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The double cone geometry is stable to brane nucleation: In gauge/gravity duality, the bulk double cone geometry has been argued to
account for a key feature of the spectral form factor known as the ramp. This
feature is deeply associated with quantum chaos in the dual field theory. The
connection with the ramp has been demonstrated in detail for two-dimensional
theories of bulk gravity, but it appears natural in higher dimensions as well.
In a general bulk theory the double cone might thus be expected to dominate the
semiclassical bulk path integral for the boundary spectral form factor in the
ramp regime. While other known spacetime wormholes have been shown to be
unstable to brane nucleation when they dominate over known disconnected
(factorizing) solutions, we argue that the double cone is stable to
semiclassical brane nucleation at the probe-brane level in a variety of string-
and M-theory settings. Possible implications for the AdS/CFT factorization
problem are briefly discussed. | IIA Ten-forms and the Gauge Algebras of Maximal Supergravity Theories: We show that IIA supergravity can be extended with two independent 10-form
potentials. These give rise to a single BPS IIA 9-brane. We investigate the
bosonic gauge algebra of both IIA and IIB supergravity in the presence of
10-form potentials and point out an intriguing relation with the symmetry
algebra $E_{11}$, which has been conjectured to be the underlying symmetry of
string theory/M-theory. |
Probing magnetic line defects with two-point functions: This paper studies magnetic line defects in the Wilson-Fisher $O(N)$ model. A
powerful method to probe the system is to consider mixed two-point functions of
the order parameter and the energy operator in the presence of the defect. A
recently developed dispersion relation allows us to bootstrap these mixed
correlators to leading order in the $\epsilon$-expansion. We also carry out
explicit diagrammatic calculations, finding perfect agreement with the
bootstrap, and we conclude extracting the new CFT data predicted by the
two-point functions. | On extremal transitions of Calabi-Yau threefolds and the singularity of
the associated 7-space from rolling: M-theory compactification leads one to consider 7-manifolds obtained by
rolling Calabi-Yau threefolds in the web of Calabi-Yau moduli spaces. The
resulting 7-space in general has singularities governed by the extremal
transition undergone. After providing some background in Sec. 1, the simplest
case of conifold transitions is studied in Sec. 2. In Sec. 3 we employ
topological methods, Smale's classification theorem of smooth simply-connected
spin closed 5-manifolds, and a computer code in the Appendix to understand the
5-manifolds that appear as the link of the singularity of a singuler Calabi-Yau
threefolds from a Type II primitive contraction of a smooth one.
From this we obtain many locally admissible extremal transition pairs of
Calabi-Yau threefolds, listed in Sec. 4. Their global realization will require
further study. As a mathematical byproduct in the pursuit of the subject, we
obtain a formula to compute the topology of the boundary of the tubular
neighborhood of a Gorenstein rational singular del Pezzo surface embedded in a
smooth Calabi-Yau threefold as a divisor. |
Neutrino spin oscillations in gravitational fields in noncommutative
higher dimensions: Investigation of neutrino spin oscillation in the gravitational fields of
black holes(BH) is one of the interesting topics in neutrino physics. On the
other hand, in recent years, many studies have been devoted to the exploration
of different physical phenomena in higher dimensions. Noncommutative geometry
has also been in the focus of researchers in the past years to explore deeper
and more accurate the structure of space time. In this work, the neutrino spin
oscillation in the noncommutative higher dimensions gravitational fields of
Schwarzschild and Reissner-Nordstrom metrics are studied. The effects of
noncommutativity of space are calculated and its role in different dimensions
are discussed. Finally upper bounds on noncommutativity parameter are obtained. | Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective
Field Theory: We describe a systematic framework for finding the conservative potential of
compact binary systems with spin based on scattering amplitudes of particles of
arbitrary spin and effective field theory. An arbitrary-spin formalism is
generally required in the classical limit. By matching the tree and one-loop
amplitudes of four spinning particles with those of a suitably-chosen effective
field theory, we obtain the spin1-spin2 terms of a two-body effective
Hamiltonian through O(G^2) and valid to all orders in velocity. Solving
Hamilton's equations yields the impulse and spin changes of the individual
bodies. We write them in a surprisingly compact form as appropriate derivatives
of the eikonal phase obtained from the amplitude. It seems likely this
structure persists to higher orders. We also point out various double-copy
relations for general spin. |
Non-Trivial Vacua in Higher-Derivative Gravitation: A discussion of an extended class of higher-derivative classical theories of
gravity is presented. A procedure is given for exhibiting the new propagating
degrees of freedom, at the full non-linear level, by transforming the
higher-derivative action to a canonical second-order form. For general
fourth-order theories, described by actions which are general functions of the
scalar curvature, the Ricci tensor and the full Riemann tensor, it is shown
that the higher-derivative theories may have multiple stable vacua. The vacua
are shown to be, in general, non-trivial, corresponding to deSitter or
anti-deSitter solutions of the original theory. It is also shown that around
any vacuum the elementary excitations remain the massless graviton, a massive
scalar field and a massive ghost-like spin-two field. The analysis is extended
to actions which are arbitrary functions of terms of the form $\nabla^{2k}R$,
and it is shown that such theories also have a non-trivial vacuum structure. | From conformal to confining field theories using holography: We construct a new family of Type IIB backgrounds that are dual to five
dimensional conformal field theories compactified and deformed by VEVs of
certain operators. This generates an RG flow into a smooth background dual to
non-SUSY gapped field theories in four dimensions. We study various holographic
observables: a monotonic quantity associated with the number of degrees of
freedom, Wilson loops that interpolate between conformal and confining
behaviour with the possibility of screening, Entanglement Entropy, etc. We also
give a prescription to compute the Holographic Complexity in this type of
backgrounds and calculate the spectrum of spin-two glueballs of the field
theories. |
Bouncing cosmology in modified Gauss-Bonnet gravity: We explore bounce cosmology in $F(\mathcal{G})$ gravity with the Gauss-Bonnet
invariant $\mathcal{G}$. We reconstruct $F(\mathcal{G})$ gravity theory to
realize the bouncing behavior in the early universe and examine the stability
conditions for its cosmological solutions. It is demonstrated that the bouncing
behavior with an exponential as well as a power-law scale factor naturally
occurs in modified Gauss-Bonnet gravity. We also derive the $F(\mathcal{G})$
gravity model to produce the ekpyrotic scenario. Furthermore, we construct the
bounce with the scale factor composed of a sum of two exponential functions and
show that not only the early-time bounce but also the late-time cosmic
acceleration can occur in the corresponding modified Gauss-Bonnet gravity.
Also, the bounce and late-time solutions in this unified model is explicitly
analyzed. | Analytic solutions of neutral hyperbolic black holes with scalar hair: We find analytic solutions of hyperbolic black holes with scalar hair in
anti-de Sitter (AdS) space, and they do not have spherical or planar
counterparts. The system is obtained by taking a neutral limit of an
Einstein-Maxwell-dilaton system whose special cases are maximal gauged
supergravities, while the dilaton is kept nontrivial. There are phase
transitions between these black holes and the hyperbolic Schwarzschild-AdS
black hole. We discuss two AdS/CFT applications of these hyperbolic black
holes. One is phase transitions of holographic Renyi entropies, and the other
is phase transitions of quantum field theories in de Sitter space. In addition,
we give a C-metric solution as a generalization of the hyperbolic black holes
with scalar hair. |
Vortex and droplet in holographic D-wave superconductors: We investigate non-trivial localized solutions of the condensate in a
(2+1)-dimensional D-wave holographic superconductor model in the presence of a
background magnetic field. The calculation is done in the context of the
(3+1)-dimensional dual gravity theory of a charged massive spin-2 field in an
AdS black hole background. By using numeric techniques, we find both vortex and
droplet solutions. These solutions are important for studying the full phase
diagram of D-wave superconductors. | On relation between Nekrasov functions and BS periods in pure SU(N) case: We investigate the duality between the Nekrasov function and the quantized
Seiberg-Witten prepotential, first guessed in [1] and further elaborated in [2]
and [3]. We concentrate on providing more thorough checks than the ones
presented in [3] and do not discuss the motivation and historical context of
this duality. The check of the conjecture up to $o (\hbar^6, \ln (\Lambda))$ is
done by hands for arbitrary $N$ (explicit formulas are presented). Moreover,
details of the calculation that are essential for the computerization of the
check are worked out. This allows us to test the conjecture up to $\hbar^6$ and
up to higher powers of $\Lambda$ for $N = 2,3,4$. Only the case of pure SU(N)
gauge theory is considered. |
Deconfinement transition in three-dimensional compact U(1) gauge
theories coupled to matter fields: It is shown that permanent confinement in three-dimensional compact U(1)
gauge theory can be destroyed by matter fields in a deconfinement transition.
