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Thermodynamic geometry and interacting microstructures of BTZ black
holes: In this work, we present a study to probe the nature of interactions between
black hole microstructures for the case of the BTZ black holes. Even though BTZ
black holes without any angular momentum or electric charge thermodynamically
behave as an ideal gas, i.e. with non-interacting microstructures; in the
presence of electric charge or angular momentum, BTZ black holes are associated
with repulsive interactions among the microstructures. We extend the study to
the case of exotic BTZ black holes with mass $M = \alpha m + \gamma
\frac{j}{l}$ and angular momentum $J=\alpha j + \gamma l m$, for arbitrary
values of $ (\alpha, \gamma)$ ranging from purely exotic $(\alpha=0,\gamma=1)$,
slightly exotic $(\alpha > \frac{1}{2},\gamma < \frac{1}{2})$ and highly exotic
$(\alpha < \frac{1}{2}, \gamma > \frac{1}{2})$. We find that unlike the normal
BTZ black holes (the case $\alpha =1,\gamma =0$), there exist both attraction
as well as repulsion dominated regions in all the cases of exotic BTZ black
holes.
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Conserved Killing charges of quadratic curvature gravity theories in
arbitrary backgrounds: We extend the Abbott-Deser-Tekin procedure of defining conserved quantities
of asymptotically constant-curvature spacetimes, and give an analogous
expression for the conserved charges of geometries that are solutions of
quadratic curvature gravity models in generic D-dimensions and that have
arbitrary asymptotes possessing at least one Killing isometry. We show that the
resulting charge expression correctly reduces to its counterpart when the
background is taken to be a space of constant curvature and, moreover, is
background gauge invariant. As applications, we compute and comment on the
energies of two specific examples: the three dimensional Lifshitz black hole
and a five dimensional companion of the first, whose energy has never been
calculated beforehand.
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Droplet-Edge Operators in Nonrelativistic Conformal Field Theories: We consider the large-charge expansion of the charged ground state of a
Schrodinger-invariant, nonrelativistic conformal field theory in a harmonic
trap, in general dimension d. In the existing literature, the energy in the
trap has been computed to next-to-leading order (NLO) at large charge Q, which
comes from the classical contribution of two higher-derivative terms in the
effective field theory. In this note, we explain the structure of operators
localized at the edge of the droplet, where the density drops to zero. We list
all operators contributing to the ground-state energy with nonnegative powers
of Q in the large-Q expansion. As a test, we use dimensional regularization to
reproduce the calculation of the NLO ground state energy by Kravec and Pal ,
and we recover the same universal coefficient for the logarithmic term as in
that work. We refine the derivation by presenting a systematic operator
analysis of the possible edge counterterms, showing that different choices of
cutoff procedures must yield the same renormalized result up to an enumerable
list of Wilson coefficients for conformally invariant local counterterms at the
droplet edge. We also demonstrate the existence of a previously unnoticed edge
contribution to the ground-state operator dimension of order Q^{{2\over 3} -
{1\over d}} in d spatial dimensions. Finally, we show there is no bulk or edge
counterterm scaling as Q^0 in two spatial dimensions, which establishes the
universality of the order Q^0 term in large-Q expansion of the lowest charged
operator dimension in d=2.
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Branes in the OSP(1|2) WZNW model: The boundary OSP(1|2) WZNW model possesses two types of branes, which are
localized on supersymmetric Euclidean AdS$_2$ and on two-dimensional
superspheres. We compute the coupling of closed strings to these branes with
two different methods. The first one uses factorization constraints and the
other one a correspondence to boundary N=1 super-Liouville field theory, which
we proof with path integral techniques. We check that the results obey the
Cardy condition and reproduce the semi-classical computations. For the check we
also compute the spectral density of open strings that are attached to the
non-compact branes.
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Low Energy Vortex Dynamics in Abelian Higgs Systems: The low energy dynamics of the vortices of the Abelian Chern-Simons-Higgs
system is investigated from the adiabatic approach. The difficulties involved
in treating the field evolution as motion on the moduli space in this system
are shown. Another two generalized Abelian Higgs systems are discusssed with
respect to their vortex dynamics at the adiabatic limit. The method works well
and we find bound states in the first model and scattering at right angles in
the second system.
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Stochastic Behavior of Effective Field Theories Across Threshold: We explore how the existence of a field with a heavy mass influences the low
energy dynamics of a quantum field with a light mass by expounding the
stochastic characters of their interactions which take on the form of
fluctuations in the number of (heavy field) particles created at the threshold,
and dissipation in the dynamics of the light fields, arising from the
backreaction of produced heavy particles. We claim that the stochastic nature
of effective field theories is intrinsic, in that dissipation and fluctuations
are present both above and below the threshold. Stochasticity builds up
exponentially quickly as the heavy threshold is approached from below, becoming
dominant once the threshold is crossed. But it also exists below the threshold
and is in principle detectable, albeit strongly suppressed at low energies. The
results derived here can be used to give a quantitative definition of the
`effectiveness' of a theory in terms of the relative weight of the
deterministic versus the stochastic behavior at different energy scales.
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Spontaneous symmetry breaking in light front field theory: A semiclassical picture of spontaneous symmetry breaking in light front field
theory is formulated. It is based on a finite-volume quantization of
self-interacting scalar fields obeying antiperiodic boundary conditions. This
choice avoids a necessity to solve the zero mode constraint and enables one to
define unitary operators which shift scalar field by a constant. The operators
simultaneously transform the light-front vacuum to coherent states with lower
energy than the Fock vacuum and with non-zero expectation value of the scalar
field. The new vacuum states are non-invariant under the discrete or continuous
symmetry of the Hamiltonian. Spontaneous symmetry breaking is described in this
way in the two-dimensional \lambda\phi^4 theory and in the three-dimensional
O(2)-symmetric sigma model. A qualitative treatment of topological kink
solutions in the first model and a derivation of the Goldstone theorem in the
second one is given. Symmetry breaking in the case of periodic boundary
conditions is also briefly discussed.
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Quantum Field Theory at high multiplicity: The Higgsplosion mechanism: This master thesis seeks to understand what happens to a Quantum Field Theory
when we are in the high multiplicity regime. The motivation for this study
comes from a newly (2017) proposed mechanism that would happen in scalar
theories in this limit, the Higgsplosion. We review what is known so far about
the perturbative results in this regime and some other results coming from
different approaches. We study the consequences of this mechanism for a normal
scalar theory and if it can happen in the Standard Model. The goal is to
understand if this mechanism can really happen in usual field theory, this
question will be answered in the perturbative regime because a more general
solution is still unknown. Additionally, a new possible interpretation for the
Higgsplosion mechanism is proposed and discussed.
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Thermodynamics of Dual CFTs for Kerr-AdS Black Holes: Recently Gibbons {\it et al.} in hep-th/0408217 defined a set of conserved
quantities for Kerr-AdS black holes with the maximal number of rotation
parameters in arbitrary dimension. This set of conserved quantities is defined
with respect to a frame which is non-rotating at infinity. On the other hand,
there is another set of conserved quantities for Kerr-AdS black holes, defined
by Hawking {\it et al.} in hep-th/9811056, which is measured relative to a
frame rotating at infinity. Gibbons {\it et al.} explicitly showed that the
quantities defined by them satisfy the first law of black hole thermodynamics,
while those quantities defined by Hawking {\it et al.} do not obey the first
law. In this paper we discuss thermodynamics of dual CFTs to the Kerr-AdS black
holes by mapping the bulk thermodynamic quantities to the boundary of the AdS
space. We find that thermodynamic quantities of dual CFTs satisfy the first law
of thermodynamics and Cardy-Verlinde formula only when these thermodynamic
quantities result from the set of bulk quantities given by Hawking {\it et
al.}. We discuss the implication of our results.
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The Pure Spinor Formulation of Superstrings: In this lectures we outline the construction of pure spinor superstrings. We
consider both the open and closed pure spinor superstrings in critical and
noncritical dimensions and on flat and curved target spaces with RR flux. We
exhibit the integrability properties of pure spinor superstrings on curved
backgrounds with RR fluxes.
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One-shot holography: Following the work of [2008.03319], we define a generally covariant
max-entanglement wedge of a boundary region $B$, which we conjecture to be the
bulk region reconstructible from $B$. We similarly define a covariant
min-entanglement wedge, which we conjecture to be the bulk region that can
influence the boundary state on $B$. We prove that the min- and
max-entanglement wedges obey various properties necessary for this conjecture,
such as nesting, inclusion of the causal wedge, and a reduction to the usual
quantum extremal surface prescription in the appropriate special cases. These
proofs rely on one-shot versions of the (restricted) quantum focusing
conjecture (QFC) that we conjecture to hold. We argue that this QFC implies a
one-shot generalized second law (GSL) and quantum Bousso bound. Moreover, in a
particular semiclassical limit we prove this one-shot GSL directly using
algebraic techniques. Finally, in order to derive our results, we extend both
the frameworks of one-shot quantum Shannon theory and state-specific
reconstruction to finite-dimensional von Neumann algebras, allowing nontrivial
centers.
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One-Dimensional Sectors From the Squashed Three-Sphere: Three-dimensional $\mathcal{N} = 4$ superconformal field theories contain 1d
topological sectors consisting of twisted linear combinations of half-BPS local
operators that can be inserted anywhere along a line. After a conformal mapping
to a round three-sphere, the 1d sectors are now defined on a great circle of
$S^3$. We show that the 1d topological sectors are preserved under the
squashing of the sphere. For gauge theories with matter hypermultiplets, we use
supersymmetric localization to derive an explicit description of the
topological sector associated with the Higgs branch. Furthermore, we find that
the dependence of the 1d correlation functions on the squashing parameter $b$
can be removed after appropriate rescalings. One can introduce real mass and
Fayet-Iliopolous parameters that, after appropriate rescalings, modify the 1d
theory on the squashed sphere precisely as they do on the round sphere. In
addition, we also show that when a generic 3d $\mathcal{N}=4$ theory is
deformed by real mass parameters, this deformation translates into a universal
deformation of the corresponding 1d theory.
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Notes on generalized global symmetries in QFT: It was recently argued that quantum field theories possess one-form and
higher-form symmetries, labelled `generalized global symmetries.' In this
paper, we describe how those higher-form symmetries can be understood
mathematically as special cases of more general 2-groups and higher groups, and
discuss examples of quantum field theories admitting actions of more general
higher groups than merely one-form and higher-form symmetries. We discuss
analogues of topological defects for some of these higher symmetry groups,
relating some of them to ordinary topological defects. We also discuss
topological defects in cases in which the moduli `space' (technically, a stack)
admits an action of a higher symmetry group. Finally, we outline a proposal for
how certain anomalies might potentially be understood as describing a
transmutation of an ordinary group symmetry of the classical theory into a
2-group or higher group symmetry of the quantum theory, which we link to WZW
models and bosonization.
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New results in the deformed N=4 SYM theory: We investigate various perturbative properties of the deformed N=4 SYM
theory. We carry out a three-loops calculation of the chiral matter superfield
propagator and derive the condition on the couplings for maintaining finiteness
at this order. We compute the 2-, 3- and 4-point functions of composite
operators of dimension 2 at two loops. We identify all the scalar operators
(chiral and non-chiral) of bare dimension 4 with vanishing one-loop anomalous
dimension. We compute some 2- and 3-point functions of these operators at two
loops and argue that the observed finite corrections cannot be absorbed by a
finite renormalization of the operators.
|
Physical States in Matter-Coupled Dilaton Gravity: We revisit the quantization of matter-coupled, two-dimensional dilaton
gravity. At the classical level and with a cosmological term, a series of field
transformations leads to a set of free fields of indefinite signature. Without
matter the system is represented by two scalar fields of opposite signature.
With a particular quantization for the scalar with negative kinetic energy, the
system has zero central charge and we find some physical states satisfying {\it
all} the Virasoro conditions. With matter, the constraints cannot be solved
because of the Virasoro anomaly. We discuss two avenues for consistent
quantization: modification of the constraints, and BRST quantization. The first
avenue appears to lead to very few physical states. The second, which roughly
corresponds to satisfying half of the Virasoro conditions, results in a rich
spectrum of physical states. This spectrum, however, differs significantly from
that of free matter fields propagating on flat two-dimensional space-time.
|
The Complexity of Learning (Pseudo)random Dynamics of Black Holes and
Other Chaotic Systems: It has been recently proposed that the naive semiclassical prediction of
non-unitary black hole evaporation can be understood in the fundamental
description of the black hole as a consequence of ignorance of high-complexity
information. Validity of this conjecture implies that any algorithm which is
polynomially bounded in computational complexity cannot accurately reconstruct
the black hole dynamics. In this work, we prove that such bounded quantum
algorithms cannot accurately predict (pseudo)random unitary dynamics, even if
they are given access to an arbitrary set of polynomially complex observables
under this time evolution; this shows that "learning" a (pseudo)random unitary
is computationally hard. We use the common simplification of modeling black
holes and more generally chaotic systems via (pseudo)random dynamics. The
quantum algorithms that we consider are completely general, and their attempted
guess for the time evolution of black holes is likewise unconstrained: it need
not be a linear operator, and may be as general as an arbitrary (e.g.
decohering) quantum channel.
|
New Einstein-Hilbert type action of space-time and matter
-Nonlinear-supersymmetric general relativity theory-: The geometric argument of the general relativity principle can be carried out
on (unstable) Riemann space-time just inspired by nonlinear representation of
supersymmetry(NLSUSY), where tangent space is specified by Grassmann degrees of
freedom $\psi$ for SL(2,C) besides the ordinary Minkowski one $x^{a}$ for
SO(1,3) and gives straightforwardly new Einstein-Hilbert(EH)-type action with
global NLSUSY invariance(NLSUSYGR)) equipped with the cosmological term. Due to
the NLSUSY nature of space-time NLSUSYGR would collapse(Big Collapse)
spontaneously to ordinary E-H action of graviton, NLSUSY action of
Nambu-Goldstone fermion $\psi$ and their gravitational interaction.
Simultaneously the universal attractive gravitational force would constitute
the NG fermion-composites corresponding to the eigenstates of liner-SUSY(LSUSY)
super-Poincar\'{e}(sP) symmetry of space-time, which gives a new paradigm for
the unification of space-time and matter, which can . bridge naturally the
cosmology and the low energy particle physics and provides new insights into
unsolved problems of cosmology, SM and mysterious relations between them, e.g.
the space-time dimension {\it four}, the origin of SUSY breaking, the dark
energy and dark matter, the dark energy density$\sim$( neutrino mass$)^{4}$,
the tiny neutrino mass, the three-generations structure of quarks and leptons,
the rapid expansion of space-time, the magnitude of bare gauge coupling
constant, etc..
|
Interactions of Irregular Gaiotto States in Liouville Theory: We compute the correlation functions of irregular Gaiotto states appearing in
the colliding limit of the Liouville theory by using "regularizing" conformal
transformations mapping the irregular (coherent) states to regular vertex
operators in the Liouville theory. The $N$-point correlation functions of the
irregular vertex operators of arbitrary ranks are expressed in terms of
$N$-point correlators of primary fields times the factor that involves
regularized higher-rank Schwarzians of the above conformal transformation. In
particular, in the case of three-point functions the general answer is
expressed in terms of DOZZ (Dorn-Otto-Zamolodchikov-Zamolodchikov) structure
constants times exponents of regularized higher-derivative Schwarzians. The
explicit examples of the regularization are given for the ranks one and two.
|
The Standard Model in the Latticized Bulk: We construct the manifestly gauge invariant effective Lagrangian in 3+1
dimensions describing the Standard Model in 4+1 dimensions, following the
transverse lattice technique. We incorporate split generation fermions and we
explore naturalness for two Higgs configurations: a universal Higgs VEV, common
to each transverse brane, and a local Higgs VEV centered on a single brane with
discrete exponential attenuation to other branes, emulating the
split-generation model. Extra dimensions, with explicit Higgs, do not
ameliorate the naturalness problem.
|
Quasi-Local Conserved Charges in Covariant Theory of Gravity: In any generally covariant theory of gravity, we show the relationship
between the linearized asymptotically conserved current and its non-linear
completion through the identically conserved current. Our formulation for
conserved charges is based on the Lagrangian description, and so completely
covariant. By using this result, we give a prescription to define quasi-local
conserved charges in any higher derivative gravity. As applications of our
approach, we demonstrate the angular momentum invariance along the radial
direction of black holes and reproduce more efficiently the linearized
potential on the asymptotic AdS space.
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Matrix string states in pure 2d Yang Mills theories: We quantize pure 2d Yang-Mills theory on a torus in the gauge where the field
strength is diagonal. Because of the topological obstructions to a global
smooth diagonalization, we find string-like states in the spectrum similar to
the ones introduced by various authors in Matrix string theory. We write
explicitly the partition function, which generalizes the one already known in
the literature, and we discuss the role of these states in preserving modular
invariance. Some speculations are presented about the interpretation of 2d
Yang-Mills theory as a Matrix string theory.
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Collisions of weakly-bound kinks in the Christ-Lee model: We investigate soliton collisions a one-parameter family of scalar field
theories in 1+1 dimensions which was first discussed by Christ and Lee. The
models have a sextic potential with three local minima, and for suitably small
values of the parameter its kinks have an internal structure in the form of two
weakly-bound subkinks. We show that for these values of the parameter kink
collisions are best understood as an independent sequence of collisions of
these subkinks, and that a static mode analysis is not enough to explain
resonant structures emerging in this model. We also emphasise the role of
radiation and oscillon formation in the collision process.
|
The Entropy for General Extremal Black Holes: We use the Kerr/CFT correspondence to calculate the entropy for all known
extremal stationary and axisymmetric black holes. This is done with the help of
two ansatzs that are general enough to cover all such known solutions.
