown to be an
artifact of the de Sitter limit and are cured for finite duration inflation.
For gravitational wave observables, we stress the need to regularize stress
tensors that do not presume a prior scale separation in their construction (as
with the standard Isaacson form), deriving an improved stress tensor fit to
purpose. We conclude by highlighting the inextricable connection between
inferring $N_{\rm eff}$ bounds from vacuum tensor perturbations and the process
of background renormalization. | hep-th |
Revisiting Gribov's Copies Inside The Horizon: In this work, we recover the problem of legitimate topologically trivial
Gribov copies inside the Gribov horizon. We avoid the reducibility problem
which hampered the standard construction of van Baal, and then we are able to
build a valid example with spherical symmetry. We also apply the same technique
in the presence of a background of a Polyakov instanton in a Euclidian 3D
spacetime, in order to study the effect of a non trivial environment in the
generation of multiple copies inside the horizon. | hep-th |
A local and integrable lattice regularization of the massive Thirring
model: The light--cone lattice approach to the massive Thirring model is
reformulated using a local and integrable lattice Hamiltonian written in terms
of discrete fermi fields. Several subtle points concerning boundary conditions,
normal--ordering, continuum limit, finite renormalizations and decoupling of
fermion doublers are elucidated. The relations connecting the six--vertex
anisotropy and the various coupling constants of the continuum are analyzed in
detail. | hep-th |
Sasaki-Ricci flow equation on five-dimensional Sasaki-Einstein space
$Y^{p,q}$: We analyze the transverse K\"{a}hler-Ricci flow equation on Sasaki-Ein\-stein
space $Y^{p,q}$. Explicit solutions are produced representing new
five-dimensional Sasaki structures. Solutions which do not modify the
transverse metric preserve the Sasaki-Einstein feature of the contact
structure. If the transverse metric is altered, the deformed metrics remain
Sasaki, but not Einstein. | hep-th |
Simple Current Extensions and Mapping Class Group Representations: The conjecture of Fuchs, Schellekens and Schweigert on the relation of
mapping class group representations and fixed point resolution in simple
current extensions is investigated, and a cohomological interpretation of the
untwisted stabilizer is given. | hep-th |
Gauge Fields, Fermions and Mass Gaps in 6D Brane Worlds: We study fluctuations about axisymmetric warped brane solutions in 6D minimal
gauged supergravity. Much of our analysis is general and could be applied to
other scenarios. We focus on bulk sectors that could give rise to Standard
Model gauge fields and charged matter. We reduce the dynamics to Schroedinger
type equations plus physical boundary conditions, and obtain exact solutions
for the Kaluza-Klein wave functions and discrete mass spectra. The power-law
warping, as opposed to exponential in 5D, means that zero mode wave functions
can be peaked on negative tension branes, but only at the price of localizing
the whole Kaluza-Klein tower there. However, remarkably, the codimension two
defects allow the Kaluza-Klein mass gap to remain finite even in the infinite
volume limit. In principle, not only gravity, but Standard Model fields could
`feel' the extent of large extra dimensions, and still be described by an
effective 4D theory. | hep-th |
Syncyclons or Solitonic Signals from Extra Dimensions: In theories where spacetime is a direct product of Minkowski space ($M^4$)
and a d dimensional compact space ($K^d$), there can exist topological solitons
that simultaneously wind around $R^3$ (or $R^2$ or $R^1$) in $M^4$ and the
compact dimensions. A paradigmatic non-gravitational example of such
``co-winding" solitons is furnished by Yang-Mills theory defined on $M^4 X
S^1$. Pointlike, stringlike and sheetlike solitons can be identified by
transcribing and generalizing the proceedure used to construct the periodic
instanton (caloron) solutions. Asymptotically the classical pointlike objects
have non-Abelian magnetic dipole fields together with a non-Abelian scalar
potential while the ``color" electric charge is zero. However quantization of
collective coordinates associated with zeromodes and coupling to fermions can
radically change these quantum numbers due to fermion number fractionalization
and its non-Abelian generalization. Interpreting the YM group as color (or the
Electroweak SU(2) group) and assuming that an extra circular dimension exists
thus implies the existence of topologically stable solitonic objects which
carry baryon(lepton) number and a mass O($1/g^2R$), where R is the radius of
the compact dimension. | hep-th |
Gibbs entropy from entanglement in electric quenches: In quantum electrodynamics with charged fermions, a background electric field
is the source of the chiral anomaly which creates a chirally imbalanced state