This is a consequence of a non-trivial infrared fixed point caused by matter,
and an anomalous scaling dimension of the gauge field. This leads to a
logarithmic interaction between the defects of the gauge-fields, which form a
gas of magnetic monopoles. In the presence of logarithmic interactions, the
original electric charges are unconfined. The confined phase which is permanent
in the absence of matter fields is reached at a critical electric charge, where
the interaction between magnetic charges is screened by a pair unbinding
transition in a Kosterlitz-Thouless type of phase-transition. | Modulated Ground State of Gravity Theories with Stabilized Conformal
Factor: We discuss the stabilization of the conformal factor by higher derivative
terms in a conformally reduced $R+R^2$ Euclidean gravity theory. The flat
spacetime is unstable towards the condensation of modes with nonzero momentum,
and they "condense" in a modulated phase above a critical value of the coupling
$\beta$ of the $R^2$ term. By employing a combination of variational, numerical
and lattice methods we show that in the semiclassical limit the corresponding
functional integral is dominated by a single nonlinear plane wave of frequency
$\approx 1/\sqrt{\beta} \lp$. We argue that the ground state of the theory is
characterized by a spontaneous breaking of translational invariance at
Planckian scales. |
Black Holes and Higher Composition Laws: We describe various relations between Bhargava's higher composition laws,
which generalise Gauss's original composition law on integral binary quadratic
forms, and extremal black hole solutions appearing in string/M-theory and
related models. The cornerstone of these correspondences is the identification
of the charge cube of the STU black hole with Bhargava's cube of integers,
which underpins the related higher composition laws. | AdS/CFT Casimir Energy for Rotating Black Holes: We show that if one chooses the Einstein Static Universe as the metric on the
conformal boundary of Kerr-AdS spacetime, then the Casimir energy of the
boundary conformal field theory can easily be determined. The result is
independent of the rotation parameters, and the total boundary energy then
straightforwardly obeys the first law of thermodynamics. Other choices for the
metric on the conformal boundary will give different, more complicated,
results. As an application, we calculate the Casimir energy for free self-dual
tensor multiplets in six dimensions, and compare it with that of the
seven-dimensional supergravity dual. They differ by a factor of 5/4. |
Curvature Singularity as the Vertex Operator: The submitted paper regards the example of the Conformal Field Theory on a 2d
manifold which metric has a point-like singularity.Since this manifold is not
conformally equivalent to that with the flat space-time metric,it's naturally
to expect that the theory cannot be trivially reduced to the well-known
consideration of the CFT on a plane,and some modifications are
needed.Particularly,this paper shows how the vacuum of the theory on a singular
surface differs from the vacuum of the BPZ theory.Namely,this vacuum would not
be SL(2,C)-invariant and the expressions for the correlation functions should
be modified. As a consequence of that,some "effective mass" is brought to the
theory. | An Analysis of Anomaly Cancellation for Theories in D=10: We prove that the swampland for D=10 N=1 SUGRA coupled to D=10 N=1 SYM is
only populated by U(1)^496 and E_8 x U(1)^248. With this goal in mind, we
review the anomalies for classical and exceptional groups, retrieving trace
identities up to the sixth power of the curvature for each class of groups. We
expand this idea for low-dimensional groups, for which the trace of the sixth
power is known to factorize, and we retrieve such factorization. We obtain the
total anomaly polynomials for individual low dimensional groups and
combinations of them and finally we investigate their non-factorization, in
such a way that U(1)^496and E_8 xU(1)^248 are non-trivially shown to be the
only anomaly-free theories allowed in D=10. Using the method developed for
checking the factorization of gauge theories, we retrieve the Green-Schwarz
terms for the two theories populating the swampland. |
Supersymmetric solitons in gauged $\mathcal{N}=8$ supergravity: We consider soliton solutions in AdS$_{4}$ with a flat slicing and Wilson
loops around one cycle. We study the phase structure and find the ground state
and identify supersymmetric solutions as a function of the Wilson loops. We
work in the context of a scalar field truncation of gauged $\mathcal{N}=8$
supergravity, where all the dilatons are equal and all the axions vanish in the
STU model. In this theory, we construct new soliton solutions parameterized by
two Wilson lines. We find that there is a degeneracy of supersymmetric
solutions. We also show that, for alternate boundary conditions, there exists a
non-supersymmetric soliton solution with energy lower than the supersymmetric
one. | Crystals, instantons and quantum toric geometry: We describe the statistical mechanics of a melting crystal in three
dimensions and its relation to a diverse range of models arising in
combinatorics, algebraic geometry, integrable systems, low-dimensional gauge
theories, topological string theory and quantum gravity. Its partition function
can be computed by enumerating the contributions from noncommutative instantons
to a six-dimensional cohomological gauge theory, which yields a dynamical
realization of the crystal as a discretization of spacetime at the Planck
scale. We describe analogous relations between a melting crystal model in two
dimensions and N=4 supersymmetric Yang-Mills theory in four dimensions. We
elaborate on some mathematical details of the construction of the quantum
geometry which combines methods from toric geometry, isospectral deformation
theory and noncommutative geometry in braided monoidal categories. In
particular, we relate the construction of noncommutative instantons to deformed
ADHM data, torsion-free modules and a noncommutative twistor correspondence. |
String Creation, D-branes and Effective Field Theory: This paper addresses several unsettled issues associated with string creation
in systems of orthogonal Dp-D(8-p) branes. The interaction between the branes
can be understood either from the closed string or open string picture. In the
closed string picture it has been noted that the DBI action fails to capture an
extra RR exchange between the branes. We demonstrate how this problem persists
upon lifting to M-theory. These D-brane systems are analysed in the closed
string picture by using gauge-fixed boundary states in a non-standard lightcone
gauge, in which RR exchange can be analysed precisely. The missing piece in the
DBI action also manifests itself in the open string picture as a mismatch
between the Coleman-Weinberg potential obtained from the effective field theory
and the corresponding open string calculation. We show that this difference can
be reconciled by taking into account the superghosts in the (0+1)effective
theory of the chiral fermion, that arises from gauge fixing the spontaneously
broken world-line local supersymmetries. | Discrete symmetry breaking and restoration at finite temperature in 3D
Gross-Neveu model: Dynamical spontaneous breaking of some discrete symmetries including special
parities and time reversal and their restoration at finite temperature T are
researched in 3D Gross-Neveu model by means of Schwinger-Dyson equation in the
real-time thermal field theory in the fermion bubble diagram approximation.
When the momentum cut-off $\Lambda$ is large enough, the equation of critical
chemical potential $\mu_c$ and critical temperature $T_c$ will be
$\Lambda$-independent and identical to the one obtained by auxialiary scalar
field approach. The dynamical fermion mass m, as the order parameter of
symmetry breaking, has the same $(T_c-T)^{1/2}$ behavior as one in 4D NJL-model
when T is less than and near $T_c$ and this shows the second-order phase
transition feature of the symmetry restoration at $T>T_c$. It is also proven
that no scalar bound state could exist in this model. |
Determination of Boundary Contributions in Recursion Relation: In this paper, we propose a new algorithm to systematically determine the
missing boundary contributions, when one uses the BCFW on-shell recursion
relation to calculate tree amplitudes for general quantum field theories. After
an instruction of the algorithm, we will use several examples to demonstrate
its application, including amplitudes of color-ordered phi-4 theory, Yang-Mills
theory, Einstein-Maxwell theory and color-ordered Yukawa theory with phi-4
interaction. | Homotopy Lie Superalgebra in Yang-Mills Theory: The Yang-Mills equations are formulated in the form of generalized
Maurer-Cartan equations, such that the corresponding algebraic operations are
shown to satisfy the defining relations of homotopy Lie superalgebra. |
3 Definitions of BF Theory on Homology 3-Spheres: 3-dimensional BF theory with gauge group $G$ (= Chern-Simons theory with
non-compact gauge group $TG$) is a deceptively simple yet subtle topological
gauge theory. Formally, its partition function is a sum/integral over the
moduli space $\mathcal{M}$ of flat connections, weighted by the Ray-Singer
torsion. In practice, however, this formal expression is almost invariably
singular and ill-defined.
In order to improve upon this, we perform a direct evaluation of the path
integral for certain classes of 3-manifolds (namely integral and rational
Seifert homology spheres). By a suitable choice of gauge, we sidestep the issue
of having to integrate over $\mathcal{M}$ and reduce the partition function to
a finite-dimensional Abelian matrix integral which, however, itself requires a
definition. We offer 3 definitions of this integral, firstly via residues, and
then via a large $k$ limit of the corresponding $G\times G$ or $G_C$
Chern-Simons matrix integrals (obtained previously). We then check and discuss
to which extent the results capture the expected sum/integral over all flat
connections. | Quantum Loops in Non-Local Gravity: In this proceedings, I will consider quantum aspects of a non-local,
infinite-derivative scalar field theory - a ${\it toy \, model}$ depiction of a
covariant infinite-derivative, non-local extension of Einstein's general
relativity which has previously been shown to be free from ghosts around the
Minkowski background. The graviton propagator in this theory gets an
exponential suppression making it ${\it asymptotically \, free}$, thus
providing strong prospects of resolving various classical and quantum
divergences. In particular, I will find that at $1$-loop, the $2$-point
function is still divergent, but once this amplitude is renormalized by adding
appropriate counter terms, the ultraviolet (UV) behavior of all other $1$-loop
diagrams as well as the $2$-loop, $2$-point function remains well under
control. I will go on to discuss how one may be able to generalize our
computations and arguments to arbitrary loops. |
Three-Dimensional Gauge Theories and ADE Monopoles: We study three-dimensional N=4 gauge theories with product gauge groups
constructed from ADE Dynkin diagrams. One-loop corrections to the metric on the
Coulomb branch are shown to coincide with the metric on the moduli space of
well-seperated ADE monopoles. We propose that this correspondence is exact. | On massive spin-2 in the Fradkin-Vasiliev formalism. II. General massive
case: In this work we apply the Fradkin-Vasiliev formalism based on the frame-like
gauge invariant description of the massive and massless spin 2 to the
construction of the cubic interactions vertices for massive spin 2
self-interaction as well as its gravitational interaction. In the first case we
show that the vertex can be reduced (by field redefinitions) to the set of the
trivially gauge invariant terms. There are four such terms which are not
equivalent om-shell and do not contain more than four derivatives. Moreover,
one their particular combination reproduces the minimal (with no more than two
derivatives) vertex. As for the gravitational vertex, we show that due to the
presence of the massless spin 2 there exist two abelian vertices (besides the
three trivially gauge invariant ones) which are not equivalent to any trivially
gauge invariant terms and can not be removed by field redefinitions. Moreover,
their existence appears to be crucial for the possibility to reproduce the
minimal two derivatives vertex. |
D branes in string theory, II: In these lectures we review the properties of a boosted and rotated boundary
state and of a boundary state with an abelian gauge field deriving from it the
Dirac-Born-Infeld action and a newly constructed class of classical solutions.
We also review the construction of the boundary state for the stable non-BPS
state of type I theory corresponding to the perturbative state present at the
first excited level of the SO(32) heterotic string and transforming according
to the spinor representation of SO(32) (Lectures presented at the YITP Workshop
on ``Developments in Superstring and M-theory'', Kyoto, Japan, October 1999). | S-Dual Gravity in the Axial Gauge: We investigate an action that includes simultaneously original and dual
gravitational fields (in the first order formalism), where the dual fields are
completely determined in terms of the original fields through axial gauge
conditions and partial (non-covariant) duality constraints. We introduce two
kinds of matter, one that couples to the original metric, and dual matter that
couples to the dual metric. The linear response of both metrics to the
corresponding stress energy tensors coincides with Einstein's equations. In the
presence of nonvanishing standard and dual cosmological constants a stable
solution with a time independent dual scale factor exists that could possibly
solve the cosmological constant problem, provided our world is identified with
the dual sector of the model. |
Stationary Strings and Principal Killing Triads in 2+1 Gravity: A new tool for the investigation of 2+1 dimensional gravity is proposed. It
is shown that in a stationary 2+1 dimensional spacetime, the eigenvectors of
the covariant derivative of the timelike Killing vector form a rigid structure,
the {\it principal Killing triad}. Two of the triad vectors are null, and in
many respects they play the role similar to the principal null directions in
the algebraically special 4-D spacetimes. It is demonstrated that the principal
Killing triad can be efficiently used for classification and study of
stationary 2+1 spacetimes.
One of the most interesting applications is a study of minimal surfaces in a
stationary spacetime. A {\it principal Killing surface} is defined as a surface
formed by Killing trajectories passing through a null ray, which is tangent to
one of the null vectors of the principal Killing triad. We prove that a
principal Killing surface is minimal if and only if the corresponding null
vector is geodesic. Furthermore, we prove that if the 2+1 dimensional spacetime
contains a static limit, then the only regular stationary timelike minimal
2-surfaces that cross the static limit, are the minimal principal Killing
surfaces.
A timelike minimal surface is a solution to the Nambu-Goto equations of
motion and hence it describes a cosmic string configuration. A stationary
string interacting with a 2+1 dimensional rotating black hole is discussed in
detail. | Resumming perturbative series in the presence of monopole bubbling
effects: Monopole bubbling effect is screening of magnetic charges of singular Dirac
monopoles by regular 't Hooft-Polyakov monopoles. We study properties of weak
coupling perturbative series in the presence of monopole bubbling effects as
well as instantons. For this purpose, we analyze supersymmetric 't Hooft loop
in four dimensional $\mathcal{N}=2$ supersymmetric gauge theories with
Lagrangians and non-positive beta functions. We show that the perturbative
series of the 't Hooft loop is Borel summable along positive real axis for
fixed instanton numbers and screened magnetic charges. It turns out that the
exact result of the 't Hooft loop is the same as the sum of the Borel
resummations over instanton numbers and effective magnetic charges. We also
obtain the same result for supersymmetric dyonic loops. |
Entanglement entropy of singular surfaces under relevant deformations in
holography: In the vacuum state of a CFT, the entanglement entropy of singular surfaces
contains a logarithmic universal term which is only due to the singularity of
the entangling surface. We consider the relevant perturbation of a three
dimensional CFT for singular entangling surface. We observe that in addition to
the universal term due to the entangling surface, there is a new logarithmic
term which corresponds to a relevant perturbation of the conformal field theory
with a coefficient depending on the scaling dimension of the relevant operator.