Considering only the contribution from the Einstein-Hilbert action to the
central charge(s), we find that the entropy obtained by using Cardy's formula
exactly matches with the Bekenstein-Hawking entropy.
|
The quantum cosmological tilt and the origin of dark matter: A promising candidate for cold dark matter is primordial black holes (PBH)
formed from strong primordial quantum fluctuations. A necessary condition for
the formation of PBH's is a change of sign in the tilt governing the anomalous
scale invariance of the power spectrum from red at large scales into blue at
small scales. Non-perturbative information on the dependence of the power
spectrum tilt on energy scale can be extracted from the quantum Fisher
information measuring the energy dependence of the quantum phases defining the
de Sitter vacua. We show that this non-perturbative quantum tilt goes from a
red tilted phase, at large scales, into a blue tilted phase at small scales
converging to $n_s=2$ in the UV. This allows the formation of PBH's in the
range of masses $\lesssim 10^{20} gr$.
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Matrix models from localization of five-dimensional supersymmetric
noncommutative U(1) gauge theory: We study localization of five-dimensional supersymmetric $U(1)$ gauge theory
on $\mathbb{S}^3 \times \mathbb{R}_{\theta}^{2}$ where
$\mathbb{R}_{\theta}^{2}$ is a noncommutative (NC) plane. The theory can be
isomorphically mapped to three-dimensional supersymmetric $U(N \to \infty)$
gauge theory on $\mathbb{S}^3$ using the matrix representation on a separable
Hilbert space on which NC fields linearly act. Therefore the NC space
$\mathbb{R}_{\theta}^{2}$ allows for a flexible path to derive matrix models
via localization from a higher-dimensional supersymmetric NC $U(1)$ gauge
theory. The result shows a rich duality between NC $U(1)$ gauge theories and
large $N$ matrix models in various dimensions.
|
q-deformed lattice gauge theory and 3-manifold invariants: The notion of $q$-deformed lattice gauge theory is introduced. If the
deformation parameter is a root of unity, the weak coupling limit of a 3-$d$
partition function gives a topological invariant for a corresponding
3-manifold. It enables us to define the generalized Turaev-Viro invariant for
cell complexes. It is shown that this invariant is determined by an action of a
fundamental group on a universal covering of a complex. A connection with
invariants of framed links in a manifold is also explored. A model giving a
generating function of all simplicial complexes weighted with the invariant is
investigated.
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Localised anti-branes in non-compact throats at zero and finite T: We investigate the 3-form singularities that are typical to anti-brane
solutions in supergravity and check whether they can be cloaked by a finite
temperature horizon. For anti-D3-branes in the Klebanov-Strassler background,
this was already shown numerically to be impossible when the branes are
partially smeared. In this paper, we present analytic arguments that also
localised branes remain with singular 3-form fluxes at both zero and finite
temperature. These results may have important, possibly fatal, consequences for
constructions of meta-stable de Sitter vacua through uplifting.
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A semiclassical analysis of the fluctuation eigenvalues and the one-loop
energy of the folded spinning superstring in AdS_5 x S^5: We systematically construct a semiclassical expansion for the eigenvalues of
the 2nd order quantum fluctuations of the folded spinning superstring rotating
in the AdS_3 part of AdS_5 x S^5 with two alternative methods; by using the
exact expression of the Bloch momentum generated by the curvature induced
periodic potentials and by using the large energy expansion of the dispersion
relation. We then calculate the one-loop correction to the energy by summing
over the eigenvalues. Our results are extremely accurate for strings whose ends
are not too close to the AdS radius. Finally we derive the small spin Regge
expansion in the context of zeta function approximation.
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Constrained quantization and $θ$-angles: We apply a new and mathematically rigorous method for the quantization of
constrained systems to two-dimensional gauge theories. In this method, which
quantizes Marsden-Weinstein symplectic reduction, the inner product on the
physical state space is expressed through a certain integral over the gauge
group. The present paper, the first of a series, specializes to the Minkowski
theory defined on a cylinder. The integral in question is then constructed in
terms of the Wiener measure on a loop group. It is shown how $\th$-angles
emerge in the new method, and the abstract theory is illustrated in detail in
an example.
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Triangle (Causal) Distributions in the Causal Approach: The tensor Feynman amplitudes are reduced to scalar integrals by a procedure
of Passarino and Veltman. We provide an alternative approach based on the
causal formalism.
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First-order solitons with internal structures in an extended
Maxwell-$CP(2)$ model: We study a Maxwell-$CP(2)$ model coupled to a real scalar field through a
dielectric function multiplying the Maxwell term. In such a context, we look
for first-order rotationally symmetric solitons by means of the Bogomol'nyi
algorithm, i.e. by minimizing the total energy of the effective model. We
perform our investigation by choosing an explicit form of the dielectric
function. The numerical solutions show regular vortices whose shapes
dramatically differ from their canonical counterparts. We can understood such
differences as characterizing the existence of an internal structure.
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Quantum curves and conformal field theory: To a given algebraic curve we assign an infinite family of quantum curves
(Schr\"odinger equations), which are in one-to-one correspondence with, and
have the structure of, Virasoro singular vectors. For a spectral curve of a
matrix model we build such quantum curves out of an appropriate representation
of the Virasoro algebra, encoded in the structure of the
$\alpha/\beta$-deformed matrix integral and its loop equation. We generalize
this construction to a large class of algebraic curves by means of a refined
topological recursion. We also specialize this construction to various specific
matrix models with polynomial and logarithmic potentials, and among other
results, show that various ingredients familiar in the study of conformal field
theory (Ward identities, correlation functions and a representation of Virasoro
operators acting thereon, BPZ equations) arise upon specialization of our
formalism to the multi-Penner matrix model.
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The Matrix Product Ansatz for integrable U(1)^N models in
Lunin-Maldacena backgrounds: We obtain through a Matrix Product Ansatz (MPA) the exact solution of the
most general $N$-state spin chain with $U(1)^N$ symmetry and nearest neighbour
interaction. In the case N=6 this model contain as a special case the
integrable SO(6) spin chain related to the one loop mixing matrix for anomalous
dimensions in ${\cal N} = 4$ SYM, dual to type $IIB$ string theory in the
generalised Lunin-Maldacena backgrounds. This MPA is construct by a map between
scalar fields and abstract operators that satisfy an appropriate associative
algebra. We analyses the Yang-Baxter equation in the N=3 sector and the
consistence of the algebraic relations among the matrices defining the MPA and
find a new class of exactly integrable model unknown up to now.
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Branes, Geometry and N=1 Duality with Product Gauge Groups of SO and Sp: We study N=1 dualities in four dimensional supersymmetric gauge theories as
the worldvolume theory of D4 branes with one compact direction in type IIA
string theory. We generalize the previous work for SO(N_{c1}) x Sp(N_{c2}) with
the superpotential W=Tr X^4 to the case of W= Tr X^4(k+1) in terms of brane
configuration. We conjecture that the new dualities for the product gauge
groups of SO(N_{c1}) x Sp(N_{c2}) x SO(N_{c3}), SO(N_{c1}) x Sp(N_{c2}) x
SO(N_{c3}) x Sp(N_{c4}) and higher multiple product gauge groups can be
obtained by reversing the ordering of NS5 branes and D6 branes while preserving
the linking numbers. We also describe the above dualities in terms of wrapping
D6 branes around 3 cycles of Calabi-Yau threefolds in type IIA string theory.
The theory with adjoint matter can be regarded as taking multiple copies of NS5
brane in the configuration of brane or geometric approaches.
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Higher Spin Conformal Symmetry for Matter Fields in 2+1 Dimensions: A simple realization of the conformal higher spin symmetry on the free $3d$
massless matter fields is given in terms of an auxiliary Fock module both in
the flat and $AdS_3$ case. The duality between non-unitary field-theoretical
representations of the conformal algebra and the unitary (singleton--type)
representations of the $3d$ conformal algebra $sp(4,\R)$ is formulated
explicitly in terms of a certain Bogolyubov transform.
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Dirac Born Infeld (DBI) Cosmic Strings: Motivated by brane physics, we consider the non-linear Dirac-Born-Infeld
(DBI) extension of the Abelian-Higgs model and study the corresponding cosmic
string configurations. The model is defined by a potential term, assumed to be
of the mexican hat form, and a DBI action for the kinetic terms. We show that
it is a continuous deformation of the Abelian-Higgs model, with a single
deformation parameter depending on a dimensionless combination of the scalar
coupling constant, the vacuum expectation value of the scalar field at
infinity, and the brane tension. By means of numerical calculations, we
investigate the profiles of the corresponding DBI-cosmic strings and prove that
they have a core which is narrower than that of Abelian-Higgs strings. We also
show that the corresponding action is smaller than in the standard case
suggesting that their formation could be favoured in brane models. Moreover we
show that the DBI-cosmic string solutions are non-pathological everywhere in
parameter space. Finally, in the limit in which the DBI model reduces to the
Bogomolnyi-Prasad-Sommerfield (BPS) Abelian-Higgs model, we find that DBI
cosmic strings are no longer BPS: rather they have positive binding energy. We
thus argue that, when they meet, two DBI strings will not bind with the
corresponding formation of a junction, and hence that a network of DBI strings
is likely to behave as a network of standard cosmic strings.
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Counterpart of the Weyl tensor for Rarita-Schwinger type fields: In dimensions larger than 3 a modified field strength for Rarita-Schwinger
type fields is constructed whose components are not constrained by the field
equations. In supergravity theories the result provides a modified
(supercovariant) gravitino field strength related by supersymmetry to the
(supercovariantized) Weyl tensor. In various cases, such as for free
Rarita-Schwinger type gauge fields and for gravitino fields in several
supergravity theories, the modified field strength coincides on-shell with the
usual field strength. A corresponding result for first order derivatives of
Dirac type spinor fields is also presented.
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A review on radiation of oscillons and oscillatons: Numerical simulations show that a massive real scalar field in a nonlinear
theory can form long-lived oscillating localized states. For a self-interacting
scalar on a fixed background these objects are named oscillons, while for the
self-gravitating case they are called oscillatons. This extensive review is
about the history and various general properties of these solutions, though
mainly focusing on the small but nonzero classical scalar field radiation
emitted by them. The radiation for higher amplitude states can be calculated by
a spectral numerical method. For small and moderately large amplitudes an
analytical approach based on complex extension, asymptotic matching and Borel
summation can be used. This procedure for the calculation of the energy loss
rate is explained in a detailed way in this review, starting with the simplest
one-dimensional scalar oscillons at first, and reaching to $3+1$ dimensional
self-gravitating oscillatons based on that experience.
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The Principle of Maximal Transcendentality and the Four-Loop Collinear
Anomalous Dimension: We use the principle of maximal transcendentality and the universal nature of
subleading infrared poles to extract the analytic value of the four-loop
collinear anomalous dimension in planar ${\cal N}=4$ super-Yang-Mills theory
from recent QCD results, obtaining $\hat{\cal G}_{0}^{(4)} = - 300 \zeta_7 -
256 \zeta_2 \zeta_5 - 384 \zeta_3 \zeta_4$. This value agrees with a previous
numerical result to within 0.2 percent. It also provides the Regge trajectory,
threshold soft anomalous dimension and rapidity anomalous dimension through
four loops.
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g-function flow in perturbed boundary conformal field theories: The g-function was introduced by Affleck and Ludwig as a measure of the
ground state degeneracy of a conformal boundary condition. We consider this
function for perturbations of the conformal Yang-Lee model by bulk and boundary
fields using conformal perturbation theory, the truncated conformal space
approach and the thermodynamic Bethe Ansatz (TBA). We find that the TBA
equations derived by LeClair et al describe the massless boundary flows, up to
an overall constant, but are incorrect when one considers a simultaneous bulk
perturbation; however the TBA equations do correctly give the `non-universal'
linear term in the massive case, and the ratio of g-functions for different
boundary conditions is also correctly produced. This ratio is related to the
Y-system of the Yang-Lee model and by comparing the perturbative expansions of
the Y-system and of the g-functions we obtain the exact relation between the UV
and IR parameters of the massless perturbed boundary model.
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Turing's Landscape: decidability, computability and complexity in string
theory: I argue that questions of algorithmic decidability, computability and
complexity should play a larger role in deciding the "ultimate" theoretical
description of the Landscape of string vacua. More specifically, I examine the
notion of the average rank of the (unification) gauge group in the Landscape,
the explicit construction of Ricci-flat metrics on Calabi-Yau manifolds as well
as the computability of fundamental periods to show that undecidability
questions are far more pervasive than that described in the work of Denef and
Douglas.
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Perturbative Evaluation of the Effective Action for a Self-Interacting
Conformal Field on a Manifold with Boundary: In a series of three projects a new technique which allows for higher-loop
renormalisation on a manifold with boundary has been developed and used in
order to assess the effects of the boundary on the dynamical behaviour of the
theory. Commencing with a conceptual approach to the theoretical underpinnings
of the, underlying, spherical formulation of Euclidean Quantum Field Theory
this overview presents an outline of the stated technique's conceptual
development, mathematical formalism and physical significance.
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Chiral torsional effect with finite temperature, density and curvature: We scrutinize the novel chiral transport phenomenon driven by spacetime
torsion, namely the chiral torsional effect (CTE). We calculate the
torsion-induced chiral currents with finite temperature, density and curvature
in the most general torsional gravity theory. The conclusion complements the
previous study on the CTE by including curvature and substantiates the relation
between the CTE and the Nieh-Yan anomaly. We also analyze the response of
chiral torsional current to an external electromagnetic field. The resulting
topological current is analogous to that in the axion electrodynamics.
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Soft theorems in curved spacetime: In this paper, we derive a soft photon theorem in the near horizon region of
the Schwarzschild black hole from the Ward identity of the near horizon large
gauge transformation. The flat spacetime soft photon theorem can be recovered
as a limiting case of the curved spacetime. The soft photons on the horizon are
indeed soft electric hairs. This accomplishes the triangle equivalence on the
black hole horizon.
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Confinement of neutral fermions by a pseudoscalar double-step potential
in (1+1) dimensions: The problem of confinement of neutral fermions in two-dimensional space-time
is approached with a pseudoscalar double-step potential in the Dirac equation.
Bound-state solutions are obtained when the coupling is of sufficient
intensity. The confinement is made plausible by arguments based on effective
mass and anomalous magnetic interaction.
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Numerical approach to SUSY quantum mechanics and the gauge/gravity
duality: We demonstrate that Monte-Carlo simulation is a practical tool to study
nonperturbative aspects of supersymmetric quantum mechanics. As an example we
study D0-brane quantum mechanics in the context of superstring theory.
Numerical data nicely reproduce predictions from gravity side, including the
coupling constant dependence of the string alpha' correction. This strongly
suggests the duality to hold beyond the supergravity approximation. Although
detail of the stringy correction cannot be obtained by state-of-the-art
techniques in gravity side, in the matrix quantum mechanics we can obtain
concrete values. Therefore the Monte-Carlo simulation combined with the duality
provides a powerful tool to study the superstring theory.
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N=2 gauge theories and quantum phases: The partition function of general N = 2 supersymmetric SU(2) Yang-Mills
theories on a four-sphere localizes to a matrix integral. We show that in the
decompactification limit, and in a certain regime, the integral is dominated by
a saddle point. When this takes effect, the free energy is exactly given in
terms of the prepotential, $F=-R^2 Re (4\pi i {\cal F}) $, evaluated at the
singularity of the Seiberg-Witten curve where the dual magnetic variable $a_D$
vanishes. We also show that the superconformal fixed point of massive
supersymmetric QCD with gauge group SU(2) is associated with the existence of a
quantum phase transition. Finally, we discuss the case of N=2* SU(2) Yang-Mills
theory and show that the theory does not exhibit phase transitions.
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More on correlators and contact terms in {\cal N}=4 SYM at order g^4: We compute two-point functions of chiral operators Tr(\Phi^k) for any k, in
{\cal N}=4 supersymmetric SU(N) Yang-Mills theory. We find that up to the order
g^4 the perturbative corrections to the correlators vanish for all N. The
cancellation occurs in a highly non trivial way, due to a complicated interplay
between planar and non planar diagrams. In complete generality we show that
this same result is valid for any simple gauge group. Contact term
contributions signal the presence of ultraviolet divergences. They are
arbitrary at the tree level, but the absence of perturbative renormalization in
the non singular part of the correlators allows to compute them unambiguously
at higher orders. In the spirit of the AdS/CFT correspondence we comment on
their relation to infrared singularities in the supergravity sector.
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Integrability and Scheme-Independence of Even Dimensional Quantum
Geometry Effective Action: We investigate how the integrability conditions for conformal anomalies
constrain the form of the effective action in even-dimensional quantum
geometry. We show that the effective action of four-dimensional quantum
geometry (4DQG) satisfying integrability has a manifestly diffeomorphism
invariant and regularization scheme-independent form. We then generalize the
arguments to six dimensions and propose a model of 6DQG. A hypothesized form of
the 6DQG effective action is given.