of fermions. This chiral state is realized through the production of entangled
pairs of right-moving fermions and left-moving antifermions (or vice versa,
depending on the orientation of the electric field). Here we show that the
statistical Gibbs entropy associated with these pairs is equal to the entropy
of entanglement between the right-moving particles and left-moving
antiparticles. We then derive an asymptotic expansion for the entanglement
entropy in terms of the cumulants of the multiplicity distribution of produced
particles and explain how to re-sum this asymptotic expansion. Finally, we
study the time dependence of the entanglement entropy in a specific
time-dependent pulsed background electric field, the so-called "Sauter pulse",
and illustrate how our resummation method works in this specific case. We also
find that short pulses (such as the ones created by high energy collisions)
result in an approximately thermal distribution for the produced particles. | hep-th |
Mesons from (non) Abelian T-dual backgrounds: In this work we study mesonic excitations in a Quantum Field Theory dual to
the non Abelian T-dual of $AdS_5\times S^5$, using a D6 brane probe on the
Sfetsos-Thompson background. Before and after the duality, we observe
interesting differences between the spectra and interpret them. The spectrum of
masses and the interactions among mesonic excitations teach valuable lessons
about the character of non-Abelian T-duality and its implications for
Holography. The case of Abelian T-duality is also studied. | hep-th |
Noncommutative differential geometry with higher order derivatives: We build a toy model of differential geometry on the real line, which
includes derivatives of the second order. Such construction is possible only
within the framework of noncommutative geometry. We introduce the metric and
briefly discuss two simple physical models of scalar field theory and gauge
theory in this geometry. | hep-th |
Supersymmetry Enhancement of D-p-branes and M-branes: We examine the supersymmetry of classical D-brane and M-brane configurations
and explain the dependence of Killing spinors on coordinates. We find that one
half supersymmetry is broken in the bulk and that supersymmetry near the
D-brane horizon is restored for $p\leq 3$, for solutions in the stringy frame,
but only for $p=3$ in the10d canonical frame. We study the enhancement for the
case of four intersecting D-3-branes in 10 dimensions and the implication of
this for the size of the infinite throat of the near horizon geometry in
non-compactified theory. We found some indications of universality of near
horizon geometries of various intersecting brane configurations. | hep-th |
Gravity = Yang-Mills: This essay's title is justified by discussing a class of Yang-Mills-type
theories of which standard Yang-Mills theories are special cases but which is
broad enough to include gravity as a double field theory. We use the framework
of homotopy algebras, where conventional Yang-Mills theory is the tensor
product ${\cal K}\otimes \frak{g}$ of a `kinematic' algebra ${\cal K}$ with a
color Lie algebra $\frak{g}$. The larger class of Yang-Mills-type theories are
given by the tensor product of ${\cal K}$ with more general Lie-type algebras
of which ${\cal K}$ itself is an example, up to anomalies that can be cancelled
for the tensor product with a second copy $\bar{\cal K}$. Gravity is then given
by ${\cal K}\otimes \bar{\cal K}$. | hep-th |
Coset Symmetries in Dimensionally Reduced Bosonic String Theory: We discuss the dimensional reduction of various effective actions,
particularly that of the closed Bosonic string and pure gravity, to two and
three dimensions. The result for the closed Bosonic string leads to coset
symmetries which are in agreement with those recently predicted and argued to
be present in a new unreduced formulation of this theory. We also show that
part of the Geroch group appears in the unreduced duality symmetric formulation
of gravity recently proposed. We conjecture that this formulation can be
extended to a non-linear realisation based on a Kac-Moody algebra which we
identify. We also briefly discuss the proposed action of Bosonic M-theory. | hep-th |
3d mirror for Argyres-Douglas theories: 3d mirrors for all 4d $\mathcal{N}=2$ Argyres-Douglas (AD) theories
engineered using 6d $(2,0)$ theory are found. The basic steps are: 1): Find a
punctured sphere representation for the AD theories (this is achieved in our
previous studies of S duality); 2): Attach a 3d theory for each puncture; 3):
Glue together the 3d theory for each puncture. We found the 3d mirror quiver
gauge theory for the AD theories engineered using 6d $A$ and $D$ type theories.
These 3d mirrors are useful for studying the properties of original 4d theory
such as Higgs branch, S-duality, etc; We also construct many new 3d
$\mathcal{N}=4$ SCFTs. | hep-th |
Berry's phase in noncommutative spaces: We introduce the perturbative aspects of noncommutative quantum mechanics.