We also find a new power law divergence in the holographic entanglement
entropy. In addition, we study the effect of a relevant perturbation in the
Gauss-Bonnet gravity for a singular entangling surface. Again a logarithmic
term shows up. This new term is proportional to both the dimension of the
relevant operator and the Gauss-Bonnet coupling. We also introduce the
renormalized entanglement entropy for a kink region which in the UV limit
reduces to a universal positive finite term. | The Scattering Variety: The so-called Scattering Equations which govern the kinematics of the
scattering of massless particles in arbitrary dimensions have recently been
cast into a system of homogeneous polynomials. We study these as affine and
projective geometries which we call Scattering Varieties by analyzing such
properties as Hilbert series, Euler characteristic and singularities.
Interestingly, we find structures such as affine Calabi-Yau threefolds as well
as singular K3 and Fano varieties. |
The spectrum of BPS branes on a noncompact Calabi-Yau: We begin the study of the spectrum of BPS branes and its variation on lines
of marginal stability on O_P^2(-3), a Calabi-Yau ALE space asymptotic to
C^3/Z_3. We show how to get the complete spectrum near the large volume limit
and near the orbifold point, and find a striking similarity between the
descriptions of holomorphic bundles and BPS branes in these two limits. We use
these results to develop a general picture of the spectrum. We also suggest a
generalization of some of the ideas to the quintic Calabi-Yau. | Towards an Entanglement Measure for Mixed States in CFTs Based on
Relative Entropy: Relative entropy of entanglement (REE) is an entanglement measure of
bipartite mixed states, defined by the minimum of the relative entropy
$S(\rho_{AB}|| \sigma_{AB})$ between a given mixed state $\rho_{AB}$ and an
arbitrary separable state $\sigma_{AB}$. The REE is always bounded by the
mutual information $I_{AB}=S(\rho_{AB} || \rho_{A}\otimes \rho_{B})$ because
the latter measures not only quantum entanglement but also classical
correlations. In this paper we address the question of to what extent REE can
be small compared to the mutual information in conformal field theories (CFTs).
For this purpose, we perturbatively compute the relative entropy between the
vacuum reduced density matrix $\rho^{0}_{AB}$ on disjoint subsystems $A \cup B$
and arbitrarily separable state $\sigma_{AB}$ in the limit where two subsystems
A and B are well separated, then minimize the relative entropy with respect to
the separable states. We argue that the result highly depends on the spectrum
of CFT on the subsystems. When we have a few low energy spectrum of operators
as in the case where the subsystems consist of a finite number of spins in spin
chain models, the REE is considerably smaller than the mutual information.
However in general our perturbative scheme breaks down, and the REE can be as
large as the mutual information. |
Strong Coupling Qed Breaks Chiral Symmetry: We show that the strong coupling limit of d-dimensional quantum
electrodynamics with $2^{d}/2^{[d/2]}$ flavors of fermions can be mapped onto
the s=1/2 quantum Heisenberg antiferromagnet in d-1 space dimensions. The
staggered N\'eel order parameter is the expectation value of a mass operator in
QED and the spin-waves are pions. We speculate that the chiral symmetry
breaking phase transition corresponds to a transition between the flux phase
and the conventional N\'eel ordered phase of an antiferromagnetic t-J model. | Complex Burgers' equation in 2D SU(N) YM: An integro-differential equation satisfied by an eigenvalue density defined
as the logarithmic derivative of the average inverse characteristic polynomial
of a Wilson loop in two dimensional pure Yang Mills theory with gauge group
SU(N) is derived from two associated complex Burgers' equations, with viscosity
given by 1/(2N). The Wilson loop does not intersect itself and Euclidean
space-time is assumed flat and infinite. This result provides an extension of
the infinite N solution of Durhuus and Olesen to finite N, but this extension
is not unique. |
On the Rényi entropy of Lifshitz and hyperscaling violating black
holes: We study R\'enyi entropies for geometries with Lifshitz scaling and
hyperscaling violation. We calculate them for specific values of the Lifshitz
parameter, and analyze the dual spectrum of the ground state. In the large
$d-\theta$ limit they show that the ground state is unique in specific
parameter ranges. We also calculate the R\'enyi entropies perturbatively around
$n=1$, and derive constraints using the R\'enyi entropy inequalities, which
correspond to the thermodynamic stability of the black holes. | Matter From Geometry: We provide a local geometric description of how charged matter arises in type
IIA, M-theory, or F-theory compactifications on Calabi-Yau manifolds. The basic
idea is to deform a higher singularity into a lower one through Cartan
deformations which vary over space. The results agree with expectations based
on string dualities. |
Non-Linear Massive Gravity with Additional Primary Constraint and
Absence of Ghosts: We complete the Hamiltonian analysis of specific model of non-linear massive
gravity that was started in arXiv:1112.5267. We identify the primary constraint
and corresponding secondary constraint. We show that they are the second class
constraints and hence they lead to the elimination of the additional scalar
mode. We also find that the remaining constraints are the first class
constraints with the structure that corresponds to the manifestly
diffeomorphism invariant theory. Finally we determine the number of physical
degrees of freedom and we show that it corresponds to the number of physical
modes of massive gravity. | An M-theory solution from null roots in E11: We find a purely gravitational classical solution of
M-theory/eleven-dimensional supergravity which corresponds to a solution of the
E10 brane sigma-model involving a null root. This solution is not
supersymmetric and is regularly embedded into E11. |
Non-Relativistic Strings and Limits of the AdS/CFT Correspondence: Using target space null reduction of the Polyakov action we find a novel
covariant action for strings moving in a torsional Newton-Cartan geometry.
Sending the string tension to zero while rescaling the Newton-Cartan clock
1-form, so as to keep the string action finite, we obtain a non-relativistic
string moving in a new type of non-Lorentzian geometry that we call
$U(1)$-Galilean geometry. We apply this to strings on $AdS_5 \times S^5$ for
which we show that the zero tension limit is realized by the Spin Matrix theory
limits of the AdS/CFT correspondence. This is closely related to limits of spin
chains studied in connection to integrability in AdS/CFT. The simplest example
gives a covariant version of the Landau-Lifshitz sigma-model. | Hamilton-Jacobi formulation for singular systems with second order
Lagrangians: Recently the Hamilton-Jacobi formulation for first order constrained systems
has been developed. In such formalism the equations of motion are written as
total differential equations in many variables. We generalize the
Hamilton-Jacobi formulation for singular systems with second order Lagrangians
and apply this new formulation to Podolsky electrodynamics, comparing with the
results obtained through Dirac's method. |
A Possible Higher Order Correction to the chiral Vortical Conductivity
in a Gauge Field Plasma: The two loop contributions to the chiral vortical conductivity are
considered. The Kubo formula together with the anomalous Ward identity of the
axial vector current suggest that there may be a nonzero correction to the
coefficient of the $T^2$ term of the conductivity. | Trispectrum from Co-dimension 2(n) Galileons: A generalized theory of multi-field galileons has been recently put forward.
This model stems from the ongoing effort to embed generic galileon theories
within brane constructions. Such an approach has proved very useful in
connecting interesting and essential features of these theories with geometric
properties of the branes embedding. We investigate the cosmological
implications of a very restrictive multi-field galileon theory whose leading
interaction is solely quartic in the scalar field and lends itself nicely to an
interesting cosmology. The trispectrum of curvature fluctuations has features
which are quite distinctive with respect to their P(X,\phi) counterpart. We
also show that, despite an absent cubic Lagrangian in the full theory,
non-Gaussianities in this model cannot produce the combination a of small
bispectrum alongside with a large trispectrum. We further expand on this point
to draw a lesson on what having a symmetry in the full background independent
theory entails at the level of fluctuations and vice-versa. |
Treating 'thooft-Polyakov Monopole as Constrained System: The 'tHooft-Polyakov monopole is treated as constrained system using the
Hamilton-Jacobi method. The set of the Hamilton-Jacobi partial differential
equations and the equations of motion are obtained. The quantization of the
system is also discussed. | Sphere partition functions and cut-off AdS: We consider sphere partition functions of TT deformed large N conformal field
theories in d=2,3,4,5 and 6 dimensions, computed using the flow equation. These
are shown to non-perturbatively match with bulk computations of $AdS_{d+1}$
with a finite radial cut-off. We then demonstrate how the flow equation can be
independently derived from a regularization procedure in defining TT operators
through a local Callan-Symanzik equation. Finally, we show that the sphere
partition functions, modulo bulk-counterterm contributions, can be reproduced
from Wheeler-DeWitt wave functions. |
Higher-spin dynamics and Chern-Simons theories: We review the construction of consistent higher-spin theories based on
Chern-Simons actions. To this end we first introduce the required higher-spin
algebras and discuss curvature and torsion tensors in an unconstrained way.
Finally we perform a perturbative analysis of the Chern-Simons theory in D=5
for a non-maximally symmetric AdS(4) background and obtain the required
four-dimensional Fronsdal equations in the compensator formulation. | Non singular bounce in modified gravity: We investigate bouncing solutions in the framework of the non-singular
gravity model of Brandenberger, Mukhanov and Sornborger. We show that a
spatially flat universe filled with ordinary matter undergoing a phase of
contraction reaches a stage of minimal expansion factor before bouncing in a
regular way to reach the expanding phase. The expansion can be connected to the
usual radiation- and matter-dominated epochs before reaching a final expanding
de Sitter phase. In general relativity (GR), a bounce can only take place
provided that the spatial sections are positively curved, a fact that has been
shown to translate into a constraint on the characteristic duration of the
bounce. In our model, on the other hand, a bounce can occur also in the absence
of spatial curvature, which means that the timescale for the bounce can be made
arbitrarily short or long. The implication is that constraints on the bounce
characteristic time obtained in GR rely heavily on the assumed theory of
gravity. Although the model we investigate is fourth order in the derivatives
of the metric (and therefore unstable vis-a-vis the perturbations), this
generic bounce dynamics should extend to string-motivated non singular models
which can accommodate a spatially flat bounce. |
Spinning solutions for the bosonic M2-brane with $C_{\pm}$ fluxes: In this work we obtain classical solutions of the bosonic sector of the
supermembrane theory with two-form fluxes associated to a quantized constant
$C_{\pm}$ background. This theory satisfies a flux condition on the worldvolume
that induces monopoles over it. Classically it is stable as it does not contain
string-like spikes with zero energy in distinction with the general case. At
quantum level the bosonic membrane has a purely discrete spectrum but the
relevance is that the same property holds for its supersymmetric spectrum. We
find for this theory spinning membrane solutions, some of them including the
presence of a non-vanishing symplectic gauge connection defined on its
worldvolume in different approximations. By using the duality found between
this theory and the so-called supermembrane with central charges, rotating
membrane solutions found in that case, are also solutions of the M2-brane with
$C_{\pm}$ fluxes. We generalize this result to other embeddings. We find new
distinctive rotating membrane solutions, some of them including the presence of
a non-vanishing symplectic gauge connection defined on its worldvolume. We
obtain numerical and analytical solutions in different approximations
characterizing the dynamics of the membrane with fluxes $C_{\pm}$ for different
ans\"atze of the dynamical degrees of freedom. Finally we discuss the physical
admissibility of some of these ans\"atze to model the components of the
symplectic gauge field. | String from Large N Gauge Fields via Graph Summation on a P+ - x+
Lattice: I describe renewed efforts to establish a string description of large N_c QCD
by summing large ``fishnet'' diagrams. Earlier work on fishnets indicated that
the usual relativistic (zero thickness) string theory can arise at strong 't
Hooft coupling, at best yielding a highly idealized description, which fails to
incorporate such salient features of continuum QCD as asymptotic freedom and
point-like constituents. The recently conjectured AdS/CFT correspondence is
compatible with such limitations because it also gives a simple picture of
large N_c gauge theory only at strong coupling. In order to better understand
how string theory could emerge from large N_c QCD at strong coupling, Klaus
Bering, Joel Rozowsky, and I have developed an improved implementation of my
effort of the late seventies to digitize the planar diagrams of large N_c
light-cone quantized QCD by discretizing both P+ and x+. This discretization
allows a strong coupling limit of the sum of planar diagrams to be defined and
studied. It also provides a natural framework to explore the possible dual
relationship between QCD in light-cone gauge and string theory quantized on the
light-cone. |
Boundary states in the open string channel and CFT near a corner: We generalize the idea of boundary states to the open string channel. They
describe emission and absorption of open strings in the presence of
intersecting D-branes. We construct the explicit oscillator representation for
the free boson and fermionic ghost. The inner product of such states describes
a disk amplitude of rectangular shape and possesses modular covariance with a
nontrivial conformal weight. We compare the result obtained here with those
obtained using two different methods, one employing the path integral formalism
and one employing the conformal anomaly. We find that all these methods give
consistent results. In our method, we must be careful in our treatment of the
singularity of the CFT near the corners. Specifically, we derive the correction
to the conformal weight of the primary field inserted at the corner, and it
gives the modular weight of the rectangle amplitude. We also carry out explicit
computations of the correlation functions. | Off-Shell N=2 Linear Multiplets in Five Dimensions: We present a superconformal tensor calculus for an arbitrary number of five
dimensional N=2 linear multiplets. We also demonstrate how to construct higher
derivative invariants and higher order supersymmetric off-diagonal models.