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Deconstruction, Lattice Supersymmetry, Anomalies and Branes: We study the realization of anomalous Ward identities in deconstructed
(latticized) supersymmetric theories. In a deconstructed four-dimensional
theory with N=2 supersymmetry, we show that the chiral symmetries only appear
in the infrared and that the anomaly is reproduced in the usual framework of
lattice perturbation theory with Wilson fermions. We then realize the theory on
the world-volume of fractional D-branes on an orbifold. In this brane
realization, we show how deconstructed theory anomalies can be computed via
classical supergravity. Our methods and observations are more generally
applicable to deconstructed/latticized supersymmetric theories in various
dimensions.
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Supertranslation Goldstone and de Sitter Tachyons: Supertranslation Goldstone lies in certain "exceptional series"
representations of $SL(2,\mathbb{C})$. Interestingly, $m^2=-3$ scalar tachyon
in three dimensional de Sitter space also lies in the same representation. In
this note, we analyze these theories, focusing on representation-theoretical
aspects, and emphasize that "modulo certain polynomials", there is a unitary
representation of the corresponding symmetry group.
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Mirror quintic vacua: hierarchies and inflation: We study the moduli space of type IIB string theory flux compactifications on
the mirror of the CY quintic 3-fold in P4. We focus on the dynamics of the four
dimensional moduli space, defined by the axio-dilaton {\tau} and the complex
structure modulus z. The z-plane has critical points, the conifold, the
orbifold and the large complex structure with non trivial monodromies. We find
the solutions to the Picard-Fuchs equations obeyed by the periods of the CY in
the full z-plane as a series expansion in z around the critical points to
arbitrary order. This allows us to discard fake vacua, which appear as a result
of keeping only the leading order term in the series expansions. Due to
monodromies vacua are located at a given sheet in the z-plane. A dS vacuum
appears for a set of fluxes. We revisit vacua with hierarchies among the 4D and
6D physical scales close to the conifold point and compare them with those
found at leading order in [1, 2]. We explore slow-roll inflationary directions
of the scalar potential by looking at regions where the multi-field slow-roll
parameters {\epsilon} and {\eta} are smaller than one. The value of {\epsilon}
depends strongly on the approximation of the periods and to achieve a stable
value, several orders in the expansion are needed. We do not find realisations
of single field axion monodromy inflation. Instead, we find that inflationary
regions appear along linear combinations of the four real field directions and
for certain configurations of fluxes.
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Higher Derivative Fermionic Field Theories: We carry out the extension of the covariant Ostrogradski method to fermionic
field theories. Higher-derivative Lagrangians reduce to second order
differential ones with one explicit independent field for each degree of
freedom.
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Neumann-Rosochatius system for rotating strings in $AdS_3 \times
S^3\times S^3\times S^1$ with flux: Strings on $AdS_3 \times S^3\times S^3\times S^1$ with mixed flux exhibit
exact integrability. We wish to construct an integrable Neumann-Rosochatius
(NR) model of strings starting with the type IIB supergravity action in $AdS_3
\times S^3\times S^3\times S^1$ with pure NSNS flux. We observe that the forms
of the Lagrangian and the Uhlenbeck integrals of motion of the considered
system are NR-like with some suitable deformations which eventually appear due
to the presence of flux. We utilize the integrable framework of the deformed NR
model to analyze rigidly rotating spiky strings moving only in $S^3\times S^1$.
We further present some mathematical speculations on the rounding-off nature of
the spike in the presence of non-zero angular momentum $J$ in $S^1$.
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Non Abelian Dual Maps in Path Space: We study an extension of the procedure to construct duality transformations
among abelian gauge theories to the non abelian case using a path space
formulation. We define a pre-dual functional in path space and introduce a
particular non local map among Lie algebra valued 1-form functionals that
reduces to the ordinary Hodge-* duality map of the abelian theories. Further,
we establish a full set of equations on path space representing the ordinary
Yang Mills equations and Bianchi identities of non abelian gauge theories of
4-dimensional euclidean space.
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Microscopic Origin of the Shear Relaxation Time in Causal Dissipative
Fluid Dynamics: In this paper we show how to compute the shear relaxation time from an
underlying microscopic theory. We prove that the shear relaxation time in
Israel-Stewart-type theories is given by the inverse of the pole of the
corresponding retarded Green's function, which is nearest to the origin in the
complex energy plane. Consequently, the relaxation time in such theories is a
microscopic, and not a macroscopic, i.e., fluid-dynamical time scale.
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Semiclassical and quantum Liouville theory on the sphere: We solve the Riemann-Hilbert problem on the sphere topology for three
singularities of finite strength and a fourth one infinitesimal, by determining
perturbatively the Poincare' accessory parameters. In this way we compute the
semiclassical four point vertex function with three finite charges and a fourth
infinitesimal. Some of the results are extended to the case of n finite charges
and m infinitesimal. With the same technique we compute the exact Green
function on the sphere with three finite singularities. Turning to the full
quantum problem we address the calculation of the quantum determinant on the
background of three finite charges and the further perturbative corrections.
The zeta function technique provides a theory which is not invariant under
local conformal transformations. Instead by employing a regularization
suggested in the case of the pseudosphere by Zamolodchikov and Zamolodchikov we
obtain the correct quantum conformal dimensions from the one loop calculation
and we show explicitly that the two loop corrections do not change such
dimensions. We expect such a result to hold to all order perturbation theory.
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Current-current deformations, conformal integrals and correlation
functions: Motivated by the recent work on $T\bar{T}$-type deformations of 2D CFTs, a
especial class of single-trace deformations of AdS$_3$/CFT$_2$ correspondence
has been investigated. From the worldsheet perspective, this corresponds to a
marginal deformation of the $\sigma $-model on AdS$_3$ that yields a string
background that interpolates between AdS$_3$ and a flat linear dilaton
solution. Here, with the intention of studying this worldsheet CFT further, we
consider it in the presence of a boundary. In a previous paper, we computed
different correlation functions of this theory on the disk, including the bulk
1-point function, the boundary-boundary 2-point function, and the bulk-boundary
2-point function. This led us to compute the anomalous dimension of both bulk
and boundary vertex operators, which first required a proper regularization of
the ultraviolet divergences of the conformal integrals. Here, we extend the
analysis by computing the bulk-bulk 2-point function on the disk and other
observables on the sphere. We prove that the renormalization of the vertex
operators proposed in our previous works is consistent with the form of the
sphere $N$-point functions.
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Henon-Heiles potential as a bridge between nontopological solitons of
different types: We apply the Hubbard-Stratanovich transformation to the Lagrangian for
nontopological solitons of the Coleman type in a two-dimensional theory. The
resulted theory with an extra real scalar field can be supplemented with a
cubic term to obtain a model with exact analytical solution.
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Open Strings on AdS_2 Branes: We study the spectrum of open strings on AdS_2 branes in AdS_3 in an NS-NS
background, using the SL(2,R) WZW model. When the brane carries no fundamental
string charge, the open string spectrum is the holomorphic square root of the
spectrum of closed strings in AdS_3. It contains short and long strings, and is
invariant under spectral flow. When the brane carries fundamental string
charge, the open string spectrum again contains short and long strings in all
winding sectors. However, branes with fundamental string charge break half the
spectral flow symmetry. This has different implications for short and long
strings. As the fundamental string charge increases, the brane approaches the
boundary of AdS_3. In this limit, the induced electric field on the worldvolume
reaches its critical value, producing noncommutative open string theory on
AdS_2.
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Wilson loop via AdS/CFT duality: The Wilson loop in N=4 supersymmetric Yang-Mills theory admits a dual
description as a macroscopic string configuration in the adS/CFT
correspondence. We discuss the correction to the quark anti-quark potential
arising from the fluctuations of the superstring.
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Boundary form factors in finite volume: We describe the volume dependence of matrix elements of local boundary fields
to all orders in inverse powers of the volume. Using the scaling boundary
Lee-Yang model as testing ground, we compare the matrix elements extracted from
boundary truncated conformal space approach to exact form factors obtained
using the bootstrap method. We obtain solid confirmation for the boundary form
factor bootstrap, which is different from all previously available tests in
that it is a non-perturbative and direct comparison of exact form factors to
multi-particle matrix elements of local operators, computed from the
Hamiltonian formulation of the quantum field theory.
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Single Particle Excitations in the Lattice E_8 Ising Model: We present analytic expressions for the single particle excitation energies
of the 8 quasi-particles in the lattice $E_8$ Ising model and demonstrate that
all excitations have an extended Brillouin zone which, depending on the
excitation, ranges from 0<P < 4\pi to 0< P< 12 \pi. These are compared with
exact diagonalizations for systems through size 10 and with the E_8 fermionic
representations of the characters of the critical system in order to study the
counting statistics.
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Supersymmetry and exceptional points: A conceptual bridge is provided between SUSY and the three-Hilbert-space
upgrade of quantum theory a.k.a. ${\cal PT}-$symmetric or quasi-Hermitian. In
particular, a natural theoretical link is found between SUSY and the presence
of Kato's exceptional points (EPs), both being related to the phenomenon of
degeneracy of energy levels. Regularized spiked harmonic oscillator is recalled
for illustration.
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A note on the Einstein equation in string theory: We show, using purely classical considerations and logical extrapolation of
results belonging to point particle theories, that the metric background field
in which a string propagates must satisfy an Einstein or an Einstein-like
equation. Additionally, there emerge restrictions on the worldsheet curvature,
which seems to act as a source for spacetime gravity, even in the absence of
other matter fields.
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Global torus blocks in the necklace channel: We continue studying of global conformal blocks on the torus in a special
(necklace) channel. Functions of such multi-point blocks are explicitly found
under special conditions on the blocks' conformal dimensions. We have verified
that these blocks satisfy the Casimir equations, which were derived in previous
studies.
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The supergravity dual of 3d supersymmetric gauge theories with
unquenched flavors: We obtain the supergravity dual of N=1 supersymmetric gauge theory in 2+1
dimensions with a large number of unquenched massless flavors. The geometries
found are obtained by solving the equations of motion of supergravity coupled
to a suitable continuous distribution of flavor branes. The background obtained
preserves two supersymmetries. We find that when N_c\ge 2N_f the behavior of
the solutions is compatible with having an asymptotically free dual gauge
theory with dynamical quarks. On the contrary, when N_c<2N_f the theory
develops a Landau pole in the UV. We also find a new family of (unflavored)
backgrounds generated by D5-branes that wrap a three-cycle of a cone with G_2
holonomy.
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Path Integral for Separable Hamiltonians of Liouville-type: A general path integral analysis of the separable Hamiltonian of
Liouville-type is reviewed. The basic dynamical principle used is the Jacobi's
principle of least action for given energy which is reparametrization
invariant, and thus the gauge freedom naturally appears. The choice of gauge in
path integral corresponds to the separation of variables in operator formalism.
The gauge independence and the operator ordering are closely related. The path
integral in this formulation sums over orbits in space instead of space-time.
An exact path integral of the Green's function for the hydrogen atom in
parabolic coordinates is ilustrated as an example, which is also interpreted as
one-dimensional quantum gravity with a quantized cosmological constant.
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Baby universes in 2d and 4d theories of quantum gravity: The validity of the Coleman mechanism, which automatically tunes the
fundamental constants, is examined in two-dimensional and four-dimensional
quantum gravity theories. First, we consider two-dimensional Euclidean quantum
gravity on orientable closed manifolds coupled to conformal matter of central
charge $c \leq1$. The proper time Hamiltonian of this system is known to be
written as a field theory of noncritical strings, which can also be viewed as a
third quantization in two dimensions. By directly counting the number of random
surfaces with various topologies, we find that the contribution of the baby
universes is too small to realize the Coleman mechanism. Next, we consider
four-dimensional Lorentzian gravity. Based on the difference between the
creation of the mother universe from nothing and the annihilation of the mother
universe into nothing, we introduce a non-Hermitian effective Hamiltonian for
the multiverse. We show that Coleman's idea is satisfied in this model and that
the cosmological constant is tuned to be nearly zero. Potential implications
for phenomenology are also discussed.
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On 2d CFTs that interpolate between minimal models: We investigate exactly solvable two-dimensional conformal field theories that
exist at generic values of the central charge, and that interpolate between
A-series or D-series minimal models. When the central charge becomes rational,
correlation functions of these CFTs may tend to correlation functions of
minimal models, or diverge, or have finite limits which can be logarithmic.
These results are based on analytic relations between four-point structure
constants and residues of conformal blocks.
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On the Gauge/Gravity Correspondence and the Open/Closed String Duality: In this article we review the conditions for the validity of the
gauge/gravity correspondence in both supersymmetric and non-supersymmetric
string models. We start by reminding what happens in type IIB theory on the
orbifolds C^2/Z_2 and C^3/(Z_2 x Z_2), where this correspondence beautifully
works. In these cases, by performing a complete stringy calculation of the
interaction among D3 branes, it has been shown that the fact that this
correspondence works is a consequence of the open/closed duality and of the
absence of threshold corrections. Then we review the construction of type 0
theories with their orbifolds and orientifolds having spectra free from both
open and closed string tachyons and for such models we study the validity of
the gauge/gravity correspondence, concluding that this is not a peculiarity of
supersymmetric theories, but it may work also for non-supersymmetric models.
Also in these cases, when it works, it is again a consequence of the
open/closed string duality and of vanishing threshold corrections.
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Exact solutions of noncommutative vacuum Einstein field equations and
plane-fronted gravitational waves: We construct a class of exact solutions of the noncommutative vacuum Einstein
field equations, which are noncommutative analogues of the plane-fronted
gravitational waves in classical gravity.
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Correlation functions in finite temperature CFT and black hole
singularities: We compute thermal 2-point correlation functions in the black brane $AdS_5$
background dual to 4d CFT's at finite temperature for operators of large
scaling dimension. We find a formula that matches the expected structure of the
OPE. It exhibits an exponentiation property, whose origin we explain. We also
compute the first correction to the two-point function due to graviton
emission, which encodes the proper time from the event horizon to the black
hole singularity.
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Do all 5d SCFTs descend from 6d SCFTs?: We present examples of 5d SCFTs that serve as counter-examples to a recently
actively studied conjecture according to which it should be possible to obtain
all 5d SCFTs by integrating out BPS particles from 6d SCFTs compactified on a
circle. We further observe that it is possible to obtain these 5d SCFTs from 6d
SCFTs if one allows integrating out BPS strings as well. Based on this
observation, we propose a revised version of the conjecture according to which
it should be possible to obtain all 5d SCFTs by integrating out both BPS
particles and BPS strings from 6d SCFTs compactified on a circle. We describe a
general procedure to integrate out BPS strings from a 5d theory once a
geometric description of the 5d theory is given. We also discuss the
consequences of the revised conjecture for the classification program of 5d
SCFTs.
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Conformal Invariance in noncommutative geometry and mutually interacting
Snyder Particles: A system of relativistic Snyder particles with mutual two-body interaction
that lives in a Non-Commutative Snyder geometry is studied. The underlying
novel symplectic structure is a coupled and extended version of (single
particle) Snyder algebra. In a recent work by Casalbuoni and Gomis, Phys.Rev.
D90, 026001 (2014), a system of interacting conventional particles (in
commutative spacetime) was studied with special emphasis on it's Conformal
Invariance. Proceeding along the same lines we have shown that our interacting
Snyder particle model is also conformally invariant. Moreover, the conformal
Killing vectors have been constructed. Our main emphasis is on the Hamiltonian
analysis of the conformal symmetry generators. We demonstrate that the Lorentz
algebra remains undeformed but validity of the full conformal algebra requires
further restrictions.
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Phases of planar AdS black holes with axionic charge: Planar AdS black holes with axionic charge have finite DC conductivity due to
momentum relaxation. We obtain a new family of exact asymptotically AdS$_4$
black branes with scalar hair, carrying magnetic and axion charge, and we study
the thermodynamics and dynamic stability of these, as well as of a number of
previously known electric and dyonic solutions with axion charge and scalar
hair. The scalar hair for all solutions satisfy mixed boundary conditions,
which lead to modified holographic Ward identities, conserved charges and free
energy, relative to those following from the more standard Dirichlet boundary
conditions. We show that properly accounting for the scalar boundary conditions
leads to well defined first law and other thermodynamic relations. Finally, we
compute the holographic quantum effective potential for the dual scalar
operator and show that dynamical stability of the hairy black branes is
equivalent to positivity of the energy density.
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Closure of the Operator Product Expansion in the Non-Unitary Bootstrap: We use the numerical conformal bootstrap in two dimensions to search for
finite, closed sub-algebras of the operator product expansion (OPE), without
assuming unitarity. We find the minimal models as special cases, as well as
additional lines of solutions that can be understood in the Coulomb gas
formalism. All the solutions we find that contain the vacuum in the operator
algebra are cases where the external operators of the bootstrap equation are
degenerate operators, and we argue that this follows analytically from the
expressions in arXiv:1202.4698 for the crossing matrices of Virasoro conformal
blocks. Our numerical analysis is a special case of the "Gliozzi" bootstrap
method, and provides a simpler setting in which to study technical challenges
with the method.
In the supplementary material, we provide a Mathematica notebook that
automates the calculation of the crossing matrices and OPE coefficients for
degenerate operators using the formulae of Dotsenko and Fateev.
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Spin-Statistics and CPT Theorems in Noncommutative Field Theory: We show that Pauli's spin-statistics relation remains valid in noncommutative
quantum field theories (NC QFT), with the exception of some peculiar cases of
noncommutativity between space and time. We also prove that, while the
individual symmetries C and T, and in some cases also P, are broken, the CPT
theorem still holds in general for noncommutative field theories, in spite of
the inherent nonlocality and violation of Lorentz invariance.