Then we study the Berry's phase in the framework of noncommutative quantum
mechanics. The results show deviations from the usual quantum mechanics which
depend on the parameter of space/space noncommtativity. | hep-th |
Moduli Thermalization and Finite Temperature Effects in "Big" Divisor
Large Volume D3/D7 Swiss-Cheese Compactification: In the context of Type IIB compactified on a large volume Swiss-Cheese
orientifold in the presence of a mobile space-time filling D3-brane and stacks
of fluxed D7-branes wrapping the "big" divisor Sigma_B of a Swiss-Cheese Calabi
Yau in WCP^4 [1,1,1,6,9], we explore various implications of moduli dynamics
and discuss their couplings and decay into MSSM (-like) matter fields early in
the history of universe to reach thermal equilibrium. Like finite temperature
effects in O'KKLT, we observe that the local minimum of zero-temperature
effective scalar potential is stable against any finite temperature corrections
(up to two-loops) in large volume scenarios as well. Also, we find that moduli
are heavy enough to avoid any cosmological moduli problem. | hep-th |
Casimir force in noncommutative Randall-Sundrum models revisited: We propose another method to compute the Casimir force in noncommutative
Randall-Sundrum braneworld model considered by K. Nouicer and Y. Sabri
recently. Our method can be used to compute the Casimir force to any order in
the noncommutative parameter. Contrary to the claim made by K. Nouicer and Y.
Sabri that repulsive Casimir force can appear in the first order approximation,
we show that the Casimir force is always attractive at any order of
approximation. | hep-th |
Loops in AdS: From the Spectral Representation to Position Space II: We continue the study of AdS loop amplitudes in the spectral representation
and in position space. We compute the finite coupling 4-point function in
position space for the large-$N$ conformal Gross Neveu model on $AdS_3$. The
resummation of loop bubble diagrams gives a result proportional to a tree-level
contact diagram. We show that certain families of fermionic Witten diagrams can
be easily computed from their companion scalar diagrams. Thus, many of the
results and identities of [1] are extended to the case of external fermions. We
derive a spectral representation for ladder diagrams in AdS. Finally, we
compute various bulk 2-point correlators, extending the results of [1]. | hep-th |
The Standard Model with gravity couplings: In this paper, we examine the coupling of matter fields to gravity within the
framework of the Standard Model of particle physics. The coupling is described
in terms of Weyl fermions of a definite chirality, and employs only
(anti)self-dual or left-handed spin connection fields. It is known from the
work of Ashtekar and others that such fields can furnish a complete description
of gravity without matter. We show that conditions ensuring the cancellation of
perturbative chiral gauge anomalies are not disturbed. We also explore a global
anomaly associated with the theory, and argue that its removal requires that
the number of fundamental fermions in the theory must be multiples of 16. In
addition, we investigate the behavior of the theory under discrete
transformations P, C and T; and discuss possible violations of these discrete
symmetries, including CPT, in the presence of instantons and the
Adler-Bell-Jackiw anomaly. | hep-th |
Why is AI hard and Physics simple?: We discuss why AI is hard and why physics is simple. We discuss how physical
intuition and the approach of theoretical physics can be brought to bear on the
field of artificial intelligence and specifically machine learning. We suggest
that the underlying project of machine learning and the underlying project of
physics are strongly coupled through the principle of sparsity, and we call
upon theoretical physicists to work on AI as physicists. As a first step in
that direction, we discuss an upcoming book on the principles of deep learning
theory that attempts to realize this approach. | hep-th |
Many-Particle Quantum Cosmology: The Einstein-Friedmann Universe as whole quantum object can be treated as
bosonic string mass groundstate, called a tachyon, having negative mass square
and a speed more than the speed of light. I present a brief review of results
obtained from this point of view called Many-Particle Quantum Gravity approach
- the monodromy problem in the Fock space, thermodynamics of the Universe, and
the extremal tachyon mass model. | hep-th |
Higher Order Corrections to Holographic Black Hole Chemistry: We investigate the holographic Smarr relation beyond the large N limit. By
making use of the holographic dictionary, we find that the bulk correlates of
sub-leading 1/N corrections to this relation are related to the couplings in
Lovelock gravity theories. We likewise obtain a holographic equation of state,
and check its validity for a variety of interesting and non-trivial black
holes, including rotating planar black holes in Gauss-Bonnet-Born-Infeld
gravity, and non-extremal rotating black holes in minimal 5d gauged
supergravity. We provide an explanation of the N-dependence of the holographic
Smarr relation in terms of contributions due to planar and non-planar diagrams
in the dual theory. | hep-th |
Effective long distance $q\bar{q} $ potential in holographic RG flows: We study the $q\bar{q}$ potential in strongly coupled non-conformal field
theories with a non-trivial renormalization group flow via holography. We focus
on the properties of this potential at an inter-quark separation $L$ large
compared to the characteristic scale of the field theory. These are determined
by the leading order IR physics plus a series of corrections, sensitive to the
properties of the RG-flow. To determine those corrections, we propose a general
method applying holographic Wilsonian renormalization to a dual string. We
apply this method to examine in detail two sets of examples, $3+1$-dimensional
theories with an RG flow ending in an IR fixed point; and theories that are
confining in the IR, in particular, the Witten QCD and Klebanov-Strassler
models. In both cases, we find corrections with a universal dependence on the
inter-quark separation. When there is an IR fixed point, that correction decays
as a power $\sim 1/L^4$. We explain that dependence in terms of a double-trace
deformation in a one-dimensional defect theory. For a confining theory, the
decay is exponential $\sim e^{-ML}$, with $M$ a scale of the order of the
glueball mass. We interpret this correction using an effective flux tube
description as produced by a background internal mode excitation induced by
sources localized at the endpoints of the flux tube. We discuss how these
results could be confronted with lattice QCD data to test whether the
description of confinement via the gauge/gravity is qualitatively correct. | hep-th |
Quantized rotating Taub-bolt instantons: We argue that previously suggested metrics for rotating Taub-bolt instantons
do not satisfy all the necessary regularity conditions, and we present a family
of new regular rotating Taub-bolts labelled by an odd integer $k$. There are
two types of rotating bolt solutions. The first infinite sequence starts with
non-rotating Taub-NUT with positive mass $M_k=N$ for $a=0$ and goes to $(k-2)N$
for $|a|\to \infty$ (or $N$ for $k=1$), where $a$ is the rotation parameter.