Finally, we show the procedure required for the derivation of the
supersymmetric completion of the non-Abelian $F^4$ action. |
The finiteness of the four dimensional antisymmetric tensor field model
in a curved background: A renormalizable rigid supersymmetry for the four dimensional antisymmetric
tensor field model in a curved space-time background is constructed. A closed
algebra between the BRS and the supersymmetry operators is only realizable if
the vector parameter of the supersymmetry is a covariantly constant vector
field. This also guarantees that the corresponding transformations lead to a
genuine symmetry of the model. The proof of the ultraviolet finiteness to all
orders of perturbation theory is performed in a pure algebraic manner by using
the rigid supersymmetry. | Temperature dependence of the anomalous effective action of fermions in
two and four dimensions: The temperature dependence of the anomalous sector of the effective action of
fermions coupled to external gauge and pseudo-scalar fields is computed at
leading order in an expansion in the number of Lorentz indices in two and four
dimensions. The calculation preserves chiral symmetry and confirms that a
temperature dependence is compatible with axial anomaly saturation. The result
checks soft-pions theorems at zero temperature as well as recent results in the
literature for the pionic decay amplitude into static photons in the chirally
symmetric phase. The case of chiral fermions is also considered. |
Noncommutative Scalar Quasinormal Modes of the Reissner Nordström
Black Hole: Aiming to search for a signal of space-time noncommutativity, we study a
quasinormal mode spectrum of the Reissner Nordstr\"om black hole in the
presence of a deformed space-time structure. In this context we study a
noncommutative (NC) deformation of a scalar field, minimally coupled to a
classical Reissner Nordstr\"om background. Our model is thus semiclassical from
the beginning and scalar field is in addition minimally coupled to U(1) gauge
field. The deformation is performed via particularly chosen Killing twist to
yield a geometrical form of the action, which maintains the diffeomorphism
invariance manifest, as well as the invariance under a deformed gauge symmetry
group. We find the quasinormal mode solutions of the equations of motion
governing the matter content of the model in some particular range of system
parameters which corresponds to a near extremal limit. In addition, we obtain a
well defined analytical condition which allows for a detailed numerical
analysis. Moreover, there exists a parameter range, rather restrictive though,
which allows for obtaining a QNM spectrum in a closed analytic form. We also
argue within a semiclassical approach that NC deformation does not affect the
Hawking temperature of thermal radiation. | Scalar Quantum Field Theory in Disordered Media: A free massive scalar field in inhomogeneous random media is investigated.
The coefficients of the Klein-Gordon equation are taken to be random functions
of the spatial coordinates. The case of an annealed-like disordered medium,
modeled by centered stationary and Gaussian processes, is analyzed. After
performing the averages over the random functions, we obtain the two-point
causal Green's function of the model up to one-loop. The disordered scalar
quantum field theory becomes qualitatively similar to a $\lambda\phi^{4}$
self-interacting theory with a frequency-dependent coupling. |
Toward Construction of Exact Operator Solution of $A_N$-Toda Field
Theory: Quantum $A_N$-Toda field theory in two dimensions is investigated based on
the method of quantizing canonical free field. Toda exponential operator
associated with the fundamental weight $\lambda^1$ is constructed. | Conformal Scalar Propagation on the Schwarzschild Black-Hole Geometry: The vacuum activity generated by the curvature of the Schwarzschild
black-hole geometry close to the event horizon is studied for the case of a
massless, conformal scalar field. The associated approximation to the unknown,
exact propagator in the Hartle-Hawking vacuum state for small values of the
radial coordinate above $ r = 2M$ results in an analytic expression which
manifestly features its dependence on the background space-time geometry. This
approximation to the Hartle-Hawking scalar propagator on the Schwarzschild
black-hole geometry is, for that matter, distinct from all other. It is shown
that the stated approximation is valid for physical distances which range from
the event horizon to values which are orders of magnitude above the scale
within which quantum and backreaction effects are comparatively pronounced. An
expression is obtained for the renormalised $ <\phi^2(x)>$ in the
Hartle-Hawking vacuum state which reproduces the established results on the
event horizon and in that segment of the exterior geometry within which the
approximation is valid. In contrast to previous results the stated expression
has the superior feature of being entirely analytic. The effect of the
manifold's causal structure to scalar propagation is also studied. |
Poisson-Lie T-duality of String Effective Actions: A New Approach to the
Dilaton Puzzle: For a particular class of backgrounds, equations of motion for string sigma
models targeted in mutually dual Poisson-Lie groups are equivalent. This
phenomenon is called the Poisson-Lie T-duality. On the level of the
corresponding string effective actions, the situation becomes more complicated
due to the presence of the dilaton field.
A novel approach to this problem using Levi-Civita connections on Courant
algebroids is presented. After the introduction of necessary geometrical tools,
formulas for the Poisson-Lie T-dual dilaton fields are derived. This provides a
version of Poisson-Lie T-duality for string effective actions. | A note on the existence of soliton solutions in the Chern-Simons-CP(1)
model: We study a gauged Chern-Simons-CP(1) system. We show that contrary to
previous claims the model in the absences of a potential term cannot support
finite size soliton solution in $R^2$. |
The unequal mass sunrise integral expressed through iterated integrals
on $\overline{\mathcal M}_{1,3}$: We solve the two-loop sunrise integral with unequal masses systematically to
all orders in the dimensional regularisation parameter $\varepsilon$. In order
to do so, we transform the system of differential equations for the master
integrals to an $\varepsilon$-form. The sunrise integral with unequal masses
depends on three kinematical variables. We perform a change of variables to
standard coordinates on the moduli space ${\mathcal M}_{1,3}$ of a genus one
Riemann surface with three marked points. This gives us the solution as
iterated integrals on $\overline{\mathcal M}_{1,3}$. On the hypersurface
$\tau=\mbox{const}$ our result reduces to elliptic polylogarithms. In the equal
mass case our result reduces to iterated integrals of modular forms. | On massive higher spin supermultiplets in d=3: In this paper, using a frame-like gauge invariant formulation of the massive
higher spin bosons and fermions, we develop a direct construction of the
completely off-shell cubic vertices describing an interaction of the massless
gravitino with the massive higher spin supermultiplets. To achieve the
invariance under the local supersymmetry we introduce all necessary
supertransformations (both for the physical as well as for the auxiliary
fields) and thus all the supercurrents constructed are conserved on-shell. As
an illustration of the technique used we present some lower superspin examples
and then we consider the arbitrary superspin. We also check that the whole
construction is completely consistent with all bosonic and fermionic gauge
symmetries of the fields entering the supermultiplets. |
Geometrically Constrained Localized Configurations: First-Order
Framework and Analytical Solutions: This work deals with the presence of topological structures in models of two
real scalar fields in the two-dimensional spacetime. The subject concerns the
presence of a geometric constriction, which appears with a modification of the
kinetic term of one of the two fields. We elaborate on the construction of a
first-order framework, which directly contributes to find analytical solutions.
We describe several distinct possibilities, in particular, the case where the
first-order equations do not separate. This is much harder, but we use the
integrating factor to deal with analytical configurations. The proposed
methodology help us deal with localized structures of both the N\'eel and Bloch
type very naturally, and we end the work suggesting some possibilities of
applications in distinct areas of nonlinear science. | Antibracket as the Hamiltonian Structure of a classical integrable
system: The time evolution in a supersymmetric extension of the
Kodomtsev-Petviashvilli hierarchy, a classical integrable system, is shown to
be Hamiltonian. The canonical bracket associated to the Hamiltonian evolution
is the classical analog of the antibracket encountered in the quantization of
gauge theories. This provides a new understanding of supersymmetric Hamiltonian
systems. |
Twistor Space Structure of the Box Coefficients of N=1 One-loop
Amplitudes: We examine the coefficients of the box functions in N=1 supersymmetric
one-loop amplitudes. We present the box coefficients for all six point N=1
amplitudes and certain all $n$ example coefficients. We find for ``next-to
MHV'' amplitudes that these box coefficients have coplanar support in twistor
space. | Planes, branes and automorphisms: I. Static branes: This is the first of a series of papers devoted to the group-theoretical
analysis of the conditions which must be satisfied for a configuration of
intersecting M5-branes to be supersymmetric. In this paper we treat the case of
static branes. We start by associating (a maximal torus of) a different
subgroup of Spin(10) with each of the equivalence classes of supersymmetric
configurations of two M5-branes at angles found by Ohta & Townsend. We then
consider configurations of more than two intersecting branes. Such a
configuration will be supersymmetric if and only if the branes are G-related,
where G is a subgroup of Spin(10) contained in the isotropy of a spinor. For
each such group we determine (a lower bound for) the fraction of the
supersymmetry which is preserved. We give examples of configurations consisting
of an arbitrary number of non-coincident intersecting fivebranes with
fractions: 1/32, 1/16, 3/32, 1/8, 5/32, 3/16 and 1/4, and we determine the
resulting (calibrated) geometry. |
Trans-Planckian censorship constraints on properties and cosmological
applications of axion-like fields: We use the Trans-Planckian Censorship Conjecture (TCC) to constrain the decay
constants $f$ characterizing a set of N identical axion-like fields with cosine
potentials, improving upon the precision of other Swampland conjectures and
existing string-theoretic arguments. We find that consistency with the TCC
requires any such set of axion-like fields to satisfy $f\sqrt{N} \lesssim
0.6M_{pl}$, where $M_{pl}$ is the reduced Planck mass. We show that this bound
makes models of axion-driven inflation incapable of simultaneously producing
the required number of e-foldings and the observed scalar spectral tilt. In
contrast, we find that models of axion quintessence can be simultaneously
compatible with the TCC and observational data, provided that the axions'
initial field values are set near the maxima of their potentials to within
roughly $\pm \frac{\pi}{5}f$. | One-loop Amplitudes in Six-Dimensional (1,1) Theories from Generalised
Unitarity: Recently, the spinor helicity formalism and on-shell superspace were
developed for six-dimensional gauge theories with (1,1) supersymmetry. We
combine these two techniques with (generalised) unitarity, which is a powerful
technique to calculate scattering amplitudes in any massless theory. As an
application we calculate one-loop superamplitudes with four and five external
particles in the (1,1) theory and perform several consistency checks on our
results. |
Lagrangian Formulation of an Infinite Derivative Real Scalar Field
Theory in the Framework of the Covariant Kempf-Mangano Algebra in a
$(D+1)$-dimensional Minkowski Space-time: In 2017, G. P. de Brito and co-workers suggested a covariant generalization
of the Kempf-Mangano algebra in a $(D+1)$-dimensional Minkowski space-time [A.