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Higgs branch localization in three dimensions: We show that the supersymmetric partition function of three-dimensional N=2
R-symmetric Chern-Simons-matter theories on the squashed S^3 and on S^2 x S^1
can be computed with the so-called Higgs branch localization method,
alternative to the more standard Coulomb branch localization. For theories that
could be completely Higgsed by Fayet-Iliopoulos terms, the path integral is
dominated by BPS vortex strings sitting at two circles in the geometry. In this
way, the partition function directly takes the form of a sum, over a finite
number of points on the classical Coulomb branch, of a vortex-string times an
antivortex-string partition functions.
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Two-field cosmological models and the uniformization theorem: We propose a class of two-field cosmological models derived from gravity
coupled to non-linear sigma models whose target space is a non-compact and
geometrically-finite hyperbolic surface, which provide a wide generalization of
so-called $\alpha$-attractor models and can be studied using uniformization
theory. We illustrate cosmological dynamics in such models for the case of the
hyperbolic triply-punctured sphere.
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Finding the Mirror of the Beauville Manifold: We construct the mirror of the Beauville manifold. The Beauville manifold is
a Calabi-Yau manifold with non-abelian fundamental group. We use the conjecture
of Batyrev and Borisov to find the previously misidentified mirror of its
universal covering space, $\mathbb{P}^7[2,2,2,2]$. The monomial-divisor mirror
map is essential in identifying how the fundamental group of the Beauville
manifold acts on the mirror of $\mathbb{P}^7[2,2,2,2]$. Once we find the mirror
of the Beauville manifold, we confirm the existence of the threshold bound
state around the conifold point, which was originally conjectured in
hep-th/0106262. We also consider how the quantum symmetry group acts on the
D-branes that become massless at the conifold point and show the action
proposed in hep-th/0102018 is compatible with mirror symmetry.
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c < 1 String from Two Dimensional Black Holes: We study a topological string description of the c < 1 non-critical string
whose matter part is defined by the time-like linear dilaton CFT. We show that
the topologically twisted N=2 SL(2,R)/U(1) model (or supersymmetric 2D black
hole) is equivalent to the c < 1 non-critical string compactified at a specific
radius by comparing their physical spectra and correlation functions. We
examine another equivalent description in the topological Landau-Ginzburg model
and check that it reproduces the same scattering amplitudes. We also discuss
its matrix model dual description.
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Boundary conformal invariants and the conformal anomaly in five
dimensions: In odd dimensions the integrated conformal anomaly is entirely due to the
boundary terms \cite{Solodukhin:2015eca}. In this paper we present a detailed
analysis of the anomaly in five dimensions. We give the complete list of the
boundary conformal invariants that exist in five dimensions. Additionally to 8
invariants known before we find a new conformal invariant that contains the
derivatives of the extrinsic curvature along the boundary. Then, for a
conformal scalar field satisfying either the Dirichlet or the conformal
invariant Robin boundary conditions we use the available general results for
the heat kernel coefficient $a_5$, compute the conformal anomaly and identify
the corresponding values of all boundary conformal charges.
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Black holes with Lambert W function horizons: We consider Einstein gravity with a negative cosmological constant endowed
with distinct matter sources. The different models analyzed here share the
following two properties: (i) they admit static symmetric solutions with planar
base manifold characterized by their mass and some additional Noetherian
charges, and (ii) the contribution of these latter in the metric has a slower
falloff to zero than the mass term, and this slowness is of logarithmic order.
Under these hypothesis, it is shown that, for suitable bounds between the mass
and the additional Noetherian charges, the solutions can represent black holes
with two horizons whose locations are given in term of the real branches of the
Lambert W functions. We present various examples of such black hole solutions
with electric, dyonic or axionic charges with AdS and Lifshitz asymptotics. As
an illustrative example, we construct a purely AdS magnetic black hole in five
dimensions with a matter source given by three different Maxwell invariants.
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Bouncing cosmologies in massive gravity on de Sitter: In the framework of massive gravity with a de Sitter reference metric, we
study homogeneous and isotropic solutions with positive spatial curvature.
Remarkably, we find that bounces can occur when cosmological matter satisfies
the strong energy condition, in contrast to what happens in classical general
relativity. This is due to the presence in the Friedmann equations of
additional terms, which depend on the scale factor and its derivatives and can
be interpreted as an effective fluid. We present a detailed study of the system
using a phase space analysis. After having identified the fixed points of the
system and investigated their stability properties, we discuss the cosmological
evolution in the global physical phase space. We find that bouncing solutions
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Energy Bounds in Designer Gravity: We consider asymptotically anti-de Sitter gravity coupled to tachyonic scalar
fields with mass at or slightly above the Breitenlohner-Freedman bound in d
greater than or equal to 4 spacetime dimensions. The boundary conditions in
these ``designer gravity'' theories are defined in terms of an arbitrary
function W. We give a general argument that the Hamiltonian generators of
asymptotic symmetries for such systems will be finite, and proceed to construct
these generators using the covariant phase space method. The direct calculation
confirms that the generators are finite and shows that they take the form of
the pure gravity result plus additional contributions from the scalar fields.
By comparing the generators to the spinor charge, we derive a lower bound on
the gravitational energy when i) W has a global minimum, ii) the
Breitenlohner-Freedman bound is not saturated, and iii) the scalar potential V
admits a certain type of "superpotential."
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Educing the volume out of the phase space boundary: We explicitly show that, in a system with T-duality symmetry, the
configuration space volume degrees of freedom may hide on the surface boundary
of the region of accessible states with energy lower than a fixed value. This
means that, when taking the decompactification limit (big volume limit), a
number of accessible states proportional to the volume is recovered even if no
volume dependence appears when energy is high enough. All this behavior is
contained in the exact way of computing sums by making integrals. We will also
show how the decompactification limit for the gas of strings can be defined in
a microcanonical description at finite volume.
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Condensed matter and AdS/CFT: I review two classes of strong coupling problems in condensed matter physics,
and describe insights gained by application of the AdS/CFT correspondence. The
first class concerns non-zero temperature dynamics and transport in the
vicinity of quantum critical points described by relativistic field theories. I
describe how relativistic structures arise in models of physical interest,
present results for their quantum critical crossover functions and
magneto-thermoelectric hydrodynamics. The second class concerns symmetry
breaking transitions of two-dimensional systems in the presence of gapless
electronic excitations at isolated points or along lines (i.e. Fermi surfaces)
in the Brillouin zone. I describe the scaling structure of a recent theory of
the Ising-nematic transition in metals, and discuss its possible connection to
theories of Fermi surfaces obtained from simple AdS duals.
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String Tensions and Three Dimensional Confining Gauge Theories: In the context of gauge/gravity duality, we try to understand better the
proposed duality between the fractional D2-brane supergravity solutions of
(Nucl. Phys. B 606 (2001) 18, hep-th/0101096) and a confining 2+1 dimensional
gauge theory. Based on the similarities between this fractional D2-brane
solution and D3-brane supergravity solutions with more firmly established gauge
theory duals, we conjecture that a confining q-string in the 2+1 dimensional
gauge theory is dual to a wrapped D4-brane. In particular, the D4-brane looks
like a string in the gauge theory directions but wraps a S**3 in S**4 in the
transverse geometry. For one of the supergravity solutions, we find a near
quadratic scaling law for the tension: $T \sim q (N-q)$. Based on the tension,
we conjecture that the gauge theory dual is SU(N) far in the infrared. We also
conjecture that a quadratic or near quadratic scaling is a generic feature of
confining 2+1 dimensional SU(N) gauge theories.
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Logarithmic corrections to the entropy of the exact string black hole: Exploiting a recently constructed target space action for the exact string
black hole, logarithmic corrections to the leading order entropy are studied.
There are contributions from thermal fluctuations and from corrections due to
alpha'>0 which for the microcanonical entropy appear with different signs and
therefore may cancel each other, depending on the overall factor in front of
the action. For the canonical entropy no such cancellation occurs. Remarks are
made regarding the applicability of the approach and concerning the
microstates. As a byproduct a formula for logarithmic entropy corrections in
generic 2D dilaton gravity is derived.
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D4-branes wrapped on four-dimensional orbifolds through consistent
truncation: We construct a consistent truncation of six-dimensional matter coupled $F(4)$
gauged supergravity on a cornucopia of two-dimensional surfaces including a
spindle, disc, domain wall and other novel backgrounds to four-dimensional
minimal gauged supergravity. Using our consistent truncation we uplift known
AdS$_2\times {\Sigma}_1$ solutions giving rise to four-dimensional orbifold
solutions, AdS$_2\times{\Sigma}_1\ltimes{\Sigma}_2$. We further uplift our
solutions to massive type IIA supergravity by constructing the full uplift
formulae for six-dimensional U$(1)^2$-gauged supergravity including all fields
and arbitrary Romans mass and gauge coupling. The solutions we construct are
naturally interpreted as the near-horizon geometries of asymptotically AdS$_6$
black holes with a four-dimensional orbifold horizon. Alternatively, one may
view them as the holographic duals of superconformal quantum mechanical
theories constructed by compactifying five-dimensional USp$(2N)$ theory living
on a stack of D4-D8 branes on the four-dimensional orbifolds. As a first step
to identifying these quantum mechanical theories we compute the
Bekenstein--Hawking entropy holographically.
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Superradiant instability of Kerr-de Sitter black holes in scalar-tensor
theory: We investigate in detail the mechanism of superradiance to render the
instability of Kerr-de Sitter black holes in scalar-tensor gravity. Our results
provide more clues to examine the scalar-tensor gravity in the astrophysical
black holes in the universe with cosmological constant. We also discuss the
spontaneous scalarization in the de Sitter background and find that this
instability can also happen in the spherical de Sitter configuration in a
special style.
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Brane solutions and integrability: a status report: We review the status of the integrability and solvability of the geodesics
equations of motion on symmetric coset spaces that appear as sigma models of
supergravity theories when reduced over respectively the timelike and spacelike
direction. Such geodesic curves describe respectively timelike and spacelike
brane solutions. We emphasize the applications to black holes.
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Duality invariance implies Poincare invariance: We consider all possible dynamical theories which evolve two transverse
vector fields out of a three-dimensional Euclidean hyperplane, subject to only
two assumptions: (i) the evolution is local in space, and (ii) the theory is
invariant under "duality rotations" of the vector fields into one another. The
commutators of the Hamiltonian and momentum densities are shown to be
necessarily those of the Poincare group or its zero signature contraction.
Space-time structure thus emerges out of the principle of duality.
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Towards the two-loop Lcc vertex in Landau gauge: We are interested in the structure of the Lcc vertex in the Yang-Mills
theory, where c is the ghost field and L the corresponding BRST auxiliary
field. This vertex can give us information on other vertices, and the possible
conformal structure of the theory should be reflected in the structure of this
vertex. There are five two-loop contributions to the Lcc vertex in the
Yang-Mills theory. We present here calculation of the first of the five
contributions. The calculation has been performed in the position space. One
main feature of the result is that it does not depend on any scale, ultraviolet
or infrared. The result is expressed in terms of logarithms and Davydychev
integral J(1,1,1) that are functions of the ratios of the intervals between
points of effective fields in the position space. To perform the calculation we
apply Gegenbauer polynomial technique and uniqueness method.
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The Moduli Space of the $N=2$ Supersymmetric $G_{2}$ Yang-Mills Theory: We present the hyper-elliptic curve describing the moduli space of the N=2
supersymmetric Yang-Mills theory with the $G_2$ gauge group. The exact
monodromies and the dyon spectrum of the theory are determined. It is verified
that the recently proposed solitonic equation is also satisfied by our
solution.
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Spin and Electromagnetic Duality: An Outline: An outline is given of recent work concerning the electromagnetic duality
properties of Maxwell theory on curved space-times with or without spin
structures.
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Solitons in Two--Dimensional Topological Field Theories: We consider a class of $N=2$ supersymmetric non--unitary theories in
two--dimensional Minkowski spacetime which admit classical solitonic solutions.
We show how these models can be twisted into a topological sector whose
energy--momentum tensor is a BRST commutator. There is an infinite number of
degrees of freedom associated to the zero modes of the solitons. As explicit
realizations of such models we discuss the BRST quantization of a system of
free fields, while in the interacting case we study $N=2$ complexified twisted
Toda theories.
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Properties of Confinement in Holography: We review certain properties of confinement with added focus on the ones we
study with holography. Then we discuss observables whose unique behavior can
indicate the presence of confinement. Using mainly the Wilson loop in the
gauge/gravity formalism, we study two main features of the QCD string: the
string tension dependence on the temperature while in the confining phase, and
the logarithmic broadening of the flux tube between the heavy static charges
that turns out to be a generic property of all confining theories. Finally, we
review the k-string bound state and we show that for a wide class of generic
theories the k-string observables can be expressed in terms of the single meson
bound state observables.
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Color Confinement and Massive Gluons: Color confinement is one of the central issues in QCD so that there are
various interpretations of this feature. In this paper we have adopted the
interpretation that colored particles are not subject to observation just
because colored states are unphysical in the sense of Eq. (2.16). It is shown
that there are two phases in QCD distinguished by different choices of the
gauge parameter. In one phase, called the "confinement phase", color
confinement is realized and gluons turn out to be massive. In the other phase,
called the "deconfinement phase", color confinement is not realized, but the
gluons remain massless.
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Modular Invariant Formulation of Multi-Gaugino and Matter Condensation: Using the linear multiplet formulation for the dilaton superfield, we
construct an effective lagrangian for hidden-sector gaugino condensation in
string effective field theories with arbitrary gauge groups and matter.
Nonperturbative string corrections to the K\"ahler potential are invoked to
stabilize the dilaton at a supersymmetry breaking minimum of the potential.
When the cosmological constant is tuned to zero the moduli are stabilized at
their self-dual points, and the vev's of their F-component superpartners
vanish. Numerical analyses of one- and two-condensate examples with massless
chiral matter show considerable enhancement of the gauge hierarchy with respect
to the E_8 case. The nonperturbative string effects required for dilaton
stabilization may have implications for gauge coupling unification. As a
comparison, we also consider a parallel approach based on the commonly used
chiral formulation.
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Toward an Off - Shell 11D Supergravity Limit of M - Theory: We demonstrate that in addition to the usual fourth-rank superfield $(W_{a b
c d})$ which describes the on-shell theory, a spinor superfield $(J_\a )$ can
be introduced into the 11D geometrical tensors with engineering dimensions less
or equal to one in such a way to satisfy the Bianchi identities in superspace.
The components arising from $J_\a$ are identified as some of the auxiliary
fields required for a full off-shell formulation. Our result indicates that
eleven dimensional supergravity does not have to be completely on-shell. The
$\k\-$symmetry of the supermembrane action in the presence of our partial
off-shell supergravity background is also confirmed. Our modifications to
eleven-dimensional supergravity theory are thus likely relevant for M-theory.
We suggest our proposal as a significant systematic off-shell generalization of
eleven-dimensional supergravity theory.
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Exact properties of an integrated correlator in $\mathcal{N}=4$ $SU(N)$
SYM: We present a novel expression for an integrated correlation function of four
superconformal primaries in $SU(N)$ $\mathcal{N}=4$ SYM. This integrated
correlator, which is based on supersymmetric localisation, has been the subject
of several recent developments. The correlator is re-expressed as a sum over a
two dimensional lattice that is valid for all $N$ and all values of the complex
Yang-Mills coupling $\tau$. In this form it is manifestly invariant under
$SL(2,\mathbb{Z})$ Montonen-Olive duality. Furthermore, it satisfies a
remarkable Laplace-difference equation that relates the $SU(N)$ to the
$SU(N+1)$ and $SU(N-1)$ correlators. For any fixed value of $N$ the correlator
is an infinite series of non-holomorphic Eisenstein series,
$E(s;\tau,\bar\tau)$ with $s\in \mathbb{Z}$, and rational coefficients. The
perturbative expansion of the integrated correlator is asymptotic and the
$n$-loop coefficient is a rational multiple of $\zeta(2n+1)$. The $n=1$ and
$n=2$ terms agree precisely with results determined directly by integrating the
expressions in one- and two-loop perturbative SYM. Likewise, the charge-$k$
instanton contributions have an asymptotic, but Borel summable, series of
perturbative corrections. The large-$N$ expansion of the correlator with fixed
$\tau$ is a series in powers of $N^{1/2-\ell}$ ($\ell\in \mathbb{Z}$) with
coefficients that are rational sums of $E_s$ with $s\in \mathbb{Z}+1/2$. This
gives an all orders derivation of the form of the recently conjectured
expansion. We further consider 't Hooft large-$N$ Yang-Mills theory. The
coefficient of each order can be expanded as a convergent series in $\lambda$.
For large $\lambda$ this becomes an asymptotic series with coefficients that
are again rational multiples of odd zeta values. The large-$\lambda$ series is
not Borel summable, and its resurgent non-perturbative completion is
$O(\exp(-2\sqrt{\lambda}))$.
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Higgs for Graviton: Simple and Elegant Solution: A Higgs mechanism for gravity is presented, where four scalars with global
Lorentz symmetry are employed. We show that in the broken symmetry phase a
graviton absorbs all scalars and become massive spin 2 particle with five
degrees of freedom. The resulting theory is unitary and free of ghosts.