For the second sequence of rotating Page bolts, the masses $M_k$ go through the
value $M_k=5N/4$ for $a=0$ and asymptote to $(k+2)N$ for $|a|\to \infty$. | hep-th |
$S^7$ Current Algebras: We present $S^7$-algebras as generalized Kac-Moody algebras. A number of
free-field representations is found. We construct the octonionic projective
spaces ${\O}P^N$. | hep-th |
SU(2)/SL(2) knot invariants and KS monodromies: We review the Reshetikhin-Turaev approach to construction of non-compact knot
invariants involving R-matrices associated with infinite-dimensional
representations, primarily those made from Faddeev's quantum dilogarithm. The
corresponding formulas can be obtained from modular transformations of
conformal blocks as their Kontsevich-Soibelman monodromies and are presented in
the form of transcendental integrals, where the main issue is manipulation with
integration contours. We discuss possibilities to extract more explicit and
handy expressions which can be compared with the ordinary (compact) knot
polynomials coming from finite-dimensional representations of simple Lie
algebras, with their limits and properties. In particular, the quantum
A-polynomials, difference equations for colored Jones polynomials should be the
same, just in non-compact case the equations are homogeneous, while they have a
non-trivial right-hand side for ordinary Jones polynomials. | hep-th |
Closed string exchanges on $C^2/Z_2$ in a background B-field: In an earlier work it was shown that the IR singularities arising in the
nonplanar one loop two point function of a noncommutative ${\cal N}=2$ gauge
theory can be reproduced exactly from the massless closed string exchanges. The
noncommutative gauge theory is realised on a fractional $D_3$ brane localised
at the fixed point of the $C^2/Z_2$ orbifold. In this paper we identify the
contributions from each of the closed string modes. The sum of these adds upto
the nonplanar two-point function. | hep-th |
Supersymmetric index on T^2 x S^2 and elliptic genus: We study partition function of four-dimensional $\mathcal{N}=1$
supersymmetric field theory on $T^2 \times S^2$. By applying supersymmetry
localization, we show that the $T^2 \times S^2$ partition function is given by
elliptic genus of certain two-dimensional $\mathcal{N}=(0,2)$ theory. As an
application, we discuss a relation between 4d Seiberg duality duality and 2d
$(0,2)$ triality, proposed by Gadde, Gukov and Putrov. In other examples, we
identify 4d theories giving elliptic genera of K3, M-strings and E-strings. In
the example of K3, we find that there are two 4d theories giving the elliptic
genus of K3. This would imply new four-dimensional duality. | hep-th |
General covariance, and supersymmetry without supersymmetry: An unusual four-dimensional generally covariant and supersymmetric SU(2)
gauge theory is described. The theory has propagating degrees of freedom, and
is invariant under a local (left-handed) chiral supersymmetry, which is half
the supersymmetry of supergravity. The Hamiltonian 3+1 decomposition of the
theory reveals the remarkable feature that the local supersymmetry is a
consequence of Yang-Mills symmetry, in a manner reminiscent of how general
coordinate invariance in Chern-Simons theory is a consequence of Yang-Mills
symmetry. It is possible to write down an infinite number of conserved
currents, which strongly suggests that the theory is classically integrable. A
possible scheme for non-perturbative quantization is outlined. This utilizes
ideas that have been developed and applied recently to the problem of
quantizing gravity. | hep-th |
Chasing the cuprates with dilatonic dyons: Magnetic field and momentum dissipation are key ingredients in describing
condensed matter systems. We include them in gauge/gravity and systematically
explore the bottom-up panorama of holographic IR effective field theories based
on bulk Einstein-Maxwell Lagrangians plus scalars. The class of solutions here
examined appear insufficient to capture the phenomenology of charge transport
in the cuprates. We analyze in particular the temperature scaling of the
resistivity and of the Hall angle. Keeping an open attitude, we illustrate weak
and strong points of the approach. | hep-th |
One-dimensional sigma-models with N=5,6,7,8 off-shell supersymmetries: We computed the actions for the 1D N=5 sigma-models with respect to the two
inequivalent (2,8,6) multiplets. 4 supersymmetry generators are manifest, while
the constraint originated by imposing the 5-th supersymmetry automatically
induces a full N=8 off-shell invariance. The resulting action coincides in the