Kempf and G. Mangano, Phys. Rev. D \textbf{55}, 7909 (1997); G. P. de Brito, P.
I. C. Caneda, Y. M. P. Gomes, J. T. Guaitolini Junior, and V. Nikoofard, Adv.
High Energy Phys. \textbf{2017}, 4768341 (2017)]. It is shown that
reformulation of a real scalar field theory from the viewpoint of the covariant
Kempf-Mangano algebra leads to an infinite derivative Klein-Gordon wave
equation which describes two bosonic particles in the free space (a usual
particle and a ghostlike particle). We show that in the low-energy
(large-distance) limit our infinite derivative scalar field theory behaves like
a Pais-Uhlenbeck oscillator for a spatially homogeneous field configuration
$\phi(t,\vec{\textbf{x}})=\phi(t)$. Our calculations show that there is a
characteristic length scale $\delta$ in our model whose upper limit in a
four-dimensional Minkowski space-time is close to the nuclear scalar, i.e.,
$\delta_{max}\sim \delta_{nuclear\ scale}\sim 10^{-15}\, m$. Finally, we show
that there is an equivalence between a non-local real scalar field theory with
a non-local form factor ${\cal K}(x-y)=
-\frac{\square_x}{(1-\frac{\delta^2}{2}\square_x)^2} \ \delta^{(D+1)}(x-y)$ and
an infinite derivative real scalar field theory from the viewpoint of the
covariant Kempf-Mangano algebra. | The Ising model with a boundary magnetic field on a random surface: The bulk and boundary magnetizations are calculated for the critical Ising
model on a randomly triangulated disk in the presence of a boundary magnetic
field h. In the continuum limit this model corresponds to a c = 1/2 conformal
field theory coupled to 2D quantum gravity, with a boundary term breaking
conformal invariance. It is found that as h increases, the average
magnetization of a bulk spin decreases, an effect that is explained in terms of
fluctuations of the geometry. By introducing an $h$-dependent rescaling factor,
the disk partition function and bulk magnetization can be expressed as
functions of an effective boundary length and bulk area with no further
dependence on h, except that the bulk magnetization is discontinuous and
vanishes at h = 0. These results suggest that just as in flat space, the
boundary field generates a renormalization group flow towards h = \infty. An
exact analytic expression for the boundary magnetization as a function of $h$
is linear near h = 0, leading to a finite nonzero magnetic susceptibility at
the critical temperature. |
E_{7(7)} Duality, BPS Black-Hole Evolution and Fixed Scalars: We study the general equations determining BPS Black Holes by using a
Solvable Lie Algebra representation for the homogenous scalar manifold U/H of
extended supergravity. In particular we focus on the N=8 case and we perform a
general group theoretical analysis of the Killing spinor equation enforcing the
BPS condition. Its solutions parametrize the U-duality orbits of BPS solutions
that are characterized by having 40 of the 70 scalars fixed to constant values.
These scalars belong to hypermultiplets in the N=2 decomposition of the N=8
theory. Indeed it is shown that those decompositions of the Solvable Lie
algebra into appropriate subalgebras which are enforced by the existence of BPS
black holes are the same that single out consistent truncations of the N=8
theory to intereacting theories with lower supersymmetry. As an exemplification
of the method we consider the simplified case where the only non-zero fields
are in the Cartan subalgebra H of Solv(U/H) and correspond to the radii of
string toroidal compactification. Here we derive and solve the mixed system of
first and second order non linear differential equations obeyed by the metric
and by the scalar fields. So doing we retrieve the generating solutions of
heterotic black holes with two charges. Finally, we show that the general N=8
generating solution is based on the 6 dimensional solvable subalgebra Solv
[(SL(2,\IR) /U(1))^3]. | Dilaton field induces commutative Dp-brane coordinate: It is well known that space-time coordinates and corresponding Dp-brane
world-volume become non-commutative, if open string ends on Dp-brane with
Neveu-Schwarz background field $B_{\mu \nu}$. In this paper we extend these
considerations including the dilaton field $\Phi$, linear in coordinates
$x^\mu$. In that case the conformal part of the world-sheet metric appears as
new non-commutative variable and the coordinate in direction orthogonal to the
hyper plane $\Phi = const$, becomes commutative. |
Null Brane Intersections: We study pairs of planar D-branes intersecting on null hypersurfaces, and
other related configurations. These are supersymmetric and have finite energy
density. They provide open-string analogues of the parabolic orbifold and
null-fluxbrane backgrounds for closed superstrings. We derive the spectrum of
open strings, showing in particular that if the D-branes are shifted in a
spectator dimension so that they do not intersect, the open strings joining
them have no asymptotic states. As a result, a single non-BPS excitation can in
this case catalyze a condensation of massless modes, changing significantly the
underlying supersymmetric vacuum state. We argue that a similar phenomenon can
modify the null cosmological singularity of the time-dependent orbifolds. This
is a stringy mechanism, distinct from black-hole formation and other strong
gravitational instabilities, and one that should dominate at weak string
coupling. A by-product of our analysis is a new understanding of the appearance
of 1/4 BPS threshold bound states, at special points in the moduli space of
toroidally-compactified type-II string theory. | Spontaneous symmetry breaking and gravity: Gravity is usually considered to be irrelevant as far as the physics of
elementary particles is concerned and, in particular, in the context of the
spontaneous symmetry breaking (SSB) mechanism. We describe a version of the SSB
mechanism in which gravity plays a direct role. We work in the context of
diffeomorphism invariant gauge theories, which exist for any non-abelian gauge
group G, and which have second order in derivatives field equations. We show
that any (non-trivial) vacuum solution of such a theory gives rise to an
embedding of the group SU(2) into G, and thus breaks G down to SU(2) times its
centralizer in G. The components of the connection charged under SU(2) can then
be seen to describe gravitons, with the SU(2) itself playing the role of the
chiral half of the Lorentz group. Components charged under the centralizer
describe the usual Yang-Mills gauge bosons. The remaining components describe
massive particles. This breaking of symmetry explains (in the context of models
considered) how gravity and Yang-Mills can come from a single underlying theory
while being so different in the physics they describe. Further, varying the
vacuum solution, and thus the embedding of SU(2) into G, one can break the
Yang-Mills gauge group as desired, with massless gauge bosons of one vacuum
acquiring mass in another. There is no Higgs field in our version of the SSB
mechanism, the only variable is a connection field. Instead of the symmetry
breaking by a dedicated Higgs field pointing in some direction in the field
space, our theories break the symmetry by choosing how the group of "internal"
gauge rotations of gravity (the chiral half of the Lorentz group) sits inside
the full gauge group. |
Top-Down Holographic $G$-Structure Glueball Spectroscopy at (N)LO in $N$
and Finite Gauge Coupling: The top-down type IIB holographic dual of large-$N$ thermal QCD as
constructed in arXiv:0902.1540 involving a fluxed resolved warped deformed
conifold, its delocalized type IIA SYZ mirror as well as its M-theory uplift
constructed in arXiv:1306.4339 - both in the finite gauge coupling
($g_s\stackrel{<}{\sim}1$)/`MQGP' limit of arXiv:1306.4339 - were shown
explicitly to possess a local $SU(3)/G_2$-structure in arXiv:1507.02692
Glueball spectroscopy at finite gauge coupling has thus far been missing in the
literature. In this paper, we fill this gap by calculating the masses of the
$0^{++}, 0^{-+},0^{--}, 1^{++}, 2^{++}$ (`glueball') states (which correspond
to fluctuations in the dilaton or complexified two-forms or appropriate metric
components) in the aforementioned backgrounds of $G$-structure in the `MQGP'
limit of arXiv:1306.4339, using WKB quantization conditions on one hand and
imposing Neumann/Dirichlet boundary conditions at an IR cut-off/horizon radius
$r_h$ on the solutions to the equations of motion on the other. We also discuss
$r_h=0$-limits of all calculations; in this context we also calculate the
$0^{++}, 0^{--},1^{++}, 2^{++}$ glueball masses up to NLO in $N$ and find a
$\frac{g_sM^2}{N}(g_sN_f)$-suppression similar to and further validating a
similar semi-universality of NLO corrections to transport coefficients,
observed in arXiv:1606.04949. | Relativistic Green functions in a plane wave gravitational background: We consider a massive relativistic particle in the background of a
gravitational plane wave. The corresponding Green functions for both spinless
and spin 1/2 cases, previously computed by A. Barducci and R. Giachetti
\cite{Barducci3}, are reobtained here by alternative methods, as for example,
the Fock-Schwinger proper-time method and the algebraic method. In analogy to
the electromagnetic case, we show that for a gravitational plane wave
background a semiclassical approach is also sufficient to provide the exact
result, though the lagrangian involved is far from being a quadratic one. |
Repulsive Black Holes and Higher-Derivatives: In two-derivative theories of gravity coupled to matter, charged black holes
are self-attractive at large distances, with the force vanishing at zero
temperature. However, in the presence of massless scalar fields and
four-derivative corrections, zero-temperature black holes no longer need to
obey the no-force condition. In this paper, we show how to calculate the
long-range force between such black holes. We develop an efficient method for
computing the higher-derivative corrections to the scalar charges when the
two-derivative theory has a shift symmetry, and compute the resulting force in
a variety of examples. We find that higher-derivative corrected black holes may
be self-attractive or self-repulsive, depending on the value of the Wilson
coefficients and the VEVs of scalar moduli. Indeed, we find black hole
solutions which are both superextremal and self-attractive. Furthermore, we
present examples where no choice of higher-derivative coefficients allows for
self-repulsive black hole states in all directions in charge space. This
suggests that, unlike the Weak Gravity Conjecture, which may be satisfied by
the black hole spectrum alone, the Repulsive Force Conjecture requires
additional constraints on the spectrum of charged particles. | Singleton deformation of higher-spin theory and the phase structure of
the three-dimensional O(N) vector model: We consider a singleton deformation of the AdS4 higher-spin theory dual to
the three-dimensional O(N) vector model. The singleton couples to the
higher-spin multiplet only through a marginal boundary interaction. We argue
that the effect of such a deformation is to shift N to N+1 in both sides of the
holographic correspondance and we show how the gap equations of the
three-dimensional O(N) vector model arise from the higher-spin theory. The