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Yang-Mills moduli space in the adiabatic limit: We consider the Yang-Mills equations for a matrix gauge group $G$ inside the
future light cone of 4-dimensional Minkowski space, which can be viewed as a
Lorentzian cone $C(H^3)$ over the 3-dimensional hyperbolic space $H^3$. Using
the conformal equivalence of $C(H^3)$ and the cylinder $R\times H^3$, we show
that, in the adiabatic limit when the metric on $H^3$ is scaled down, classical
Yang-Mills dynamics is described by geodesic motion in the infinite-dimensional
group manifold $C^\infty (S^2_\infty,G)$ of smooth maps from the boundary
2-sphere $S^2_\infty=\partial H^3$ into the gauge group $G$.
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A Note on Temperature and Energy of 4-dimensional Black Holes from
Entropic Force: We investigate the temperature and energy on holographic screens for
4-dimensional black holes with the entropic force idea proposed by Verlinde. We
find that the "Unruh-Verlinde temperature" is equal to the Hawking temperature
on the horizon and can be considered as a generalized Hawking temperature on
the holographic screen outside the horizons. The energy on the holographic
screen is not the black hole mass $M$ but the reduced mass $M_0$, which is
related to the black hole parameters. With the replacement of the black hole
mass $M$ by the reduced mass $M_0$, the entropic force can be written as
$F=\frac{GmM_0}{r^2}$, which could be tested by experiments.
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Gauge Invariance and the Goldstone Theorem: This manuscript was originally created for and printed in the "Proceedings of
seminar on unified theories of elementary particles" held in Feldafing Germany
from July 5 to 16 1965 under the auspices of the Max-Planck-Institute for
Physics and Astrophysics in Munich. It details and expands upon the Guralnik,
Hagen, and Kibble paper that shows that the Goldstone theorem does not require
physical zero mass particles in gauge theories and provides an example through
the model which has become the template for the unified electroweak theory and
a main component of the Standard Model.
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Comments on D3-Brane Holography: We revisit the idea that the quantum dynamics of open strings ending on $N$
D3-branes in the large $N$ limit can be described at large `t Hooft coupling by
classical closed string theory in the background created by the D3-branes in
asymptotically flat spacetime. We study the resulting thermodynamics and
compute the Hagedorn temperature and other properties of the D3-brane
worldvolume theory in this regime. We also consider the theory in which the
D3-branes are replaced by negative branes and show that its thermodynamics is
well behaved. We comment on the idea that this theory can be thought of as an
irrelevant deformation of $\mathcal{N}=4$ SYM, and on its relation to $T\bar T$
deformed $CFT_2$.
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Self-Dual Chern-Simons Solitons in (2+1)-Dimensional Einstein Gravity: We consider here a generalization of the Abelian Higgs model in curved space,
by adding a Chern--Simons term. The static equations are self-dual provided we
choose a suitable potential. The solutions give a self-dual
Maxwell--Chern--Simons soliton that possesses a mass and a spin.
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Duality Invariant Actions and Generalised Geometry: We construct the non-linear realisation of the semi-direct product of E(11)
and its first fundamental representation at lowest order and appropriate to
spacetime dimensions four to seven. This leads to a non-linear realisation of
the duality groups and introduces fields that depend on a generalised space
which possess a generalised vielbein. We focus on the part of the generalised
space on which the duality groups alone act and construct an invariant action.
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Tachyon Effective Dynamics and de Sitter Vacua: We show that the DBI action for the singlet sector of the tachyon in
two-dimensional string theory has a SL(2,R) symmetry, a real-time counterpart
of the ground ring. The action can be rewritten as that of point particles
moving in a de Sitter space, whose coordinates are given by the value of the
eigenvalue and time. The symmetry then manifests as the isometry group of de
Sitter space in two dimensions. We use this fact to write the collective field
theory for a large number of branes, which has a natural interpretation as a
fermion field in this de Sitter space. After spending some time building
geometrical insight on facts about the condensation process, the state
corresponding to a sD-brane is identified and standard results in quantum field
theory in curved space-time are used to compute the backreaction of the thermal
background.
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Validity of Maxwell Equal Area Law for Black Holes Conformally Coupled
to Scalar Fields in $\text{AdS}_5$ Spacetime: We investigate the $P-V$ criticality and the Maxwell equal area law for a
five-dimensional spherically symmetric AdS black hole with a scalar hair in the
absence of and in the presence of a Maxwell field, respectively. Especially in
the charged case, we give the exact $P-V$ critical values. More importantly, we
analyze the validity and invalidity of the Maxwell equal area law for the AdS
hairy black hole in the scenarios without and with charges, respectively.
Within the scope of validity of the Maxwell equal area law, we point out that
there exists a representative van der Waals-type oscillation in the $P-V$
diagram. This oscillating part that indicates the phase transition from a small
black hole to a large one can be replaced by an isobar. The small and large
black holes share the same Gibbs free energy. We also give the distribution of
the critical points in the parameter space both without and with charges, and
obtain for the uncharged case the fitting formula of the co-existence curve.
Meanwhile, the latent heat is calculated, which gives the energy released or
absorbed between the small and large black hole phases in the
isothermal-isobaric procedure.
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On Phases of Generic Toric Singularities: We systematically study the phases of generic toric singularities, using
methods initiated in hep-th/0612046. These correspond to Gauged Linear Sigma
Models with arbitrary charges. We show that complete information about generic
$U(1)^r$ GLSMs can be obtained by studying the GLSM Lagrangian, appropriately
modified in the different phases of the theory. This can be used to study the
different phases of $L^{a,b,c}$ spaces and their non-supersymmetric
counterparts.
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Infinitely many N=1 dualities from $m+1-m=1$: We discuss two infinite classes of 4d supersymmetric theories, ${T}_N^{(m)}$
and ${\cal U}_N^{(m)}$, labelled by an arbitrary non-negative integer, $m$. The
${T}_N^{(m)}$ theory arises from the 6d, $A_{N-1}$ type ${\cal N}=(2,0)$ theory
reduced on a 3-punctured sphere, with normal bundle given by line bundles of
degree $(m+1, -m)$; the $m=0$ case is the ${\cal N}=2$ supersymmetric $T_N$
theory. The novelty is the negative-degree line bundle. The ${\cal U}_N^{(m)}$
theories likewise arise from the 6d ${\cal N}=(2,0)$ theory on a 4-punctured
sphere, and can be regarded as gluing together two (partially Higgsed)
${T}_N^{(m)}$ theories. The ${T}_N^{(m)}$ and ${\cal U}_N^{(m)}$ theories can
be represented, in various duality frames, as quiver gauge theories, built from
$T_N$ components via gauging and nilpotent Higgsing. We analyze the RG flow of
the ${\cal U}_N^{(m)}$ theories, and find that, for all integer $m>0$, they end
up at the same IR SCFT as $SU(N)$ SQCD with $2N$ flavors and quartic
superpotential. The ${\cal U}_N^{(m)}$ theories can thus be regarded as an
infinite set of UV completions, dual to SQCD with $N_f=2N_c$. The ${\cal
U}_N^{(m)}$ duals have different duality frame quiver representations, with
$2m+1$ gauge nodes.
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Non-compact Mirror Bundles and (0,2) Liouville Theories: We study (0,2) deformations of N=2 Liouville field theory and its mirror
duality. A gauged linear sigma model construction of the ultraviolet theory
connects (0,2) deformations of Liouville field theory and (0,2) deformations of
N=2 SL(2,R)/U(1) coset model as a mirror duality. Our duality proposal from the
gauged linear sigma model completely agrees with the exact CFT analysis. In the
context of heterotic string compactifications, the deformation corresponds to
the introduction of a non-trivial gauge bundle. This non-compact
Landau-Ginzburg construction yields a novel way to study the gauge bundle
moduli for non-compact Calabi-Yau manifolds.
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Taming the Tachyon in Cubic String Field Theory: We give evidence based on level-truncation computations that the rolling
tachyon in cubic open string field theory (CSFT) has a well-defined but wildly
oscillatory time-dependent solution which goes as $e^t$ for $t \to -\infty$. We
show that a field redefinition taking the CSFT effective tachyon action to the
analogous boundary string field theory (BSFT) action takes the oscillatory CSFT
solution to the pure exponential solution $e^t$ of the BSFT action.
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Reduced Hamiltonian for intersecting shells: The gauge usually adopted for extracting the reduced Hamiltonian of a thin
spherical shell of matter in general relativity, becomes singular when dealing
with two or more intersecting shells. We introduce here a more general class of
gauges which is apt for dealing with intersecting shells. As an application we
give the hamiltonian treatment of two intersecting shells, both massive and
massless. Such a formulation is applied to the computation of the semiclassical
tunneling probability of two shells. The probability for the emission of two
shells is simply the product of the separate probabilities thus showing no
correlation in the emission probabilities in this model.
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Fermion Zero Modes in the Presence of Fluxes and a Non-perturbative
Superpotential: We study the effect of background fluxes of general Hodge type on the
supersymmetry conditions and on the fermionic zero modes on the world-volume of
a Euclidean M5/D3-brane in M-theory/type IIB string theory.
Using the naive susy variation of the modulino fields to determine the number
of zero modes in the presence of a flux of general Hodge type, an inconsistency
appears. This inconsistency is resolved by a modification of the supersymmetry
variation of the modulinos, which captures the back-reaction of the
non-perturbative effects on the background flux and the geometry.
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G-flux and Spectral Divisors: We propose a construction of G-flux in singular elliptic Calabi-Yau fourfold
compactifications of F-theory, which in the local limit allow a spectral cover
description. The main tool of construction is the so-called spectral divisor in
the resolved Calabi-Yau geometry, which in the local limit reduces to the Higgs
bundle spectral cover. We exemplify the workings of this in the case of an E_6
singularity by constructing the resolved geometry, the spectral divisor and in
the local limit, the spectral cover. The G-flux constructed with the spectral
divisor is shown to be equivalent to the direct construction from suitably
quantized linear combinations of holomorphic surfaces in the resolved geometry,
and in the local limit reduces to the spectral cover flux.
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Some Comments on Lie-Poisson Structure of Conformal Non-Abelian Thirring
Models: The interconnection between self-duality, conformal invariance and
Lie-Poisson structure of the two dimensional non-abelian Thirring model is
investigated in the framework of the hamiltonian method.
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One-loop Renormalization of Black Hole Entropy Due to Non-minimally
Coupled Matter: The quantum entanglement entropy of an eternal black hole is studied. We
argue that the relevant Euclidean path integral is taken over fields defined on
$\alpha$-fold covering of the black hole instanton. The statement that
divergences of the entropy are renormalized by renormalization of gravitational
couplings in the effective action is proved for non-minimally coupled scalar
matter. The relationship of entanglement and thermodynamical entropies is
discussed.
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Tachyon Condensation and Spectrum of Strings on D-branes: We investigate spectrum of open strings on D-branes after tachyon
condensation in bosonic string theory. We calculate 1-loop partition function
of the string and show that its limiting forms coincide with partition
functions of open strings with different boundary conditions.
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Scattering on self-dual Taub-NUT: We derive exact solutions of massless free field equations and tree-level
two-point amplitudes up to spin 2 on self-dual Taub-NUT space-time, as well as
on its single copy, the self-dual dyon. We use Killing spinors to build
analogues of momentum eigenstates, finding that, in the spirit of
color-kinematics duality, those for the self-dual dyon lift directly to provide
states on the self-dual Taub-NUT background if one replaces charge with energy.
We discover that they are forced to have faster growth at infinity than in flat
space due to the topological non-triviality of these backgrounds. The
amplitudes for massless scalars and spinning particles in the $(+\,+)$ and
$(+\,-)$ helicity configurations vanish for generic kinematics as a consequence
of the integrability of the self-dual sector. The $(-\,-)$ amplitudes are
non-vanishing and we compute them exactly in the backgrounds, which are treated
non-perturbatively. It is explained how spin is easily introduced via a
Newman-Janis imaginary shift along the spin-vector leading directly to the
additional well-known exponential factor in the dot product of the spin with
the momenta. We also observe a double copy relation between the gluon amplitude
on a self-dual dyon and graviton amplitude on a self-dual Taub-NUT space-time.
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Electrically-Charged Lifshitz Spacetimes, and Hyperscaling Violations: Electrically-charged Lifshitz spacetimes are hard to come by. In this paper,
we construct a class of such solutions in five dimensional Einstein gravity
coupled to Maxwell and $SU(2)$ Yang-Mills fields. The solutions are
electrically-charged under the Maxwell field, whose equation is sourced by the
Yang-Mills instanton(-like) configuration living in the hyperbolic four-space
of the Lifshitz spacetime. We then introduce a dilaton and construct charged
and colored Lifshitz spacetimes with hyperscaling violations. We obtain a class
of exact Lifshitz black holes. We also perform similar constructions in four
dimensions.
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Amplitudes at strong coupling as hyperkähler scalars: Alday & Maldacena conjectured an equivalence between string amplitudes in
AdS$_5 \times S^5$ and null polygonal Wilson loops in planar $\mathcal{N}=4$
super-Yang-Mills (SYM). At strong coupling this identifies SYM amplitudes with
areas of minimal surfaces in AdS. For minimal surfaces in AdS$_3$, we find that
the nontrivial part of these amplitudes, the \emph{remainder function},
satisfies an integrable system of nonlinear differential equations, and we give
its Lax form. The result follows from a new perspective on `Y-systems', which
defines a new psuedo-hyperk\"ahler structure \emph{directly} on the space of
kinematic data, via a natural twistor space defined by the Y-system equations.
The remainder function is the (pseudo-)K\"ahler scalar for this geometry. This
connection to pseudo-hyperk\"ahler geometry and its twistor theory provides a
new ingredient for extending recent conjectures for non-perturbative amplitudes
using structures arising at strong coupling.
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Two loop effective kaehler potential of (non-)renormalizable
supersymmetric models: We perform a supergraph computation of the effective Kaehler potential at one
and two loops for general four dimensional N=1 supersymmetric theories
described by arbitrary Kaehler potential, superpotential and gauge kinetic
function. We only insist on gauge invariance of the Kaehler potential and the
superpotential as we heavily rely on its consequences in the quantum theory.
However, we do not require gauge invariance for the gauge kinetic functions, so
that our results can also be applied to anomalous theories that involve the
Green-Schwarz mechanism. We illustrate our two loop results by considering a
few simple models: the (non-)renormalizable Wess-Zumino model and Super Quantum
Electrodynamics.
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Gauge-invariant and infrared-improved variational analysis of the
Yang-Mills vacuum wave functional: We study a gauge-invariant variational framework for the Yang-Mills vacuum
wave functional. Our approach is built on gauge-averaged Gaussian trial
functionals which substantially extend previously used trial bases in the
infrared by implementing a general low-momentum expansion for the vacuum-field
dispersion (which is taken to be analytic at zero momentum). When completed by
the perturbative Yang-Mills dispersion at high momenta, this results in a
significantly enlarged trial functional space which incorporates both dynamical
mass generation and asymptotic freedom. After casting the dynamics associated
with these wave functionals into an effective action for collections of soft
vacuum-field orbits, the leading infrared improvements manifest themselves as
four-gradient interactions. Those turn out to significantly lower the minimal
vacuum energy density, thus indicating a clear overall improvement of the
vacuum description. The dimensional transmutation mechanism and the dynamically
generated mass scale remain almost quantitatively robust, however, which
ensures that our prediction for the gluon condensate is consistent with
standard values. Further results include a finite group velocity for the soft
gluonic modes due to the higher-gradient corrections and indications for a
negative differential color resistance of the Yang-Mills vacuum.
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On Dimensional Reduction of Magical Supergravity Theories: We prove, by a direct dimensional reduction and an explicit construction of
the group manifold, that the nonlinear sigma model of the dimensionally reduced
three-dimensional A = R magical supergravity is F4(+4)/(USp(6)xSU(2)). This
serves as a basis for the solution generating technique in this supergravity as
well as allows to give the Lie algebraic characterizations to some of the
parameters and functions in the original D = 5 Lagrangian. Generalizations to
other magical supergravities are also discussed.
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Higher spin black hole entropy in three dimensions: A generic formula for the entropy of three-dimensional black holes endowed
with a spin-3 field is found, which depends on the horizon area A and its
spin-3 analogue, given by the reparametrization invariant integral of the
induced spin-3 field at the spacelike section of the horizon. From this result
it can be shown that the absolute value of the spin-3 analogue of the area has
to be bounded from above by A/3^(1/2). The entropy formula is constructed by
requiring the first law of thermodynamics to be fulfilled in terms of the
global charges obtained through the canonical formalism. For the static case,
in the weak spin-3 field limit, our expression for the entropy reduces to the
result found by Campoleoni, Fredenhagen, Pfenninger and Theisen, which has been
recently obtained through a different approach.
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A Twistor Description of Six-Dimensional N=(1,1) Super Yang-Mills Theory: We present a twistor space that describes super null-lines on six-dimensional
N=(1,1) superspace. We then show that there is a one-to-one correspondence
between holomorphic vector bundles over this twistor space and solutions to the
field equations of N=(1,1) super Yang-Mills theory. Our constructions naturally
reduce to those of the twistorial description of maximally supersymmetric
Yang-Mills theory in four dimensions.
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Black Hole Thermodynamics from Calculations in Strongly-Coupled Gauge
Theory: We develop an approximation scheme for the quantum mechanics of N D0-branes
at finite temperature in the 't Hooft large-N limit. The entropy of the quantum
mechanics calculated using this approximation agrees well with the
Bekenstein-Hawking entropy of a ten-dimensional non-extremal black hole with
0-brane charge. This result is in accord with the duality conjectured by
Itzhaki, Maldacena, Sonnenschein and Yankielowicz. Our approximation scheme
provides a model for the density matrix which describes a black hole in the
strongly-coupled quantum mechanics.