two cases and corresponds to a conformally flat 2D target satisfying a special
geometry of rigid type. To obtain these results we developed a computational
method (for Maple 11) which does not require the notion of superfields and is
instead based on the nowadays available list of the inequivalent
representations of the 1D N-extended supersymmetry. Its application to
systematically analyze the sigma-models off-shell invariant actions for the
remaining N=5,6,7,8 (k,8,8-k) multiplets, as well as for the N>8
representations,only requires more cumbersome computations. | hep-th |
A Lorentz-violating SO(3) model: discussing the unitarity, causality and
the 't Hooft-Polyakov monopoles: In this paper, we extend the analysis of the Lorentz-violating Quantum
Eletrodynamics to the non-Abelian case: an SO(3) Yang-Mills Lagrangian with the
addition of the non-Abelian Chern-Simons-type term. We consider the spontaneous
symmetry breaking of the model and inspect its spectrum in order to check if
unitarity and causality are respected. An analysis of the topological structure
is also carried out and we show that a 't Hooft-Polyakov solution for monopoles
is still present. | hep-th |
Superstring scattering amplitudes in higher genus: In this paper we continue the program pioneered by D'Hoker and Phong, and
recently advanced by Cacciatori, Dalla Piazza, and van Geemen, of finding the
chiral superstring measure by constructing modular forms satisfying certain
factorization constraints. We give new expressions for their proposed ans\"atze
in genera 2 and 3, respectively, which admit a straightforward generalization.
We then propose an ansatz in genus 4 and verify that it satisfies the
factorization constraints and gives a vanishing cosmological constant. We
further conjecture a possible formula for the superstring amplitudes in any
genus, subject to the condition that certain modular forms admit holomorphic
roots. | hep-th |
$ε$-Expansion in the Gross-Neveu Model from Conformal Field
Theory: We compute the anomalous dimensions of a class of operators of the form
$(\bar\psi\psi)^p$ and $(\bar\psi\psi)^p\psi$ to leading order in $\epsilon$ in
the Gross-Neveu model in $2+\epsilon$ dimensions. We use the techniques
developed in arXiv: 1505.00963. | hep-th |
Gravitating Cho-Maison Monopole: We study numerical solutions corresponding to spherically symmetric
gravitating electroweak monopole and magnetically charged black holes of the
Einstein-Weinberg-Salam theory. The gravitating electroweak monopole solutions
are quite identical to the gravitating monopole solution in SU(2)
Einsten-Yang-Mills-Higgs theory, but with distinctive characteristics. We also
found solutions representing radially excited monopole, which has no
counterpart in flat space. Both of these solutions exist up to a maximal
gravitational coupling before they cease to exist. Lastly we also report on
magnetically charged non-Abelian black holes solutions that is closely related
to the regular monopole solutions, which represents counterexample to the
`no-hair' conjecture. | hep-th |
Gauge equivalent universes in 5d Kaluza-Klein theory: We examine in the framework of 5d Kaluza-Klein theory the gauge equivalence
of $x^5$-dependent cosmological solutions each of which describes in the 4d
sector an arbitrarily evolving isotropic, homogeneous universe with some pure
gauge. We find that (1)within a certain time scale $\tau_c$
(which is characterized by the compactification radius $R_c$) any arbitrarily
evolving 4d universe is allowed to exist by field equations, and these 4d
universes with appropriate pure gauges are all gauge equivalent as long as they
are of the same topology. (2)Outside $\tau_c$ the gauge equivalence disappears
and the evolution of the universe is fixed by field equations. | hep-th |
Constraints on the quantum state of pairs produced by semiclassical
black holes: The pair-production process for a black hole (BH) is discussed within the
framework of a recently proposed semiclassical model of BH evaporation. Our
emphasis is on how the requirements of unitary evolution and strong
subadditivity act to constrain the state of the produced pairs and their
entanglement with the already emitted BH radiation. We find that the state of
the produced pairs is indeed strongly constrained but that the semiclassical
model is consistent with all requirements. We are led to the following picture:
Initially, the pairs are produced in a state of nearly maximal entanglement
amongst the partners, with a parametrically small entanglement between each
positive-energy partner and the outgoing radiation, similar to Hawking's model.