singleton deformation breaks higher-spin symmetry and gives rise to the
well-known 1/N anomalous dimensions of the boundary theory. |
Causal perturbation theory in terms of retarded products, and a proof of
the Action Ward Identity: In the framework of perturbative algebraic quantum field theory a local
construction of interacting fields in terms of retarded products is performed,
based on earlier work of Steinmann. In our formalism the entries of the
retarded products are local functionals of the off shell classical fields, and
we prove that the interacting fields depend only on the action and not on terms
in the Lagrangian which are total derivatives, thus providing a proof of
Stora's 'Action Ward Identity'. The theory depends on free parameters which
flow under the renormalization group. This flow can be derived in our local
framework independently of the infrared behavior, as was first established by
Hollands and Wald. We explicitly compute non-trivial examples for the
renormalization of the interaction and the field. | On the Global Structure of Some Natural Fibrations of Joyce Manifolds: The study of fibrations of the target manifolds of string/M/F-theories has
provided many insights to the dualities among these theories or even as a tool
to build up dualities since the work of Strominger, Yau, and Zaslow on the
Calabi-Yau case. For M-theory compactified on a Joyce manifold $M^7$, the fact
that $M^7$ is constructed via a generalized Kummer construction on a 7-torus
${\smallBbb T}^7$ with a torsion-free $G_2$-structure $\phi$ suggests that
there are natural fibrations of $M^7$ by ${\smallBbb T}^3$, ${\smallBbb T}^4$,
and K3 surfaces in a way governed by $\phi$. The local picture of some of these
fibrations and their roles in dualities between string/M-theory have been
studied intensively in the work of Acharya. In this present work, we explain
how one can understand their global and topological details in terms of bundles
over orbifolds. After the essential background is provided in Sec. 1, we give
general discussions in Sec. 2 about these fibrations, their generic and
exceptional fibers, their monodromy, and the base orbifolds. Based on these,
one obtains a 5-step-routine to understand the fibrations, which we illustrate
by examples in Sec. 3. In Sec. 4, we turn to another kind of fibrations for
Joyce manifolds, namely the fibrations by the Calabi-Yau threefolds constructed
by Borcea and Voisin. All these fibrations arise freely and naturally from the
work of Joyce. Understanding how the global structure of these fibrations may
play roles in string/M-theory duality is one of the major issues for further
pursuit. |
Converting a series in λto a series in λ^{-1}: We introduce a transformation for converting a series in a parameter,
\lambda, to a series in the inverse of the parameter \lambda^{-1}. By applying
the transform on simple examples, it becomes apparent that there exist
relations between convergent and divergent series, and also between large- and
small-coupling expansions. The method is also applied to the divergent series
expansion of Euler-Heisenberg-Schwinger result for the one-loop effective
action for constant background magnetic (or electric) field. The transform may
help us gain some insight about the nature of both divergent (Borel or
non-Borel summable series) and convergent series and their relationship, and
how both could be used for analytical and numerical calculations. | Coset Construction of Noncompact Spin(7) and G_2 CFTs: We provide a new class of exactly solvable superconformal field theories that
corresponds to type II compactification on manifolds with exceptional
holonomies. We combine N=1 Liouville field and N=1 coset models and construct
modular invariant partition functions of strings moving on these manifolds. The
resulting theories preserve spacetime supersymmetry. Also we explicitly
construct chiral currents in these models to realize consistent string
theories. |
Strings and branes with a modified measure: In string theory, the consequences of replacing the measure of integration
$\sqrt{-\gamma}d^2 x$ in the Polyakov's action by $\Phi d^2 x$ where $\Phi$ is
a density built out of degrees of freedom independent of the metric
$\gamma_{ab}$ defined in the string are studied. The string tension appears as
an integration constant of the equations of motion. The string tension can
change in different parts of the string due to the coupling of gauge fields and
point particles living in the string. The generalization to higher dimensional
extended objects is also studied. In this case there is no need of a fine tuned
cosmological term, in sharp contrast to the standard formulation of the
generalized Polyakov action for higher dimensional branes. | Probing crunching AdS cosmologies: Holographic gravity duals of deformations of CFTs formulated on de Sitter
spacetime contain FRW geometries behind a horizon, with cosmological big crunch
singularities. Using a specific analytically tractable solution within a
particular single scalar truncation of N=8 supergravity on AdS_4, we first
probe such crunching cosmologies with spacelike radial geodesics that compute
spatially antipodal correlators of large dimension boundary operators. At late
times, the geodesics lie on the FRW slice of maximal expansion behind the
horizon. The late time two-point functions factorise, and when transformed to
the Einstein static universe, they exhibit a temporal non-analyticity
determined by the maximal value of the scale factor a_{max} . Radial geodesics
connecting antipodal points necessarily have de Sitter energy E \leq a_{max},
while geodesics with E > a_{max} terminate at the crunch, the two categories of
geodesics being separated by the maximal expansion slice. The spacelike crunch
singularity is curved "outward" in the Penrose diagram for the deformed AdS
backgrounds, and thus geodesic limits of the antipodal correlators do not
directly probe the crunch. Beyond the geodesic limit, we point out that the
scalar wave equation, analytically continued into the FRW patch, has a
potential which is singular at the crunch along with complex WKB turning points
in the vicinity of the FRW crunch. We then argue that the frequency space
Green's function has a branch point determined by a_{max} which corresponds to
the lowest quasinormal frequency. |
Asymptotically spacelike warped anti-de Sitter spacetimes in generalized
minimal massive gravity: In this paper we show that warped AdS$_{3}$ black hole spacetime is a
solution of the generalized minimal massive gravity (GMMG) and introduce
suitable boundary conditions for asymptotically warped AdS$_{3}$ spacetimes.
Then we find the Killing vector fields such that transformations generated by
them preserve the considered boundary conditions. We calculate the conserved
charges which correspond to the obtained Killing vector fields and show that
the algebra of the asymptotic conserved charges is given as the semi direct
product of the Virasoro algebra with $U(1)$ current algebra. We use a
particular Sugawara construction to reconstruct the conformal algebra. Thus, we
are allowed to use the Cardy formula to calculate the entropy of the warped
black hole. We demonstrate that the gravitational entropy of the warped black
hole exactly coincide with what we obtain via Cardy's formula. As we expect the
warped Cardy formula also give us exactly the same result which we obtain from
usual Cardy's formula. We calculate mass and angular momentum of the warped
black and then check that obtained mass, angular momentum and entropy satisfy
first law of the black hole mechanics. According to the results of this paper
we belief that the dual theory of the warped AdS$_{3}$ black hole solution of
GMMG is a Warped CFT. | Crosstalk between DGP branes: If two DGP branes carry U(1) gauge theories and overlap, particles of one
brane can interact with the photons from the other brane. This coupling
modifies in particular the Coulomb potentials between charges from the same
brane in the overlapping regions. The coupling also introduces Coulomb
interactions between charges from the different branes which can generate
exotic bound states.
The effective modification of the fine structure constant in the overlap
region generates a trough in signals at the redshift of the overlap region and
an increase at smaller or larger redshift, depending on the value of the
crosstalk parameter. This implies potentially observable perturbations in the
Lyman-alpha forest if our 3-brane overlapped with another 3-brane in a region
with redshift z<6. Crosstalk can also affect structure formation by enhancing
or suppressing radiative cooling. |
Pre-Big-Bang Requires the Universe to be Exponentially Large From the
Very Beginning: We show that in a generic case of the pre-big-bang scenario, inflation will
solve cosmological problems only if the universe at the onset of inflation is
extremely large and homogeneous from the very beginning. The size of a
homogeneous part of the universe at the beginning of the stage of pre-big-bang
(PBB) inflation must be greater than $10^{19}$ $l_s$, where $l_s$ is the
stringy length. The total mass of an inflationary domain must be greater than
$10^{72} M_{s}$, where $M_{s} \sim l_s^{-1}$. If the universe is initially
radiation dominated, then its total entropy at that time must be greater than
$10^{68}$. If the universe is closed, then at the moment of its formation it
must be uniform over $10^{24}$ causally disconnected domains. The natural
duration of the PBB stage in this scenario is $M_p^{-1}$. We argue that the
initial state of the open PBB universe could not be homogeneous because of
quantum fluctuations. Independently of the issue of homogeneity, one must
introduce two large dimensionless parameters, $g_0^{-2} > 10^{53}$, and $B >
10^{91}$, in order to solve the flatness problem in the PBB cosmology. A regime
of eternal inflation does not occur in the PBB scenario. This should be
compared with the simplest versions of the chaotic inflation scenario, where
the regime of eternal inflation may begin in a universe of size $O(M_{p}^{-1})$
with vanishing initial radiation entropy, mass $O(M_p)$, and geometric entropy
O(1). We conclude that the current version of the PBB scenario cannot replace
usual inflation even if one solves the graceful exit problem in this scenario. | Supersymmetries and Hopf-duality in the Penrose Limit of AdS_3 times S^3
times T^4: We investigate various aspects of the plane wave geometries obtained from
D1/D5-brane system. We study the effect of Hopf-duality on the supersymmetries
preserved by the Penrose limit of $AdS_3\times S^3\times T^4$ geometry. In
type-IIB case, we first show that the Penrose limit makes the size of the
`would-be' internal torus comparable to that of the other directions. Based on
this observation, we consider, in taking the Penrose limit, the generalization
of the null geodesic to incorporate the tilted direction between the equator of
$S^3$ and one of the torus directions. For generic values of the tilting angle,
supersymmetries are not preserved. When the limit is taken along the torus
direction, 16 supersymmetries are preserved. For the ordinary Penrose limit, 16
generic and 8 `supernumerary' supersymmetries are observed. In the Penrose
limit of Hopf-dualized type-IIA geometry, only 4 supersymmetries are preserved.