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Noncommutative Wilson lines in higher-spin theory and correlation
functions of conserved currents for free conformal fields: We first prove that, in Vasiliev's theory, the zero-form charges studied in
1103.2360 and 1208.3880 are twisted open Wilson lines in the noncommutative $Z$
space. This is shown by mapping Vasiliev's higher-spin model on noncommutative
Yang--Mills theory. We then prove that, prior to Bose-symmetrising, the
cyclically-symmetric higher-spin invariants given by the leading order of these
$n$-point zero-form charges are equal to corresponding cyclically-invariant
building blocks of $n$-point correlation functions of bilinear operators in
free conformal field theories (CFT) in three dimensions. On the higher spin
gravity side, our computation reproduces the results of 1210.7963 using an
alternative method amenable to the computation of subleading corrections
obtained by perturbation theory in normal order. On the free CFT side, our
proof involves the explicit computation of the separate cyclic building blocks
of the correlation functions of $n$ conserved currents in arbitrary dimension
$d>2$, using polarization vectors, which is an original result. It is shown to
agree, for $d=3$, with the results obtained in 1301.3123 in various dimensions
and where polarization spinors were used.
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Gravity-induced instability and gauge field localization: The spectrum of a massless bulk scalar field \Phi, with a possible
interaction term of the form -\xi R \Phi^{2}, is investigated in the case of
RS-geometry [1]. We show that the zero mode for \xi=0, turns into a tachyon
mode, in the case of a nonzero negative value of \xi (\xi<0). As we see, the
existence of the tachyon mode destabilizes the \Phi=0 vacuum, against a new
stable vacuum with nonzero \Phi near the brane, and zero in the bulk. By using
this result, we can construct a simple model for the gauge field localization,
according to the philosophy of Dvali and Shifman (Higgs phase on the brane,
confinement in the bulk).
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Singularities in wavy strings: Extremal six-dimensional black string solutions with some non-trivial
momentum distribution along the wave are considered. These solutions were
recently shown to contain a singularity at the would-be position of the event
horizon. In the black string geometry, all curvature invariants are finite at
the horizon. It is shown that if the effects of infalling matter are included,
there are curvature invariants which diverge there. This implies that quantum
corrections will be important at the would-be horizon. The effect of this
singularity on test strings is also considered, and it is shown that it leads
to a divergent excitation of the string. The quantum corrections will therefore
be important for test objects.
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Correspondence between Feynman diagrams and operators in quantum field
theory that emerges from tensor model: A novel functorial relationship in perturbative quantum field theory is
pointed out that associates Feynman diagrams (FD) having no external line in
one theory ${\bf Th}_1$ with singlet operators in another one ${\bf Th}_2$
having an additional $U({\cal N})$ symmetry and is illustrated by the case
where ${\bf Th}_1$ and ${\bf Th}_2$ are respectively the rank $r-1$ and the
rank $r$ complex tensor model. The values of FD in ${\bf Th}_1$ agree with the
large ${\cal N}$ limit of the Gaussian average of those operators in ${\bf
Th}_2$. The recursive shift in rank by this FD functor converts numbers into
vectors, then into matrices, and then into rank $3$ tensors ${\ldots}$ This FD
functor can straightforwardly act on the $d$ dimensional tensorial quantum
field theory counterparts as well. In the case of rank 2-rank 3 correspondence,
it can be combined with the geometrical pictures of the dual of the original
FD, namely, equilateral triangulations (Grothendieck's dessins d'enfant) to
form a triality which may be regarded as a bulk-boundary correspondence.
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Renormalization Group Equations and the Lifshitz Point In Noncommutative
Landau-Ginsburg Theory: A one-loop renormalization group (RG) analysis is performed for
noncommutative Landau-Ginsburg theory in an arbitrary dimension. We adopt a
modern version of the Wilsonian RG approach, in which a shell integration in
momentum space bypasses the potential IR singularities due to UV-IR mixing. The
momentum-dependent trigonometric factors in interaction vertices,
characteristic of noncommutative geometry, are marginal under RG
transformations, and their marginality is preserved at one loop. A negative
$\Theta$-dependent anomalous dimension is discovered as a novel effect of the
UV-IR mixing. We also found a noncommutative Wilson-Fisher (NCWF) fixed point
in less than four dimensions. At large noncommutativity, a momentum space
instability is induced by quantum fluctuations, and a consequential first-order
phase transition is identified together with a Lifshitz point in the phase
diagram. In the vicinity of the Lifshitz point, we introduce two critical
exponents $\nu_m$ and $\beta_k$, whose values are determined to be 1/4 and 1/2,
respectively, at mean-field level.
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Deep multi-task mining Calabi-Yau four-folds: We continue earlier efforts in computing the dimensions of tangent space
cohomologies of Calabi-Yau manifolds using deep learning. In this paper, we
consider the dataset of all Calabi-Yau four-folds constructed as complete
intersections in products of projective spaces. Employing neural networks
inspired by state-of-the-art computer vision architectures, we improve earlier
benchmarks and demonstrate that all four non-trivial Hodge numbers can be
learned at the same time using a multi-task architecture. With 30% (80%)
training ratio, we reach an accuracy of 100% for $h^{(1,1)}$ and 97% for
$h^{(2,1)}$ (100% for both), 81% (96%) for $h^{(3,1)}$, and 49% (83%) for
$h^{(2,2)}$. Assuming that the Euler number is known, as it is easy to compute,
and taking into account the linear constraint arising from index computations,
we get 100% total accuracy.
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Holographic entanglement thermodynamics for higher dimensional charged
black hole: In this paper, we have investigated the entanglement thermodynamics for
$d$-dimensional charged $AdS$ black hole by studying the holographic
entanglement entropy in different cases. We have first computed the holographic
entanglement entropy in extremal and non-extremal cases in two different
regimes, namely, the low temperature and high temperature limits. We then
obtain the first law of entanglement thermodynamics for boundary field theory
in the low temperature regime in $d$-dimensions.
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Black hole perturbations of massive and partially massless spin-2 fields
in (anti) de Sitter spacetime: We provide a systematic and comprehensive derivation of the linearized
dynamics of massive and partially massless spin-2 particles in a Schwarzschild
(anti) de Sitter black hole background, in four and higher spacetime
dimensions. In particular, we show how to obtain the quadratic actions for the
propagating modes and recast the resulting equations of motion in a
Schr\"odinger-like form. In the case of partially massless fields in
Schwarzschild de Sitter spacetime, we study the isospectrality between modes of
different parity. In particular, we prove isospectrality analytically for modes
with multipole number $L=1$ in four spacetime dimensions, providing the
explicit form of the underlying symmetry. We show that isospectrality between
partially massless modes of different parity is broken in higher-dimensional
Schwarzschild de Sitter spacetimes.
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On a_2^(1) Reflection Matrices and Affine Toda Theories: We construct new non-diagonal solutions to the boundary Yang-Baxter-Equation
corresponding to a two-dimensional field theory with U_q(a_2^(1)) quantum
affine symmetry on a half-line. The requirements of boundary unitarity and
boundary crossing symmetry are then used to find overall scalar factors which
lead to consistent reflection matrices. Using the boundary bootstrap equations
we also compute the reflection factors for scalar bound states (breathers).
These breathers are expected to be identified with the fundamental quantum
particles in a_2^(1) affine Toda field theory and we therefore obtain a
conjecture for the affine Toda reflection factors. We compare these factors
with known classical results and discuss their duality properties and their
connections with particular boundary conditions.
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The Hamiltonian in an Aharonov-Bohm gauge field and its self-adjoint
extensions: By using the spherical coordinates in 3+1 dimensions we study the
self-adjointness of the Dirac Hamiltonian in an Aharonov-Bohm gauge field of an
infinitely thin magnetic flux tube. It is shown that the angular part of the
Dirac Hamiltonian requires self-adjoint extensions as well as its radial one.
The self-adjoint extensions of the angular part are parametrized by 2x2 unitary
matrix.
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Non-Gaussian Path Integration in Self-Interacting Scalar Field Theories: In self-interacting scalar field theories kinetic expansion is an alternative
way of calculating the generating functional for Green's functions where the
zeroth order non-Gaussian path integral becomes diagonal in x-space and reduces
to the product of an ordinary integral at each point which can be evaluated
exactly. We discuss how to deal with such functional integrals and propose a
new perturbative expansion scheme which combines the elements of the kinetic
expansion with that of usual perturbation theory. It is then shown that, when
the cutoff dependent bare parameters in the potential are fixed to have a well
defined non-Gaussian path integral without the kinetic term, the theory becomes
trivial in the continuum limit.
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Evolution of Massive Scalar Fields in the Spacetime of a Tense Brane
Black Hole: In the spacetime of a $d$-dimensional static tense brane black hole we
elaborate the mechanism by which massive scalar fields decay. The metric of a
six-dimensional black hole pierced by a topological defect is especially
interesting. It corresponds to a black hole residing on a tensional 3-brane
embedded in a six-dimensional spacetime, and this solution has gained
importance due to the planned accelerator experiments. It happened that the
intermediate asymptotic behaviour of the fields in question was determined by
an oscillatory inverse power-law. We confirm our investigations by numerical
calculations for five- and six-dimensional cases. It turned out that the
greater the brane tension is, the faster massive scalar fields decay in the
considered spacetimes.
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Effects of the hyperscaling violation and dynamical exponents on the
imaginary potential and entropic force of heavy quarkonium via holography: The imaginary potential and entropic force are two important different
mechanisms to characterize the dissociation of heavy quarkonia. In this paper,
we calculate these two quantities in strongly coupled theories with anisotropic
Lifshitz scaling and hyperscaling violation exponent using holographic methods.
We study how the results are affected by the hyperscaling violation parameter
{\theta} and the dynamical exponent z at finite temperature and chemical
potential. Also, we investigate the effect of the chemical potential on these
quantities. As a result, we find that both mechanisms show the same results:
the thermal width and the dissociation length decrease as the dynamical
exponent and chemical potential increase or as the hyperscaling violating
parameter decreases.
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Higgsing the stringy higher spin symmetry: It has recently been argued that the symmetric orbifold theory of T4 is dual
to string theory on AdS3 x S3 x T4 at the tensionless point. At this point in
moduli space, the theory possesses a very large symmetry algebra that includes,
in particular, a $W_\infty$ algebra capturing the gauge fields of a dual higher
spin theory. Using conformal perturbation theory, we study the behaviour of the
symmetry generators of the symmetric orbifold theory under the deformation that
corresponds to switching on the string tension. We show that the generators
fall nicely into Regge trajectories, with the higher spin fields corresponding
to the leading Regge trajectory. We also estimate the form of the Regge
trajectories for large spin, and find evidence for the familiar logarithmic
behaviour, thereby suggesting that the symmetric orbifold theory is dual to an
AdS background with pure RR flux.
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The transfer matrix in four-dimensional CDT: The Causal Dynamical Triangulation model of quantum gravity (CDT) has a
transfer matrix, relating spatial geometries at adjacent (discrete lattice)
times. The transfer matrix uniquely determines the theory. We show that the
measurements of the scale factor of the (CDT) universe are well described by an
effective transfer matrix where the matrix elements are labeled only by the
scale factor. Using computer simulations we determine the effective transfer
matrix elements and show how they relate to an effective minisuperspace action
at all scales.
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Stationary Black Holes in a Generalized Three-Dimensional Theory of
Gravity: We consider a generalized three-dimensional theory of gravity which is
specified by two fields, the graviton and the dilaton, and one parameter. This
theory contains, as particular cases, three-dimensional General Relativity and
three-dimensional String Theory. Stationary black hole solutions are generated
from the static ones using a simple coordinate transformation. The stationary
black holes solutions thus obtained are locally equivalent to the corresponding
static ones, but globally distinct. The mass and angular momentum of the
stationary black hole solutions are computed using an extension of the Regge
and Teitelboim formalism. The causal structure of the black holes is described.
|
Two-flux Colliding Plane Waves in String Theory: We construct the two-flux colliding plane wave solutions in higher
dimensional gravity theory with dilaton, and two complementary fluxes. Two
kinds of solutions has been obtained: Bell-Szekeres(BS) type and homogeneous
type. After imposing the junction condition, we find that only Bell-Szekeres
type solution is physically well-defined. Furthermore, we show that the future
curvature singularity is always developed for our solutions.
|
Vortices on Orbifolds: The Abelian and non-Abelian vortices on orbifolds are investigated based on
the moduli matrix approach, which is a powerful method to deal with the BPS
equation. The moduli space and the vortex collision are discussed through the
moduli matrix as well as the regular space. It is also shown that a quiver
structure is found in the Kahler quotient, and a half of ADHM is obtained for
the vortex theory on the orbifolds as the case before orbifolding.
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Time-dependent $NAdS_2$ holography with applications: We develop a method for obtaining exact time-dependent solutions in
Jackiw-Teitelboim gravity coupled to non-conformal matter and study
consequences for $NAdS_2$ holography. We study holographic quenches in which we
find that the black hole mass increases. A semi-holographic model composed of
an infrared $NAdS_2$ holographic sector representing the mutual strong
interactions of trapped impurities confined at a spatial point is proposed. The
holographic sector couples to the position of a displaced impurity acting as a
self-consistent boundary source. This effective $0+1-$dimensional description
has a total conserved energy. Irrespective of the initial velocity of the
particle, the black hole mass initially increases, but after the horizon runs
away to infinity in the physical patch, the mass vanishes in the long run. The
total energy is completely transferred to the kinetic energy or the
self-consistent confining potential energy of the impurity. For initial
velocities below a critical value determined by the mutual coupling, the black
hole mass changes sign in finite time. Above this critical velocity, the
initial condition of the particle can be retrieved from the $SL(2,R)$ invariant
exponent that governs the exponential growth of the bulk gravitational
$SL(2,R)$ charges at late time.
|
Ordinary-derivative formulation of conformal low-spin fields: Conformal fields in flat space-time of even dimension greater than or equal
to four are studied. Second-derivative formulation for spin 0,1,2 conformal
bosonic fields and first-derivative formulation for spin 1/2,3/2 conformal
fermionic fields are developed. For the spin 1,3/2,2 conformal fields, we
obtain gauge invariant Lagrangians and the corresponding gauge transformations.
Gauge symmetries are realized by involving Stueckelberg fields and auxiliary
fields. Realization of global conformal boost symmetries is obtained. Modified
Lorentz and de Donder gauge conditions are introduced. Ordinary-derivative
Lagrangian of interacting Weyl gravity in 4d is obtained. In our approach, the
field content of Weyl gravity, in addition to conformal graviton field,
includes one auxiliary rank-2 symmetric tensor field and one Stueckelberg
vector field. With respect to the auxiliary tensor field, the Lagrangian
contains, in addition to other terms, the Pauli-Fierz mass term. Using the
ordinary-derivative Lagrangian of Weyl gravity, we discuss interrelation of
Einstein AdS gravity and Weyl gravity via breaking conformal gauge symmetries.
Also, we demonstrate use of the light-cone gauge for counting on-shell degrees
of freedom in higher-derivative conformal field theories.
|
Giant Gravitons and non-conformal vacua in twisted holography: Twisted holography relates the two-dimensional chiral algebra subsector of
$\mathcal{N}=4$ SYM to the B-model topological string theory on the deformed
conifold $SL(2,\mathbb{C})$. We review the relevant aspects of the duality and
its two generalizations: the correspondence between determinant operators and
"Giant Graviton" branes and the extension to non-conformal vacua of the chiral
algebra.
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GUT theories from Calabi-Yau 4-folds with SO(10) Singularities: We consider an SO(10) GUT model from F-theory compactified on an elliptically
fibered Calabi-Yau with a D5 singularity. To obtain the matter curves and the
Yukawa couplings, we use a global description to resolve the singularity. We
identify the vector and spinor matter representations and their Yukawa
couplings and we explicitly build the G-fluxes in the global model and check
the agreement with the semi-local results. As our bundle is of type SU(2k),
some extra conditions need to be applied to match the fluxes.
|
A Coincidence Problem: How to Flow from N=2 SQCD to N=1 SQCD: We discuss, and propose a solution for, a still unresolved problem regarding
the breaking from $\N=2$ super-QCD to $\N=1$ super-QCD. A mass term $W=\mu \Tr
\Phi^2 / 2$ for the adjoint field, which classically does the required breaking
perfectly, quantum mechanically leads to a relevant operator that, in the
infrared, makes the theory flow away from pure $\N=1$ SQCD. To avoid this
problem, we first need to extend the theory from $\SU (n_c)$ to $\U (n_c)$. We
then look for the quantum generalization of the condition $W^{\prime}(m)=0$,
that is, the coincidence between a root of the derivative of the superpotential
$W(\phi)$ and the mass $m$ of the quarks. There are $2n_c -n_f$ of such points
in the moduli space. We suggest that with an opportune choice of
superpotential, that selects one of these coincidence vacua in the moduli
space, it is possible to flow from $\N=2$ SQCD to $\N=1$ SQCD. Various
arguments support this claim. In particular, we shall determine the exact
location in the moduli space of these coincidence vacua and the precise
factorization of the SW curve.
|
Bound states and the classical double copy: We extend the perturbative classical double copy to the analysis of bound
systems. We first obtain the leading order perturbative gluon radiation field
sourced by a system of interacting color charges in arbitrary time dependent
orbits, and test its validity by taking relativistic bremsstrahlung and
non-relativistic bound state limits. By generalizing the color to kinematic
replacement rules recently used in the context of classical bremsstrahlung, we
map the gluon emission amplitude to the radiation fields of dilaton gravity
sourced by interacting particles in generic (self-consistent) orbits. As an
application, we reproduce the leading post-Newtonian radiation fields and
energy flux for point masses in non-relativistic orbits from the double copy of
gauge theory.