But, as the BH evaporation progresses past the Page time, each positive-energy
partner has a stronger entanglement with the outgoing radiation and,
consequently, is less strongly entangled with its negative-energy partner. We
present some evidence that this pattern of entanglement does not require
non-local interactions, only EPR-like non-local correlations. | hep-th |
3d superconformal indices and isomorphisms of M2-brane theories: We test several expected isomorphisms between the U(N)xU(N) ABJM theory and
(SU(N)xSU(N))/Z_N theory including the BLG theory by comparing their
superconformal indices. From moduli space analysis, it is expected that this
equivalence can hold if and only if the rank N and Chern-Simons level k are
coprime. We also calculate the index of the ABJ theory and investigate whether
some theories with identical moduli spaces are isomorphic or not. | hep-th |
Holographic line defects in F(4) gauged supergravity: In this note we construct a solution of six-dimensional $F(4)$ gauged
supergravity using $AdS_2\times S^3$ warped over an interval as an ansatz. The
solution is completely regular, preserves eight of the sixteen supersymmetries
of the $AdS_6$ vacuum and is a holographic realization of a line defect in a
dual five-dimensional theory. We calculate the expectation value of the defect
and the one-point function of the stress tensor in the presence of the defect
using holographic renormalization. | hep-th |
On the Non-renormalization of the AdS Radius: We show that the relation between the 't Hooft coupling and the radius of AdS
is not renormalized at one-loop in the sigma model perturbation theory. We
prove this by computing the quantum effective action for the superstring on
AdS_5 x S^5 and showing that it does not receive any finite alpha' corrections.
We also show that the central charge of the interacting worldsheet conformal
field theory vanishes at one-loop. | hep-th |
Twistors and supertwistors for exceptional field theory: As a means of examining the section condition and its possible solutions and
relaxations, we perform twistor transforms related to versions of exceptional
field theory with Minkowski signature. The spinor parametrisation of the
momenta naturally solves simultaneously both the mass-shell condition and the
(weak) section condition. It is shown that the incidence relations for
multi-particle twistors force them to share a common section, but not to be
orthogonal. The supersymmetric extension contains additional scalar fermionic
variables shown to be kappa-symmetry invariants. We speculate on some
implications, among them a possible relation to higher spin theory. | hep-th |
On RG-flow and the Cosmological Constant: The AdS/CFT correspondence implies that the effective action of certain
strongly coupled large $N$ gauge theories satisfy the Hamilton-Jacobi equation
of 5d gravity. Using an analogy with the relativistic point particle, I
construct a low energy effective action that includes the Einstein action and
obeys a Callan-Symanzik-type RG-flow equation. It follows from the flow
equation that under quite general conditions the Einstein equations admit a
flat space-time solution, but other solutions with non-zero cosmological
constant are also allowed. I discuss the geometric interpretation of this
result in the context of warped compactifications. | hep-th |
Holographic free energy and thermodynamic geometry: We analytically obtain the free energy and thermodynamic geometry of
holographic superconductors in $2+1$-dimensions. The gravitational theory in
the bulk dual to this $2+1$-dimensional strongly coupled theory lives in the
$3+1$-dimensions and is that of a charged $AdS$ black hole together with a
massive charged scalar field. The matching method is applied to obtain the
nature of the fields near the horizon using which the holographic free energy
is computed through the gauge/gravity duality. The critical temperature is
obtained for a set of values of the matching point of the near horizon and the
boundary behaviour of the fields. The thermodynamic geometry is then computed
from the free energy of the boundary theory. From the divergence of the
thermodynamic scalar curvature, the critical temperature is obtained once
again. We then compare this result for the critical temperature with that
obtained from the matching method. | hep-th |
Gauge theory in deformed N=(1,1) superspace: We review the non-anticommutative Q-deformations of N=(1,1) supersymmetric
theories in four-dimensional Euclidean harmonic superspace. These deformations
preserve chirality and harmonic Grassmann analyticity. The associated field
theories arise as a low-energy limit of string theory in specific backgrounds
and generalize the Moyal-deformed supersymmetric field theories. A
characteristic feature of the Q-deformed theories is the half-breaking of
supersymmetry in the chiral sector of the Euclidean superspace. Our main focus
is on the chiral singlet Q-deformation, which is distinguished by preserving
the SO(4) Spin(4) ``Lorentz'' symmetry and the SU(2) R-symmetry. We present the
superfield and component structures of the deformed N=(1,0) supersymmetric
gauge theory as well as of hypermultiplets coupled to a gauge superfield:
invariant actions, deformed transformation rules, and so on. We discuss quantum
aspects of these models and prove their renormalizability in the abelian case.
For the charged hypermultiplet in an abelian gauge superfield background we
construct the deformed holomorphic effective action. | hep-th |
The Dark Dimension, the Swampland, and the Dark Matter Fraction Composed
of Primordial Near-Extremal Black Holes: In a recent publication we studied the decay rate of primordial black holes
perceiving the dark dimension, an innovative five-dimensional (5D) scenario
that has a compact space with characteristic length-scale in the micron range.