We classify all the Killing spinors according to their periodic properties
along some relevant coordinates. |
Irreducible Freedman-Townsend vertex and Hamiltonian BRST cohomology: The irreducible Freedman-Townsend vertex is derived by means of the
Hamiltonian deformation procedure based on local BRST cohomology. | Comments on F-maximization and R-symmetry in 3D SCFTs: We report preliminary results on the recently proposed F-maximization
principle in 3D SCFTs. We compute numerically in the large-N limit the free
energy on the three-sphere of an N=2 Chern-Simons-Matter theory with a single
adjoint chiral superfield which is known to exhibit a pattern of accidental
symmetries associated to chiral superfields that hit the unitarity bound and
become free. We observe that the F-maximization principle produces a U(1)
R-symmetry consistent with previously obtained bounds but inconsistent with a
postulated Seiberg-like duality. Potential modifications of the principle
associated to the decoupling fields do not appear to be sufficient to account
for the observed violations. |
Conservation and Integrability in TMG: In this work, following the paper by Romain Ruzziconi and C\'eline Zwikel
\cite{Ruzziconi:2020wrb} we extend the questions of conservation, integrability
and renormalization in Bondi gauge and in GR to the theory of Topological
Massive Gravity (TMG). We construct the phase space and renormalize the
divergences arising within the symplectic structure through a holographic
renormalization procedure. We show that the charge expressions are generically
finite, conserved and can be made integrable by a field$-$dependent
redefinition of the asymptotic symmetry parameters. | Affine Algebras, $N{=}2$ Superconformal Algebras, and Gauged WZNW Models: We find a canonical $N{=}2$ superconformal algebra (SCA) in the BRST complex
associated to any affine Lie algebra $\hat{\mathbf{h}}$ with $\mathbf{h}$
semisimple. In contrast with the similar known results for the Virasoro,
$N{=}1$ supervirasoro, and $W_3$ algebras, this SCA does not depend on the
particular "matter" representation chosen. Therefore it follows that every
gauged WZNW model with data $(\mathbf{g}\supset\mathbf{h}, k)$ has an $N{=}2$
SCA with central charge $c=3\dim\mathbf{g}$ independent of the level $k$. In
particular, this associates to every embedding $sl(2) \subset \mathbf{g}$ a
one-parameter family of $c{=}9$ $N{=}2$ supervirasoro algebras. As a by-product
of the construction, one can deduce a new set of "master equations" for
generalized $N{=}2$ supervirasoro constructions which is simpler than the one
considered thus far. |
Structures on the Conformal Manifold in Six Dimensional Theories: The tensors which may be defined on the conformal manifold for six
dimensional CFTs with exactly marginal operators are analysed by considering
the response to a Weyl rescaling of the metric in the presence of local
couplings. It is shown that there are three symmetric two index tensors only
one of which satisfies any positivity conditions. The general results are
specialised to the six dimensional conformal theory defined by free two-forms
and also to the interacting scalar $\phi^3$ theory at two loops which preserves
conformal invariance to this order. All three two index tensor contributions
are present. | The Casimir energy for two-dimensional deformed sphere: We compute the Casimir energy for a free scalar field on the spaces
$\,R^{m+1}\,\times\,\tilde S^2\,$ where $,\tilde S^2\,$ is two-dimensional
deformed two-sphere. |
Strings in Ramond-Ramond Backgrounds from the Neveu-Schwarz-Ramond
Formalism: We treat RR flux backgrounds of type II string theory in the framework of
closed superstring field theory based on the NSR formalism, focusing on two
examples: (1) the pp-wave background supported by 5-form flux, and (2)
$AdS_3\times S^3\times M_4$ supported by mixed 3-form fluxes. In both cases, we
analyze the classical string field solution perturbatively, and compute the
correction to the dispersion relation of string states to quadratic order in
the RR flux. In the first example, our result is in a delicate way consistent
with that obtained from lightcone quantization of the Green-Schwarz string. In
the second example, we will obtain numerically the mass corrections to
pulsating type IIB strings in $AdS_3\times S^3\times M_4$. Our results, valid
at finite $AdS$ radius, agree with previously known answers in the
semiclassical limit and in the BMN limit respectively. | The W_N minimal model classification: We first rigourously establish, for any N, that the toroidal modular
invariant partition functions for the (not necessarily unitary) W_N(p,q)
minimal models biject onto a well-defined subset of those of the SU(N)xSU(N)
Wess-Zumino-Witten theories at level (p-N,q-N). This permits considerable
simplifications to the proof of the Cappelli-Itzykson-Zuber classification of
Virasoro minimal models. More important, we obtain from this the complete
classification of all modular invariants for the W_3(p,q) minimal models. All
should be realised by rational conformal field theories. Previously, only those
for the unitary models, i.e. W_3(p,p+1), were classified. For all N our
correspondence yields for free an extensive list of W_N(p,q) modular
invariants. The W_3 modular invariants, like the Virasoro minimal models, all
factorise into SU(3) modular invariants, but this fails in general for larger
N. We also classify the SU(3)xSU(3) modular invariants, and find there a new
infinite series of exceptionals. |
Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver
Gauge Theories: We study the connection between N = 2 supersymmetric gauge theories, quantum
cohomology and quantum integrable systems of hydrodynamic type. We consider
gauge theories on ALE spaces of A and D-type and discuss how they describe the
quantum cohomology of the corresponding Nakajima's quiver varieties. We also
discuss how the exact evaluation of local BPS observables in the gauge theory
can be used to calculate the spectrum of quantum Hamiltonians of spin Calogero
integrable systems and spin Intermediate Long Wave hydrodynamics. This is
explicitly obtained by a Bethe Ansatz Equation provided by the quiver gauge
theory in terms of its adjacency matrix. | Micrometer Gravitinos and the Cosmological Constant: We compute the 4--dimensional cosmological constant in string
compactifications in which the Standard Model fields live on a
non-supersymmetric brane inside a supersymmetric bulk. The cosmological
constant receives contributions only from the vacuum energy of the bulk
supergravity fields, but not from the vacuum energy of the brane fields. The
latter is absorbed in a warp factor. Supersymmetry breaking on the brane at the
TeV scale implies supersymmetry breaking in the bulk at the micrometer scale.
This produces a tiny cosmological constant that agrees with experiment within a
few orders of magnitude. Our argument predicts superpartners of the graviton
with mass of order $10^{-3}$ eV. They should be observable in short-distance
tests of Einstein Gravity. |
A Superstring Theory in Four Curved Space-Time Dimensions: Neveu-Schwarz-Ramond type heterotic and type-II superstrings in four
dimensional curved space-time are constructed as exact $N=1$ superconformal
theories. The tachyon is eliminated with a GSO projection. The theory is based
on the N=1 superconformal gauged WZW model for the anti-de Sitter coset
$SO(3,2)/SO(3,1)$ with integer central extension $k=5$. The model has dynamical
duality properties in its space-time metric that are similar to the large-small
($R\rightarrow 1/R$) duality of tori. To first order in a $1/k$ expansion we
give expressions for the metric, the dilaton, the Ricci tensor and their dual
generalizations. The curvature scalar has several singularities at various
locations in the 4-dimensional manifold. This provides a new singular solution
to Einstein's equations in the presence of matter in four dimensions. A
non-trivial path integral measure which we conjectured in previous work for
gauged WZW models is verified. | Composite M-branes: We present new supersymmetric solutions of D=11 supergravity obtained by
intersecting the brane configuration interpreted as a 2-brane lying within a
5-brane. Some of these solutions can be boosted along a common string and/or
superposed with a Kaluza-Klein monopole. We also present a new embedding of the
extreme four dimensional dyonic black hole with finite horizon area. These
solutions are a consequence of a rather simple set of rules that allow us to
construct the composite M-branes. |
On the time-dependent description for the decay of unstable D-branes: We discuss how to describe time-dependent phenomena in string theory like the
decay of unstable D-branes with the help of the world-sheet formulation. It is
shown in a nontrivial well-controlled example that the coupling of the tachyons
to propagating on-shell modes which escape to infinity can lead to
time-dependent relaxation into a stationary final state. The final state
corresponds to a fixed point of the RG flow generated by the relevant field
from which the tachyon vertex operator is constructed. On the way we set up a
fairly general formalism for the description of slow time-dependent phenomena
with the help of conformal perturbation theory on the world-sheet. | Vertex Operators, $\mathbb{C}^3$ Curve and Topological Vertex: In this article, we prove the conjecture that Kodaira-Spencer theory for the
topological vertex is a free fermion theory. By dividing the $\mathbb{C}^3$
curve into core and asymptotic regions and using Boson-Fermion correspondence,
we construct a generic three-leg correlation function which reformulates the
topological vertex in a vertex operator approach. We propose a conjecture of
the correlation function identity which in a degenerate case becomes Zhou\rq{}s
identity for a Hopf link. |
Multifield Cosmological Perturbations at Third Order and the Ekpyrotic
Trispectrum: Using the covariant formalism, we derive the equations of motion for
adiabatic and entropy perturbations at third order in perturbation theory for
cosmological models involving two scalar fields. We use these equations to
calculate the trispectrum of ekpyrotic and cyclic models in which the density
perturbations are generated via the entropic mechanism. In these models, the
conversion of entropy into curvature perturbations occurs just before the big
bang, either during the ekpyrotic phase or during the subsequent kinetic energy
dominated phase. In both cases, we find that the non-linearity parameters
f_{NL} and g_{NL} combine to leave a very distinct observational imprint. | de Sitter space, extremal surfaces and "time-entanglement": We refine previous investigations on de Sitter space and extremal surfaces
anchored at the future boundary $I^+$. Since such surfaces do not return, they
require extra data or boundary conditions in the past (interior). In entirely
Lorentzian de Sitter spacetime, this leads to future-past timelike surfaces
stretching between $I^\pm$. Apart from an overall $-i$ factor (relative to
spacelike surfaces in $AdS$) their areas are real and positive. With a
no-boundary type boundary condition, the top half of these timelike surfaces
joins with a spacelike part on the hemisphere giving a complex-valued area.
Motivated by these, we describe two aspects of "time-entanglement" in simple
toy models in quantum mechanics. One is based on a future-past thermofield
double type state entangling timelike separated states, which leads to entirely
positive structures. Another is based on the time evolution operator and
reduced transition amplitudes, which leads to complex-valued entropy. |
Deep learning black hole metrics from shear viscosity: Based on AdS/CFT correspondence, we build a deep neural network to learn
black hole metrics from the complex frequency-dependent shear viscosity. The
network architecture provides a discretized representation of the holographic
renormalization group flow of the shear viscosity and can be applied to a large
class of strongly coupled field theories. Given the existence of the horizon
and guided by the smoothness of spacetime, we show that Schwarzschild and
Reissner-Nordstr\"{o}m metrics can be learned accurately. Moreover, we
illustrate that the generalization ability of the deep neural network can be
excellent, which indicates that by using the black hole spacetime as a hidden
data structure, a wide spectrum of the shear viscosity can be generated from a
narrow frequency range. These results are further generalized to an
Einstein-Maxwell-dilaton black hole. Our work might not only suggest a
data-driven way to study holographic transports but also shed some light on
holographic duality and deep learning. | AdS and pp-wave D-particle superalgebras: We derive anticommutators of supercharges with a brane charge for a
D-particle in AdS(2) x S(2) and pp-wave backgrounds. A coset GL(2|2)/(GL(1))^4
and its Penrose limit are used with the supermatrix-valued coordinates for the
AdS and the pp-wave spaces respectively. The brane charges have position
dependence, and can be absorbed into bosonic generators by shift of momenta
which results in closure of the superalgebras. |
Defining relations for W-algebras from singular vectors: It is shown that the commutation relations of W-algebras can be recovered
from the singular vectors of their simplest nontrivial, completely degenerate
highest weight representation. | Heterotic Complex Structure Moduli Stabilization for Elliptically
Fibered Calabi-Yau Manifolds: Complex structure moduli of a Calabi-Yau threefold in $N=1$ supersymmetric
heterotic compactifications can be stabilized by holomorphic vector bundles.
The stabilized moduli are determined by a computation of Atiyah class. In this
paper, we study how this mechanism work in the context of elliptically fibered
Calabi-Yau manifolds where complex structure moduli space contains two kinds of
moduli, ones from base and ones from fibration. With spectral cover bundles, we
find three types of situations when holomorphicity of bundles is determined by
algebraic cycles supported on special choice of complex structure, which allows
us to stabilize both of these two moduli. We present concrete examples for each
type and develop practical tools to analyze the stabilized moduli. Finally, by
checking the holomorphicity of the four-flux and/or local Higgs bundle data in
F-theory, we briefly study the dual complex structure moduli stabilization
scenarios. |
Demonstration of the Hayden-Preskill protocol via mutual information: We construct the Hayden-Preskill protocol by using a system of spin-1/2
particles and demonstrate information flows of this system which can mimic
black holes. We first define an analogous black hole $A$ as a collection of
such particles. Second, we take the particles from inside to outside the black
hole to define an analogous system of Hawking radiation $B$ as outside
particles. When the black hole and the radiation have the maximum entanglement
at the Page time, we take an entangled pair system $C$ and $D$. The particles
of $C$ fall into the black hole while their counterparts of $D$ remain outside.
If we assume rapid mixing of the particle states in the black hole $A \cup C$,
can the information of $C$ rapidly escape from the black hole like a mirror? We
numerically show that if we turn on the rapid mixing in the black hole, the
original information of $C$ rapidly escapes from the black hole to outside in
the form of the mutual information between $B$ and $D$. On the other hand, if
the mixing between $A$ and $C$ is not enough, the information escapes slowly.