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Supersymmetric Extension of GCA in 2d: We derive the infinite dimensional Supersymmetric Galilean Conformal Algebra
(SGCA) in the case of two spacetime dimensions by performing group contraction
on 2d superconformal algebra. We also obtain the representations of the
generators in terms of superspace coordinates. Here we find realisations of the
SGCA by considering scaling limits of certain 2d SCFTs which are non-unitary
and have their left and right central charges become large in magnitude and
opposite in sign. We focus on the Neveu-Schwarz sector of the parent SCFTs and
develop, in parallel to the GCA studies recently in (arXiv:0912.1090), the
representation theory based on SGCA primaries, Ward identities for their
correlation functions and their descendants which are null states.
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The scaling supersymmetric Yang-Lee model with boundary: We define the scaling supersymmetric Yang-Lee model with boundary as the
(1,3) perturbation of the superconformal minimal model SM(2/8) (or
equivalently, the (1,5) perturbation of the conformal minimal model M(3/8))
with a certain conformal boundary condition. We propose the corresponding
boundary S matrix, which is not diagonal for general values of the boundary
parameter. We argue that the model has an integral of motion corresponding to
an unbroken supersymmetry, and that the proposed S matrix commutes with a
similar quantity. We also show by means of a boundary TBA analysis that the
proposed boundary S matrix is consistent with massless flow away from the
ultraviolet conformal boundary condition.
|
Holography, Duality and Higher-Spin Theories: I review recent work on the holographic relation between higher-spin theories
in Anti-de Sitter spaces and conformal field theories. I present the main
results of studies concerning the higher-spin holographic dual of the
three-dimensional O(N) vector model. I discuss the special role played by
certain double-trace deformations in Conformal Field Theories that have
higher-spin holographic duals. Using the canonical formulation I show that
duality transformations in a U(1) gauge theory on AdS4 induce boundary
double-trace deformations. I argue that a similar effect takes place in the
holography of linearized higher-spin theories on AdS4.
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Symmetries at Null Boundaries: Two and Three Dimensional Gravity Cases: We carry out in full generality and without fixing specific boundary
conditions, the symmetry and charge analysis near a generic null surface for
two and three dimensional (2d and 3d) gravity theories. In 2d and 3d there are
respectively two and three charges which are generic functions over the
codimension one null surface. The integrability of charges and their algebra
depend on the state-dependence of symmetry generators which is a priori not
specified. We establish the existence of infinitely many choices that render
the surface charges integrable. We show that there is a choice, the
"fundamental basis", where the null boundary symmetry algebra is the
Heisenberg+Diff(d-2) algebra. We expect this result to be true for d>3 when
there is no Bondi news through the null surface.
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Global anomaly and a family of structures on fold product of complex
two-cycles: We propose a new set of IIB type and eleven-dimensional supergravity
solutions which consists of the $n$-fold product of two-spaces ${\bf
H}^n/\Gamma$ (where ${\bf H}^n$ denotes the product of $n$ upper half-planes
$H^2$ equipped with the co-compact action of $\Gamma \subset SL(2, {\mathbb
R})^n$) and $({\bf H}^n)^*/\Gamma$ (where $(H^2)^* = H^2\cup \{{\rm cusp of}
\Gamma\}$ and $\Gamma$ is a congruence subgroup of $SL(2, {\mathbb R})^n$). The
Freed-Witten global anomaly condition have been analyzed. We argue that the
torsion part of the cuspidal cohomology involves in the global anomaly
condition. Infinitisimal deformations of generalized complex (and K\"ahler)
structures also has been analyzed and stability theorem in the case of a
discrete subgroup of $SL(2, {\mathbb R})^n$ with the compact quotient ${\bf
H}^n/\Gamma$ was verified.
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Generalized Quantum Spring: Recently, it was found that after imposing a helix boundary condition on a
scalar field, the Casimir force coming from the quantum effect is linearly
proportional to $r$, which is the ratio of the pitch to the circumference of
the helix. This linear behavior of the Casimir force is just like that of the
force obeying the Hooke's law on a spring. In this paper, inspiring by some
complex structures that lives in the cells of human body like DNA, protein,
collagen etc., we generalize the helix boundary condition to a more general
one, in which the helix consists of a tiny helix structure, and makes up a
hierarchy of helix. After imposing this kind of boundary condition on a
massless and a massive scalar, we calculate the Casimir energy and force by
using the so-called zeta function regularization method. We find that the
Hooke's law with the generalized helix boundary condition is not exactly the
same as usual one. In this case, the force is proportional to the cube of $r$
instead. So we regard it as a generalized Hooke's law, which is complied by a
\emph{generalized quantum spring}.
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N=2 Quantum Field Theories and Their BPS Quivers: We explore the relationship between four-dimensional N=2 quantum field
theories and their associated BPS quivers. For a wide class of theories
including super-Yang-Mills theories, Argyres-Douglas models, and theories
defined by M5-branes on punctured Riemann surfaces, there exists a quiver which
implicitly characterizes the field theory. We study various aspects of this
correspondence including the quiver interpretation of flavor symmetries,
gauging, decoupling limits, and field theory dualities. In general a given
quiver describes only a patch of the moduli space of the field theory, and a
key role is played by quantum mechanical dualities, encoded by quiver
mutations, which relate distinct quivers valid in different patches. Analyzing
the consistency conditions imposed on the spectrum by these dualities results
in a powerful and novel mutation method for determining the BPS states. We
apply our method to determine the BPS spectrum in a wide class of examples,
including the strong coupling spectrum of super-Yang-Mills with an ADE gauge
group and fundamental matter, and trinion theories defined by M5-branes on
spheres with three punctures.
|
QED$_{2+1}$ with Nonzero Fermion Density and Quantum Hall Effect: A general expression for the conductivity in the QED$_{2+1}$ with nonzero
fermion density in the uniform magnetic field is derived. It is shown that the
conductivity is entirely determined by the Chern-Simons coefficient:
$\sigma_{ij}=\varepsilon_{ij}~{\cal C}$ and is a step-function of the chemical
potential and the magnetic field.
|
Superprojectors in D=10: We classify all massive irreducible representations of super Poincar\'e in
D=10. New Casimir operators of super Poincar\'e are presented whose eigenvalues
completely specify the representation. It is shown that a scalar superfield
contains three irreducible representations of massive supersymmetry and we find
the corresponding superprojectors. We apply these new tools to the quantization
of the massive superparticle and we show that it must be formulated in terms of
a superfield $B_\mn$ satisfying an adequate covariant restriction.
|
Tachyon Tunnelling in D-brane-anti-D-brane: Using the tachyon DBI action proposal for the effective theory of
non-coincident D$_p$-brane-anti-D$_p$-brane system, we study the decay of this
system in the tachyon channel. We assume that the branes separation is held
fixed, i.e. no throat formation, and then find the bounce solution which
describe the decay of the system from false to the true vacuum of the tachyon
potential. We shall show that due to the non-standard form of the kinetic term
in the effective action, the thin wall approximation for calculating the bubble
nucleation rate gives a result which is independent of the branes separation.
This unusual result might indicate that the true decay of this metastable
system should be via a solution that represents a throat formation as well as
the tachyon tunneling.
|
Quantum Aspects of Black Objects in String Theory: One of important directions in superstring theory is to reveal the quantum
nature of black hole. In this paper we embed Schwarzschild black hole into
superstring theory or M-theory, which we call a smeared black hole, and resolve
quantum corrections to it. Furthermore we boost the smeared black hole along
the 11th direction and construct a smeared quantum black 0-brane in 10
dimensions. Quantum aspects of the thermodynamic for these black objects are
investigated in detail. We also discuss radiations of a string and a D0-brane
from the smeared quantum black 0-brane.
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General static spherically symmetric solutions in Horava gravity: We derive general static spherically symmetric solutions in the Horava theory
of gravity with nonzero shift field. These represent "hedgehog" versions of
black holes with radial "hair" arising from the shift field. For the case of
the standard de Witt kinetic term (lambda =1) there is an infinity of solutions
that exhibit a deformed version of reparametrization invariance away from the
general relativistic limit. Special solutions also arise in the anisotropic
conformal point lambda = 1/3.
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Sound waves and vortices in a polarized relativistic fluid: We extend the effective theory approach to the ideal fluid limit where the
polarization of the fluid is non-zero. After describing and motivating the
equations of motion, we expand them around the hydrostatic limit, obtaining the
sound wave and vortex degrees of freedom. We discuss how the presence of
polarization affects the stability and causality of the ideal fluid limit.
|
Symmetries of post-Galilean expansions: In this letter we study an infinite extension of the Galilei symmetry group
in any dimension that can be thought of as a non-relativistic or post-Galilean
expansion of the Poincare symmetry. We find an infinite-dimensional vector
space on which this generalized Galilei group acts and usual Minkowski space
can be modeled by our construction. We also construct particle and string
actions that are invariant under these transformations.
|
The action of the Virasoro algebra in the two-dimensional Potts and loop
models at generic $Q$: The spectrum of conformal weights for the CFT describing the two-dimensional
critical $Q$-state Potts model (or its close cousin, the dense loop model) has
been known for more than 30 years. However, the exact nature of the
corresponding $\hbox{Vir}\otimes\overline{\hbox{Vir}}$ representations has
remained unknown up to now. Here, we solve the problem for generic values of
$Q$. This is achieved by a mixture of different techniques: a careful study of
"Koo--Saleur generators" [arXiv:hep-th/9312156], combined with measurements of
four-point amplitudes, on the numerical side, and OPEs and the four-point
amplitudes recently determined using the "interchiral conformal bootstrap" in
[arXiv:2005.07258] on the analytical side. We find that null-descendants of
diagonal fields having weights $(h_{r,1},h_{r,1})$ (with $r\in \mathbb{N}^*$)
are truly zero, so these fields come with simple
$\hbox{Vir}\otimes\overline{\hbox{Vir}}$ ("Kac") modules. Meanwhile, fields
with weights $(h_{r,s},h_{r,-s})$ and $(h_{r,-s},h_{r,s})$ (with
$r,s\in\mathbb{N}^*$) come in indecomposable but not fully reducible
representations mixing four simple $\hbox{Vir}\otimes\overline{\hbox{Vir}}$
modules with a familiar "diamond" shape. The "top" and "bottom" fields in these
diamonds have weights $(h_{r,-s},h_{r,-s})$, and form a two-dimensional Jordan
cell for $L_0$ and $\bar{L}_0$. This establishes, among other things, that the
Potts-model CFT is logarithmic for $Q$ generic. Unlike the case of non-generic
(root of unity) values of $Q$, these indecomposable structures are not present
in finite size, but we can nevertheless show from the numerical study of the
lattice model how the rank-two Jordan cells build up in the infinite-size
limit.
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A Cosmological Slavnov-Taylor Identity: We develop a method for treating the consistency relations of inflation that
includes the full time-evolution of the state. This approach relies only on the
symmetries of the inflationary setting, in particular a residual conformal
symmetry in the spatial part of the metric, along with general properties which
hold for any quantum field theory. As a result, the consistency relations that
emerge, which are essentially the Slavnov-Taylor identities associated with
this residual conformal symmetry, apply very generally: they are true of the
full Green's functions, hold largely independently of the particular
inflationary model, and can be used for arbitrary states. We illustrate these
techniques by showing the form assumed by the standard consistency relation
between the two and three-point functions for the primordial scalar
fluctuations when they are in a Bunch-Davies state. But because we have
included the full evolution of the state, this approach works for a general
initial state as well and does not need to have assumed that inflation began in
the Bunch-Davies state.
|
Higher Yang-Mills Theory: Electromagnetism can be generalized to Yang-Mills theory by replacing the
group U(1)$ by a nonabelian Lie group. This raises the question of whether one
can similarly generalize 2-form electromagnetism to a kind of
"higher-dimensional Yang-Mills theory". It turns out that to do this, one
should replace the Lie group by a "Lie 2-group", which is a category C where
the set of objects and the set of morphisms are Lie groups, and the source,
target, identity and composition maps are homomorphisms. We show that this is
the same as a "Lie crossed module": a pair of Lie groups G,H with a
homomorphism t: H -> G and an action of G on H satisfying two compatibility
conditions. Following Breen and Messing's ideas on the geometry of nonabelian
gerbes, one can define "principal 2-bundles" for any Lie 2-group C and do gauge
theory in this new context. Here we only consider trivial 2-bundles, where a
connection consists of a Lie(G)-valued 1-form together with an Lie(H)-valued
2-form, and its curvature consists of a Lie(G)-valued 2-form together with a
Lie(H)-valued 3-form. We generalize the Yang-Mills action for this sort of
connection, and use this to derive "higher Yang-Mills equations". Finally, we
show that in certain cases these equations admit self-dual solutions in five
dimensions.
|
Hadron structure functions at small $x$ from string theory: Deep inelastic scattering of leptons from hadrons at small values of the
Bjorken parameter $x$ is studied from superstring theory. In particular, we
focus on single-flavored scalar and vector mesons in the large $N$ limit. This
is studied in terms of different holographic dual models with flavor Dp-branes
in type IIA and type IIB superstring theories, in the strong coupling limit of
the corresponding dual gauge theories. We derive the hadronic tensor and the
structure functions for scalar and polarized vector mesons. In particular, for
polarized vector mesons we obtain the eight structure functions at small values
of the Bjorken parameter. The main result is that we obtain new relations of
the Callan-Gross type for several structure functions. These relations have
similarities for all different Dp-brane models that we consider. This would
suggest their universal character, and therefore, it is possible that they hold
for strongly coupled QCD in the large $N$ limit.
|
Nonsingular deformations of singular compactifications, the cosmological
constant, and the hierarchy problem: We consider deformations of the singular "global cosmic string"
compactifications, known to naturally generate exponentially large scales. The
deformations are obtained by allowing a constant curvature metric on the brane
and correspond to a choice of integration constant. We show that there exists a
unique value of the integration constant that gives rise to a nonsingular
solution. The metric on the brane is dS_4 with an exponentially small value of
expansion parameter. We derive an upper bound on the brane cosmological
constant. We find and investigate more general singular solutions---``dilatonic
global string" compactifications---and show that they can have nonsingular
deformations. We give an embedding of these solutions in type IIB supergravity.
There is only one class of supersymmetry-preserving singular dilatonic
solutions. We show that they do not have nonsingular deformations of the type
considered here.
|
Schwinger-Dyson equation in the complex plane -- Two simple models --: Effective mass and energy are investigated using the Schwinger-Dyson equation
(SDE) in the complex plane. As simple examples, we solve the SDE for the
(1+1)-dimensional model and the strongly coupled quantum electrodynamics (QED).
We also study some properties of the effective mass and energy in the complex
plane.
|
Holographic study of entanglement and complexity for mixed states: In this paper, we holographically quantify the entanglement and complexity
for mixed states by following the prescription of purification. The bulk theory
we consider in this work is a hyperscaling violating solution, characterized by
two parameters, hyperscaling violating exponent $\theta$ and dynamical exponent
$z$. This geometry is dual to a non-relativistic strongly coupled theory with
hidden Fermi surfaces. We first compute the holographic analogy of entanglement
of purification (EoP), denoted as the minimal area of the entanglement wedge
cross section and observe the effects of $z$ and $\theta$. Then in order to
probe the mixed state complexity we compute the mutual complexity for the BTZ
black hole and the hyperscaling violating geometry by incorporating the
holographic subregion complexity conjecture. We carry this out for two disjoint
subsystems separated by a distance and also when the subsystems are adjacent
with subsystems making up the full system. Furthermore, various aspects of
holographic entanglement entropy such as entanglement Smarr relation, Fisher
information metric and the butterfly velocity has also been discussed.
|
A non-torus link from topological vertex: The recently suggested tangle calculus for knot polynomials is intimately
related to topological string considerations and can help to build the
HOMFLY-PT invariants from the topological vertices. We discuss this interplay
in the simplest example of the Hopf link and link $L_{8n8}$. It turns out that
the resolved conifold with four different representations on the four external
legs, on the topological string side, is described by a special projection of
the four-component link $L_{8n8}$, which reduces to the Hopf link colored with
two composite representations. Thus, this provides the first explicit example
of non-torus link description through the topological vertex. It is not a real
breakthrough, because $L_{8n8}$ is just a cable of the Hopf link, still, it can
help to intensify the development of the formalism towards more interesting
examples.
|
Lattice String Field Theory: The linear dilaton in one dimension: We propose the use of lattice field theory for the study of string field
theory at the non-perturbative quantum level. We identify many potential
obstacles and examine possible resolutions thereof. We then experiment with our
approach in the particularly simple case of a one-dimensional linear dilaton
and analyse the results.
|
A Triangular Deformation of the two Dimensional Poincare Algebra: Contracting the $h$-deformation of $\SL(2,\Real)$, we construct a new
deformation of two dimensional Poincar\'e algebra, the algebra of functions on
its group and its differential structure. It is also shown that the Hopf
algebra is triangular, and its universal R matrix is also constructed
explicitly. Then, we find a deformation map for the universal enveloping
algebra, and at the end, give the deformed mass shells and Lorentz
transformation.
|
Analytical Properties of Solutions of the Schrodinger Equation and
Quantization of Charge: The Schwinger--DeWitt expansion for the evolution operator kernel is used to
investigate analytical properties of the Schr\"odinger equation solution in
time variable. It is shown, that this expansion, which is in general
asymptotic, converges for a number of potentials (widely used, in particular,
in one-dimensional many-body problems), and besides, the convergence takes
place only for definite discrete values of the coupling constant. For other
values of charge the divergent expansion determines the functions having
essential singularity at origin (beyond usual $\delta$-function). This does not
permit one to fulfil the initial condition. So, the function obtained from the
Schr\"odinger equation cannot be the evolution operator kernel. The latter,
rigorously speaking, does not exist in this case. Thus, the kernel exists only
for definite potentials, and moreover, at the considered examples the charge
may have only quantized values.
|
Irregular Singularities in the H3+ WZW Model: We propose a definition of irregular vertex operators in the H3+ WZW model.