We demonstrated that the rate of Hawking radiation of 5D black holes slows down
compared to 4D black holes of the same mass. Armed with our findings we showed
that for a species scale of ${\cal O} (10^{9}~{\rm GeV})$, an all-dark-matter
interpretation in terms of primordial black holes should be feasible for black
hole masses in the range $10^{14} \lesssim M/{\rm g} \lesssim 10^{21}$. As a
natural outgrowth of our recent study, herein we calculate the Hawking
evaporation of near-extremal 5D black holes. Using generic entropy arguments we
demonstrate that Hawking evaporation of higher-dimensional near-extremal black
holes proceeds at a slower rate than the corresponding Schwarzschild black
holes of the same mass. Assisted by this result we show that if there were 5D
primordial near-extremal black holes in nature, then a PBH all-dark-matter
interpretation would be possible in the mass range $10^{7}\sqrt{\beta} \lesssim
M/{\rm g} \lesssim 10^{21}$, where $\beta$ is a parameter that controls the
difference between mass and charge of the associated near-extremal black hole. | hep-th |
Multiple Soft Limits of Cosmological Correlation Functions: We derive novel identities satisfied by inflationary correlation functions in
the limit where two external momenta are taken to be small. We derive these
statements in two ways: using background-wave arguments and as Ward identities
following from the fixed-time path integral. Interestingly, these identities
allow us to constrain some of the O(q^2) components of the soft limit, in
contrast to their single-soft analogues. We provide several nontrivial checks
of our identities both in the context of resonant non-Gaussianities and in
small sound speed models. Additionally, we extend the relation at lowest order
in external momenta to arbitrarily many soft legs, and comment on the many-soft
extension at higher orders in the soft momentum. Finally, we consider how
higher soft limits lead to identities satisfied by correlation functions in
large-scale structure. | hep-th |
Constructing near-horizon geometries in supergravities with hidden
symmetry: We consider the classification of near-horizon geometries in a general
two-derivative theory of gravity coupled to abelian gauge fields and uncharged
scalars in four and five dimensions, with one and two commuting rotational
symmetries respectively. Assuming that the theory of gravity reduces to a 3d
non-linear sigma model (as is typically the case for ungauged supergravities),
we show that the functional form of any such near-horizon geometry may be
determined. As an example we apply this to five dimensional minimal
supergravity. We also construct an example of a five parameter near-horizon
geometry solution to this theory with S^1 X S^2 horizon topology. We discuss
its relation to the near-horizon geometries of the yet to be constructed
extremal black rings with both electric and dipole charges. | hep-th |
States and amplitudes for finite regions in a two-dimensional Euclidean
quantum field theory: We quantize the Helmholtz equation (plus perturbative interactions) in two
dimensions to illustrate a manifestly local description of quantum field
theory. Using the general boundary formulation we describe the quantum dynamics
both in a traditional time evolution setting as well as in a setting referring
to finite disk (or annulus) shaped regions of spacetime. We demonstrate that
both descriptions are equivalent when they should be. | hep-th |
Stringy Cosmic Strings and Axion Cohomology: The static stationary axially symmetric background ("infinite cosmic string")
of the $D=4$ string theory provided with an axion charge is studied in the
effective theory approach. The most general exact solution is constructed. It
is found that the Kalb-Ramond axion charge, present in the string topology
$R^{3} \times S^{1}$, produces nontrivial gravitational field configurations
which feature horizons. The corresponding ``no-hair'' theorems are proved which
stress uniqueness of black strings. Connection of the solutions with the gauged
WZWN sigma model constructions on the world sheet is discussed since they are
the only target spaces which hide their singularities behind horizons, and thus
obey the cosmic censorship conjecture. | hep-th |
On the Liouville 2D dilaton gravity models with sinh-Gordon matter: We study 1+1 dimensional dilaton gravity models which take into account
backreaction of the sinh-Gordon matter field. We found a wide class of exact
solutions which generalizes black hole solutions of the Jackiw-Teitelboim
gravity model and its hyperbolic deformation. | hep-th |
Odd Nambu bracket on Grassmann algebra: The Grassmann-odd Nambu bracket on the Grassmann algebra is proposed. | hep-th |
Wigner Representation Theory of the Poincare Group, Localization,
Statistics and the S-Matrix: It has been known that the Wigner representation theory for positive energy
orbits permits a useful localization concept in terms of certain lattices of
real subspaces of the complex Hilbert -space. This ''modular localization'' is
not only useful in order to construct interaction-free nets of local algebras
without using non-unique ''free field coordinates'', but also permits the study
of properties of localization and braid-group statistics in low-dimensional
QFT. It also sheds some light on the string-like localization properties of the
1939 Wigner's ''continuous spin'' representations.We formulate a constructive
nonperturbative program to introduce interactions into such an approach based
on the Tomita-Takesaki modular theory. The new aspect is the deep relation of