Our definition is compatible with the duality [1] between the H3+ WZW model and
Liouville theory, and we provide the explicit map between correlation functions
of irregular vertex operators in the two conformal field theories. Our
definition of irregular vertex operators is motivated by relations to partition
functions of N=2 gauge theory and scattering amplitudes in N=4 gauge theory
|
On the Hydrodynamic Description of Holographic Viscoelastic Models: We show that the correct dual hydrodynamic description of homogeneous
holographic models with spontaneously broken translations must include the
so-called "strain pressure" -- a novel transport coefficient proposed recently.
Taking this new ingredient into account, we investigate the near-equilibrium
dynamics of a large class of holographic models and faithfully reproduce all
the hydrodynamic modes present in the quasinormal mode spectrum. Moreover,
while strain pressure is characteristic of equilibrium configurations which do
not minimise the free energy, we argue and show that it also affects models
with no background strain, through its temperature derivatives. In summary, we
provide a first complete matching between the holographic models with
spontaneously broken translations and their effective hydrodynamic description.
|
Deformed Twistors and Higher Spin Conformal (Super-)Algebras in Six
Dimensions: Massless conformal scalar field in six dimensions corresponds to the minimal
unitary representation (minrep) of the conformal group SO(6,2). This minrep
admits a family of deformations labelled by the spin t of an SU(2)_T group,
which is the 6d analog of helicity in four dimensions. These deformations of
the minrep of SO(6,2) describe massless conformal fields that are symmetric
tensors in the spinorial representation of the 6d Lorentz group. The minrep and
its deformations were obtained by quantization of the nonlinear realization of
SO(6,2) as a quasiconformal group in arXiv:1005.3580. We give a novel
reformulation of the generators of SO(6,2) for these representations as
bilinears of deformed twistorial oscillators which transform nonlinearly under
the Lorentz group SO(5,1) and apply them to define higher spin algebras and
superalgebras in AdS_7. The higher spin (HS) algebra of Fradkin-Vasiliev type
in AdS_7 is simply the enveloping algebra of SO(6,2) quotiented by a two-sided
ideal (Joseph ideal) which annihilates the minrep. We show that the Joseph
ideal vanishes identically for the quasiconformal realization of the minrep and
its enveloping algebra leads directly to the HS algebra in AdS_7. Furthermore,
the enveloping algebras of the deformations of the minrep define a discrete
infinite family of HS algebras in AdS_7 for which certain 6d Lorentz covariant
deformations of the Joseph ideal vanish identically. These results extend to
superconformal algebras OSp(8*|2N) and we find a discrete infinite family of HS
superalgebras as enveloping algebras of the minimal unitary supermultiplet and
its deformations. Our results suggest the existence of a discrete family of
(supersymmetric) HS theories in AdS_7 which are dual to free (super)conformal
field theories (CFTs) or to interacting but integrable (supersymmetric) CFTs in
6d.
|
A prediction for bubbling geometries: We study the supersymmetric circular Wilson loops in N=4 Yang-Mills theory.
Their vacuum expectation values are computed in the parameter region that
admits smooth bubbling geometry duals. The results are a prediction for the
supergravity action evaluated on the bubbling geometries for Wilson loops.
|
U-folds as K3 fibrations: We study N=2 four-dimensional flux vacua describing intrinsic
non-perturbative systems of 3 and 7 branes in type IIB string theory. The
solutions are described as compactifications of a G(ravity) theory on a Calabi
Yau threefold which consists of a fibration of an auxiliary K3 surface over an
S^2 base. In the spirit of F-theory, the complex structure of the K3 surface
varying over the base codifies the details of the fluxes, the dilaton and the
warp factors in type IIB string theory. We discuss in detail some simple
examples of geometric and non-geometric solutions where the precise
flux/geometry dictionary can be explicitly worked out. In particular, we
describe non-geometric T-fold solutions exhibiting non-trivial T-duality
monodromies exchanging 3- and 7-branes.
|
Creation of quasiparticles in graphene by a time-dependent electric
field: We investigate the creation of massless quasiparticle pairs from the vacuum
state in graphene by the space homogeneous time-dependent electric field. For
this purpose the formalism of (2+1)-dimensional quantum electrodynamics is
applied to the case of a nonstationary background with arbitrary time
dependence allowing the S-matrix formulation of the problem. The number of
created pairs per unit graphene area is expressed via the asymptotic solution
at $t\to\infty$ of the second-order differential equation of an oscillator type
with complex frequency satisfying some initial conditions at $t\to-\infty$. The
obtained results are applied to the electric field with specific dependence on
time admitting the exact solution of Dirac equation. The number of created
pairs per unit area is calculated analytically in a wide variety of different
regimes depending on the parameters of electric field. The investigated earlier
case of static electric field is reproduced as a particular case of our
formalism. It is shown that the creation rate in a time-dependent field is
often larger than in a static field.
|
A landscape for the cosmological constant and the Higgs mass: The cosmological constant and the Higgs mass seem unnaturally small and
anthropically selected. We show that both can be efficiently scanned in Quantum
Field Theories with a large enough number of vacua controllable thanks to
approximated $\mathbb{Z}_2$ symmetries (even for Coleman-Weinberg potentials).
We find that vacuum decay in a landscape implies weaker bounds than previously
estimated. Special vacua where one light scalar is accidentally light avoid
catastrophic vacuum decay if its self-cubic is absent. This is what happens for
the Higgs doublet, thanks to gauge invariance. Yukawa couplings can be
efficiently scanned, as suggested by anthropic boundaries on light quark
masses. Finally, we suggest that the lack of predictivity of landscapes can be
mitigated if their probability distributions are non-Gaussian (possibly even
fractal).
|
Fourth order wave equation in Bhabha-Madhavarao spin-$\frac{3}{2}$
theory: Within the framework of the Bhabha-Madhavarao formalism, a consistent
approach to the derivation of a system of the fourth order wave equations for
the description of a spin-$\frac{3}{2}$ particle is suggested. For this purpose
an additional algebraic object, the so-called $q$-commutator ($q$ is a
primitive fourth root of unity) and a new set of matrices $\eta_{\mu}$, instead
of the original matrices $\beta_{\mu}$ of the Bhabha-Madhavarao algebra, are
introduced. It is shown that in terms of the $\eta_{\mu}$ matrices we have
succeeded in reducing a procedure of the construction of fourth root of the
fourth order wave operator to a few simple algebraic transformations and to
some operation of the passage to the limit $z \rightarrow q$, where $z$ is some
(complex) deformation parameter entering into the definition of the
$\eta$-matrices. In addition, a set of the matrices ${\cal P}_{1/2}$ and ${\cal
P}_{3/2}^{(\pm)}(q)$ possessing the properties of projectors is introduced.
These operators project the matrices $\eta_{\mu}$ onto the spins 1/2- and
3/2-sectors in the theory under consideration. A corresponding generalization
of the obtained results to the case of the interaction with an external
electromagnetic field introduced through the minimal coupling scheme is carried
out. The application to the problem of construction of the path integral
representation in parasuperspace for the propagator of a massive
spin-$\frac{3}{2}$ particle in a background gauge field within the
Bhabha-Madhavarao approach is discussed.
|
On the solution of the massless Thirring model with fermion fields
quantized in the chiral symmetric phase: Correlation functions of fermionic fields described by the massless Thirring
model are analysed within the operator formalism developed by Klaiber and the
path-integral approach with massless fermions quantized in the chiral symmetric
phase. We notice that Klaiber's composite fermion operators possess
non-standard properties under parity transformations and construct operators
with standard parity properties. We find that Klaiber's parameterization of a
one-parameter family of solutions of the massless Thirring model is not well
defined, since it is not consistent with the requirement of chiral symmetry. We
show that the dynamical dimensions of correlation functions depend on an
arbitrary parameter induced by ambiguities of the evaluation of the chiral
Jacobian. A non-perturbative renormalization of the massless Thirring model is
discussed. We demonstrate that the infrared divergences of Klaiber's
correlation functions can be transferred into ultra-violet divergences by
renormalization of the wave function of fermionic fields. This makes Klaiber's
correlation functions non-singular in the infrared limit. We show that the
requirement of non-perturbative renormalizability of the massless Thirring
model fixes a free parameter of the path-integral approach. In turn, the
operator formalism is inconsistent with non-perturbative renormalizability of
the massless Thirring model. We carry out a non-perturbative renormalization of
the sine-Gordon model and show that it is not an asymptotically free theory as
well as the massless Thirring model. We calculate the fermion condensate by
using the Fourier transform of the two-point Green function of massless
Thirring fermion fields quantized in the chiral symmetric phase.
|
Gravitational Turbulent Instability of Anti-de Sitter Space: Bizon and Rostworowski have recently suggested that anti-de Sitter spacetime
might be nonlinearly unstable to transfering energy to smaller and smaller
scales and eventually forming a small black hole. We consider pure gravity with
a negative cosmological constant and find strong support for this idea. While
one can start with a single linearized mode and add higher order corrections to
construct a nonlinear geon, this is not possible starting with a linear
combination of two or more modes. One is forced to add higher frequency modes
with growing amplitude. The implications of this turbulent instability for the
dual field theory are discussed.
|
Uncovering a Spinor-Vector Duality on a Resolved Orbifold: Spinor-vector dualities have been established in various exact string
realisations like orbifold and free fermionic constructions. This paper aims to
investigate possibility of having spinor-vector dualities on smooth geometries
in the context of the heterotic string. As a concrete working example the
resolution of the T4/Z2 orbifold is considered with an additional circle
supporting a Wilson line, for which it is known that the underlying orbifold
theory exhibits such a duality by switching on/off a generalised discrete
torsion phase between the orbifold twist and the Wilson line. Depending on this
phase complementary parts of the twisted sector orbifold states are projected
out, so that different blowup modes are available to generate the resolutions.
As a consequence, not only the spectra of the dual pairs are different, but
also the gauge groups are not identical making this duality less apparent on
the blowup and thus presumably on smooth geometries in general.
|
On the Eleven-Dimensional Origins of Polarized D0-branes: The worldvolume theory of a D0-brane contains a multiplet of fermions which
can couple to background spacetime fields. This coupling implies that a
D0-brane may possess multipole moments with respect to the various type IIA
supergravity fields. Different such polarization states of the D0-brane will
thus generate different long-range supergravity fields, and the corresponding
semi-classical supergravity solutions will have different geometries. In this
paper, we reconsider such solutions from an eleven-dimensional perspective. We
thus begin by deriving the ``superpartners'' of the eleven-dimensional
graviton. These superpartners are obtained by acting on the purely bosonic
solution with broken supersymmetries and, in theory, one can obtain the full
BPS supermultiplet of states. When we dimensionally reduce a polarized
supergraviton along its direction of motion, we recover a metric which
describes a polarized D0-brane. On the other hand, if we compactify along the
retarded null direction we obtain the short distance, or ``near-horizon'',
geometry of a polarized D0-brane, which is related to finite $N$ Matrix theory.
The various dipole moments in this case can only be defined once the
eleven-dimensional metric is ``regularized'' and, even then, they are formally
infinite. We argue, however, that this is to be expected in such a
non-asymptotically flat spacetime. Moreover, we find that the superpartners of
the D0-brane, in this $r \ra 0$ limit, possess neither spin nor D2-brane dipole
moments.
|
Diagrammar of physical and fake particles and spectral optical theorem: We prove spectral optical identities in quantum field theories of physical
particles (defined by the Feynman $i\epsilon $ prescription) and purely virtual
particles (defined by the fakeon prescription). The identities are derived by
means of purely algebraic operations and hold for every (multi)threshold
separately and for arbitrary frequencies. Their major significance is that they
offer a deeper understanding on the problem of unitarity in quantum field
theory. In particular, they apply to "skeleton" diagrams, before integrating on
the space components of the loop momenta and the phase spaces. In turn, the
skeleton diagrams obey a spectral optical theorem, which gives the usual
optical theorem for amplitudes, once the integrals on the space components of
the loop momenta and the phase spaces are restored. The fakeon
prescription/projection is implemented by dropping the thresholds that involve
fakeon frequencies. We give examples at one loop (bubble, triangle, box,
pentagon and hexagon), two loops (triangle with "diagonal", box with diagonal)
and arbitrarily many loops. We also derive formulas for the loop integrals with
fakeons and relate them to the known formulas for the loop integrals with
physical particles.
|
Bigravity in Kuchar's Hamiltonian formalism. 1. The general case: The Hamiltonian formalism of bigravity and massive gravity is studied here
for the general form of the interaction potential of two metrics. In the
theories equipped with two spacetime metrics it is natural to use the Kuchar
approach, because then the role played by the lapse and shift variables becomes
more transparent. We find conditions on the potential which are necessary and
sufficient for the existence of four first class constraints. The algebra of
constraints is calculated in Dirac brackets formed on the base of all the
second class constraints. It is the celebrated algebra of hypersurface
deformations. By fixing one metric we obtain a massive gravity theory free of
first class constraints. Then we can use symmetries of the background metric to
derive conserved quantities. These are ultralocal, if expressed in terms of the
metric interaction potential. The special case of potential providing less
number of degrees of freedom is treated in the companion paper.
|
Self-DUal SU(3) Chern-Simons Higgs Systems: We explore self-dual Chern-Simons Higgs systems with the local $SU(3)$ and
global $U(1)$ symmetries where the matter field lies in the adjoint
representation. We show that there are three degenerate vacua of different
symmetries and study the unbroken symmetry and particle spectrum in each
vacuum. We classify the self-dual configurations into three types and study
their properties.
|
Microstate solutions from black hole deconstruction: We present a new family of asymptotic AdS_3 x S^2 solutions to eleven
dimensional supergravity compactified on a Calabi-Yau threefold. They originate
from the backreaction of S^2-wrapped M2-branes, which play a central role in
the deconstruction proposal for the microscopic interpretation of the D4-D0
black hole entropy. We show that they are free of possible pathologies such as
closed timelike curves and discuss their holographic interpretation.
|
Holography in a Radiation-dominated Universe with a Positive
Cosmological Constant: We discuss the holographic principle in a radiation-dominated, closed
Friedmann-Robertson-Walker (FRW) universe with a positive cosmological
constant. By introducing a cosmological D-bound on the entropy of matter in the
universe, we can write the Friedmann equation governing the evolution of the
universe in the form of the Cardy formula. When the cosmological D-bound is
saturated, the Friedmann equation coincides with the Cardy-Verlinde formula
describing the entropy of radiation in the universe. As a concrete model, we
consider a brane universe in the background of Schwarzschild-de Sitter black
holes. It is found that the cosmological D-bound is saturated when the brane
crosses the black hole horizon of the background. At that moment, the Friedmann
equation coincides with the Cardy-Verlinde formula describing the entropy of
radiation matter on the brane.
|
The bad locus in the moduli of super Riemann surfaces with Ramond
punctures: The bad locus in the moduli of super Riemann surfaces with Ramond punctures
parametrizes those super Riemann surfaces that have more than the expected
number of independent closed holomorphic 1-forms. There is a super period map
that depends on certain discrete choices. For each such choice, the period map
blows up along a divisor that contains the bad locus. Our main result is that
away from the bad locus, at least one of these period maps remains finite. In
other words, we identify the bad locus as the intersection of the blowup
divisors. The proof abstracts the situation into a question in linear algebra,
which we then solve. We also give some bounds on the dimension of the bad
locus.
|
Equations of Motion for Massive Spin 2 Field Coupled to Gravity: We investigate the problems of consistency and causality for the equations of
motion describing massive spin two field in external gravitational and massless
scalar dilaton fields in arbitrary spacetime dimension. From the field
theoretical point of view we consider a general classical action with
non-minimal couplings and find gravitational and dilaton background on which
this action describes a theory consistent with the flat space limit. In the
case of pure gravitational background all field components propagate causally.
We show also that the massive spin two field can be consistently described in
arbitrary background by means of the lagrangian representing an infinite series
in the inverse mass. Within string theory we obtain equations of motion for the
massive spin two field coupled to gravity from the requirement of quantum Weyl
invariance of the corresponding two dimensional sigma-model. In the lowest
order in $\alpha'$ we demonstrate that these effective equations of motion
coincide with consistent equations derived in field theory.
|
Time development of conformal field theories associated with $L_{1}$ and
$L_{-1}$ operators: In this study, we examined consequences of unconventional time development of
two-dimensional conformal field theory induced by the $L_{1}$ and $L_{-1}$
operators, employing the formalism previously developed in a study of
sine-square deformation. We discovered that the retainment of the Virasoro
algebra requires the presence of a cut-off near the fixed points. The
introduction of a scale by the cut-off makes it possible to recapture the
formula for entanglement entropy in a natural and straightforward manner.
|
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