the latter with the scattering operator. | hep-th |
String duality and massless string states: We are discussing the $S$ \& $T$ duality for special class of heterotic
string configurations. This class of solutions includes various types of black
hole solutions and Taub-NUT geometries. It allows a self-dual point for both
dualities which corresponds to massless configurations. As string state this
point corresponds to $N_R=1/2$ and $N_L=0$. The string/string duality is
shortly discussed. | hep-th |
Improved Holographic QCD: We provide a review to holographic models based on Einstein-dilaton gravity
with a potential in 5 dimensions. Such theories, for a judicious choice of
potential are very close to the physics of large-N YM theory both at zero and
finite temperature. The zero temperature glueball spectra as well as their
finite temperature thermodynamic functions compare well with lattice data. The
model can be used to calculate transport coefficients, like bulk viscosity, the
drag force and jet quenching parameters, relevant for the physics of the
Quark-Gluon Plasma. | hep-th |
The Gribov problem in presence of background field for $SU(2)$
Yang-Mills theory: The Gribov problem in the presence of a background field is analyzed: in
particular, we study the Gribov copies equation in the Landau-De Witt gauge as
well as the semi-classical Gribov gap equation. As background field, we choose
the simplest non-trivial one which corresponds to a constant gauge potential
with non-vanishing component along the Euclidean time direction. This kind of
constant non-Abelian background fields is very relevant in relation with (the
computation of) the Polyakov loop but it also appears when one considers the
non-Abelian Schwinger effect. We show that the Gribov copies equation is
affected directly by the presence of the background field, constructing an
explicit example. The analysis of the Gribov gap equation shows that the larger
the background field, the smaller the Gribov mass parameter. These results
strongly suggest that the relevance of the Gribov copies (from the path
integral point of view) decreases as the size of the background field
increases. | hep-th |
Calculation of Green-Schwarz Superstring Amplitudes Using the N=2
Twistor-String Formalism: The manifestly SU(4)xU(1) super-Poincare invariant free-field N=2 twistor-
string action for the ten-dimensional Green-Schwarz superstring is quantized
using standard BRST methods. Unlike the light-cone and semi-light-cone
gauge-fixed Green-Schwarz actions, the twistor-string action does not require
interaction-point operators at the zeroes of the light-cone momentum, $\dz
x^+$, which complicated all previous calculations. After defining the vertex
operator for the massless physical supermultiplet, as well as two
picture-changing operators and an instanton-number-changing operator,
scattering amplitudes for an arbitrary number of loops and external massless
states are explicitly calculated by evaluating free-field correlation functions
of these operators on N=2 super-Riemann surfaces of the appropriate topology,
and integrating over the global moduli. Although there is no sum over spin
structures, only discrete values of the global U(1) moduli contribute to the
amplitudes. Because the spacetime supersymmetry generators do not contain ghost
fields, the amplitudes are manifestly spacetime supersymmetric, there is no
multiloop ambiguity, and the non-renormalization theorem is easily proven. By
choosing the picture-changing operators to be located at the zeroes of $\dz
x^+$, these amplitudes are shown to agree with amplitudes obtained using the
manifestly unitary light-cone gauge formalism. | hep-th |
Two interacting conformal Carroll particles: In this note we analyse two different models of two interacting conformal
Carroll particles that can be obtained as the Carrollian limit of two
relativistic conformal particles. The first model describes particles with zero
velocity and exhibits infinite dimensional symmetries which are reminiscent of
the BMS symmetries. A second model of interaction of Carrollian particles is
proposed, where the particles have non zero velocity and therefore, as a
consequence of the limit c to 0, are tachyons. Infinite dimensional symmetries
are present also in this model. | hep-th |
The ultrarelativistic limit of Kerr: The massless (or ultrarelativistic) limit of a Schwarzschild black hole with
fixed energy was determined long ago in the form of the Aichelburg-Sexl
shockwave, but the status of the same limit for a Kerr black hole is less
clear. In this paper, we explore the ultrarelativistic limit of Kerr in the
class of Kerr-Schild impulsive pp-waves by exploiting a relation between the
metric profile and the eikonal phase associated with scattering between a
scalar and the source of the metric. This gives a map between candidate metrics
and tree-level, 4-point scattering amplitudes. At large distances from the
source, we find that all candidates for the massless limit of Kerr in this
class do not have spin effects. This includes the metric corresponding to the
massless limit of the amplitude for gravitational scattering between a scalar
and a massive particle of infinite spin. One metric, discovered by Balasin and
Nachbagauer, does have spin and finite size effects at short distances, leading
to a remarkably compact scattering amplitude with many interesting properties.
We also discuss the classical single copy of the ultrarelativistic limit of
Kerr in electromagnetism. | hep-th |
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