Hence, we explicitly demonstrate the original conjecture of Hayden and
Preskill. We emphasize that enough mixing is an essential condition to make the
Hayden-Preskill protocol functionally work. | Quantum gravitational effects on boundary: Quantum gravitational effects may hold the key to some of the outstanding
problems in theoretical physics. In this work we analyze the perturbative
quantum effects on the boundary of a gravitational system and Dirichlet
boundary condtion imposed at the classical level. Our analysis reveals that for
a black hole solution there exists a clash between the quantum effects and
Dirichlet boundary condition: the solution of the one-particle-irreducible
(1PI) action no longer obeys the Dirichlet boundary condition. The analysis
also suggests that the violation of the Dirichlet boundary condition should be
tied with a certain mechanism of information storage on the boundary. |
Dynamical breakdown of time reversal invariance and causality: Irreversibility and acausality of a sub-system are established in exactly
soluble harmonic models with reversible and causal dynamics. It is shown that
initial conditions, imposed on some dynamical degrees of freedom may break time
reversal invariance for other degrees of freedom. This happens if observations
carried out in any large but finite amount of time can not resolve the spectrum
of the eliminated degrees of freedom, namely when the spectrum has a
condensation point at the ground state. Acausality follows due to the dominance
of the dynamics by almost time-independent modes. | Casimir effect in Very Special Relativity at finite temperature: Recently a great deal of interest in field theories formulated in a Lorentz
violating framework has been developed. Here the Very Special Relativity (VSR)
is considered. The main aspect in the VSR proposal is that laws of physics are
invariant under the subgroups of the Poincar\'e group preserving the basic
elements of special relativity. An important point is that the photon acquires
a mass. In this context, the energy-momentum tensor for the electromagnetic
field is calculated. From this, the Stefan-Boltzmann law and Casimir effect at
finite temperature in VSR are obtained. The effects of temperature are
introduced using the Thermo Field Dynamics (TFD) formalism. A comparative
analysis with the Casimir effect for the standard electromagnetic case is
developed. |
Vacuum polarization in a cosmic string spacetime induced by flat
boundary: In this paper we analyze the vacuum expectation values of the field squared
and the energy-momentum tensor associated to a massive scalar field in a higher
dimensional cosmic string spacetime, obeying Dirichlet or Neumann boundary
conditions on the surface orthogonal to the string. | Field spectrum and degrees of freedom in AdS/CFT correspondence and
Randall Sundrum model: Compactified AdS space can not be mapped into just one Poincare coordinate
chart. This implies that the bulk field spectrum is discrete despite the
infinite range of the coordinates. We discuss here why this discretization of
the field spectrum seems to be a necessary ingredient for the holographic
mapping. For the Randall Sundrum model we show that this discretization appears
even without the second brane. |
11D Supergravity on $AdS_4 \times S^7$ versus $AdS_7 \times S^4$: The maximally supersymmetric Freund-Rubin vacua for eleven dimensional
supergravity, namely $AdS_4 \times S^7$ and $AdS_7 \times S^4$, admit an
analytic continuation to $S^4 \times S^7$. From the full harmonic expansions on
$S^4 \times S^7$, it is shown that by analytical continuation to either
$AdS_4$, or to $AdS_7$, the detailed structure of the Kaluza-Klein spectrum can
be obtained for both vacua in a unified manner. The results are shown to be
related by a simple rule which interchanges the spacetime and internal space
representations. We also obtain the linearized field equations for the
singletons and doubletons but they can be gauged away by fixing certain
Stuckelberg shift symmetries inherited from the Kaluza-Klein reduction. | Two-Time Physics with gravitational and gauge field backgrounds: It is shown that all possible gravitational, gauge and other interactions
experienced by particles in ordinary d-dimensions (one-time) can be described
in the language of two-time physics in a spacetime with d+2 dimensions. This is
obtained by generalizing the worldline formulation of two-time physics by
including background fields. A given two-time model, with a fixed set of
background fields, can be gauged fixed from d+2 dimensions to (d-1) +1
dimensions to produce diverse one-time dynamical models, all of which are
dually related to each other under the underlying gauge symmetry of the unified
two-time theory. To satisfy the gauge symmetry of the two-time theory the
background fields must obey certain coupled differential equations that are
generally covariant and gauge invariant in the target d+2 dimensional
spacetime. The gravitational background obeys a null homothety condition while
the gauge field obeys a differential equation that generalizes a similar
equation derived by Dirac in 1936. Explicit solutions to these coupled
equations show that the usual gravitational, gauge, and other interactions in d
dimensions may be viewed as embedded in the higher d+2 dimensional space, thus
displaying higher spacetime symmetries that otherwise remain hidden. |
Classical-mechanical models without observable trajectories and the
Dirac electron: We construct a non-Grassmann spinning-particle model which, by analogy with
quantum mechanics, does not admit the notion of a trajectory within the
position space. The pseudo-classical character of the model allows us to avoid
the inconsistencies arising in the quantum-mechanical interpretation of a
one-particle sector of the Dirac equation. | Phantom Black Holes and Sigma Models: We construct static multicenter solutions of phantom Einstein-Maxwell-dilaton
theory from null geodesics of the target space, leading to regular black holes
without spatial symmetry for certain discrete values of the dilaton coupling
constant. We also discuss the three-dimensional gravitating sigma models
obtained by reduction of phantom Einstein-Maxwell, phantom Kaluza-Klein and
phantom Einstein-Maxwell-dilaton-axion theories. In each case, we generate by
group transformations phantom charged black hole solutions from a neutral seed. |
Holographic complexity of rotating black holes: Within the framework of the "complexity equals action" and "complexity equals
volume" conjectures, we study the properties of holographic complexity for
rotating black holes. We focus on a class of odd-dimensional equal-spinning
black holes for which considerable simplification occurs. We study the
complexity of formation, uncovering a direct connection between complexity of
formation and thermodynamic volume for large black holes. We consider also the
growth-rate of complexity, finding that at late-times the rate of growth
approaches a constant, but that Lloyd's bound is generically violated. | Spin(9) Average of SU(N) Matrix Models I. Hamiltonian: We apply a method of group averaging to states and operators appearing in
(truncations of) the Spin(9) x SU(N) invariant matrix models. We find that
there is an exact correspondence between the standard supersymmetric
Hamiltonian and the Spin(9) average of a relatively simple lower-dimensional
model. |
Optimal estimation of parameters for scalar fields in expanding universe
exhibiting Lorentz invariance violation: We address the optimal estimation of quantum parameters, in the framework of
local quantum estimation theory, for a massive scalar quantum field in the
expanding Robertson-Walker universe exhibiting Lorentz invariance violation
(LIV). The information about the history of the expanding spacetime in the
presence of LIV can be extracted by taking measurements on the entangled state
of particle modes. We find that, in the estimation of cosmological parameters,
the ultimate bounds to the precision of the Lorentz-invariant massive scalar
field can be improved due to the effects of LIV under some appropriate
conditions. We also show that, in the Lorentz-invariant massive scalar field
and massless scalar field due to LIV backgrounds, the optimal precision can be
achieved by choosing the particles with some suitable LIV, cosmological and
field parameters. Moreover, in the estimation of LIV parameter during the
spacetime expansion, we prove that the appropriate momentum mode of field
particles and larger cosmological parameters can provide us a better precision.
Particularly, the optimal precision of the parameters estimation can be
obtained by performing projective measurements implemented by the projectors
onto the eigenvectors of specific probe states. | One-loop polarization operator of the quantum gauge superfield for
${\cal N}=1$ SYM regularized by higher derivatives: We consider the general ${\cal N}=1$ supersymmetric gauge theory with matter,
regularized by higher covariant derivatives without breaking the BRST
invariance, in the massless limit. In the $\xi$-gauge we obtain the
(unrenormalized) expression for the two-point Green function of the quantum
gauge superfield in the one-loop approximation as a sum of integrals over the
loop momentum. The result is presented as a sum of three parts: the first one
corresponds to the pure supersymmetric Yang--Mills theory in the Feynman gauge,
the second one contains all gauge dependent terms, and the third one is the
contribution of diagrams with a matter loop. For the Feynman gauge and a
special choice of the higher derivative regulator in the gauge fixing term we
analytically calculate these integrals in the limit $k\to 0$. In particular, in
addition to the leading logarithmically divergent terms, which are determined
by integrals of double total derivatives, we also find the finite constants. |
Kac-Moody algebras and the cosmological constant: We show that the theory of gravity constructed from the non-linear
realisation of the semi-direct product of the Kac-Moody algebra A1+++ with its
vector representation does not allow a cosmological constant. The existence of
a cosmological constant in this theory is related to the breaking of the
gravitational duality symmetry. | A panoply of Schwinger-Keldysh transport: We classify all possible allowed constitutive relations of relativistic
fluids in a statistical mechanical limit using the Schwinger-Keldysh effective
action for hydrodynamics. We find that microscopic unitarity enforces genuinely
new constraints on the allowed transport coefficients that are invisible in the
classical hydrodynamic description; they are not implied by the second law or
the Onsager relations. We term these conditions Schwinger-Keldysh positivity
and provide explicit examples of the various allowed terms. |
Non-tachyonic Scherk-Schwarz compactifications, cosmology and moduli
stabilization: It is well-known that Scherk-Schwarz compactifications in string theory have
a tachyon in the closed string spectrum appearing for a critical value of a
compact radius. The tachyon can be removed by an appropriate orientifold
projection in type II strings, giving rise to tachyon-free compactifications.
We present explicit examples of this type in various dimensions, including six
and four-dimensional chiral examples, with softly broken supersymmetry in the
closed sector and non-BPS configurations in the open sector. These vacua are
interesting frameworks for studying various cosmological issues. We discuss
four-dimensional cosmological solutions and moduli stabilization triggered by
nonperturbative effects like gaugino condensation on D-branes and fluxes. | Spin Hall effect of gravitational waves: Gravitons possess a Berry curvature due to their helicity. We derive the
semiclassical equations of motion for gravitons taking into account the Berry
curvature. We show that this quantum correction leads to the splitting of the
trajectories of right- and left-handed gravitational waves in curved space, and
that this correction can be understood as a topological phenomenon. This is the
spin Hall effect (SHE) of gravitational waves. We find that the SHE of
gravitational waves is twice as large as that of light. Possible future
observations of the SHE of gravitational waves can potentially test the quantum
nature of gravitons beyond the classical general relativity. |
Relativistic Wave Equations and Compton Scattering: The recently proposed eight-component relativistic wave equation is applied
to the scattering of a photon from a free electron (Compton scattering). It is
found that in spite of the considerable difference in the structure of this
equation and that of Dirac the cross section is given by the Klein-Nishina
formula. | Dilatation operator and Cayley graphs: We use the algebraic definition of the Dilatation operator provided by
Minahan, Zarembo, Beisert, Kristijansen, Staudacher, proper for single trace
products of scalar fields, at leading order in the large-N 't Hooft limit to
develop a new approach to the evaluation of the spectrum of the Dilatation
operator. We discover a vast number of exact sequences of eigenstates. |
Open Strings and Electric Fields in Compact Spaces: We analyse open strings with background electric fields in the internal
space, T-dual to branes moving with constant velocities in the internal space.
We find that the direction of the electric fields inside a two torus, dual to
the D brane velocities, has to be quantised such that the corresponding
direction is compact. This implies that D-brane motion in the internal torus is
periodic, with a periodicity that can be parametrically large in terms of the
internal radii. By S-duality, this is mapped into an internal magnetic field in
a three torus, a quantum mechanical analysis of which yields a similar result,
i.e. the parallel direction to the magnetic field has to be compact.
Furthermore, for the magnetic case, we find the Landau level degeneracy as
being given by the greatest common divisor of the flux numbers. We carry on the
string quantisation and derive the relevant partition functions for these
models. Our analysis includes also the case of oblique electric fields which
can arise when several stacks of branes are present. Compact dimensions and/or
oblique sectors influence the energy loss of the system through pair-creation
and thus can be relevant for inflationary scenarios with branes. Finally, we
show that the compact energy loss is always larger than the non-compact one. | $S$-matrix representation of the finite temperature propagator in
$λφ^4$-QFT: The two-point Green function of the massive scalar $(3+1)$-quantum field
theory with $\lambda\phi^4$ interaction at finite temperature is evaluated up
to the 2nd order of perturbation theory. The averaging on the vacuum
fluctuations is separated from the averaging on the thermal fluctuations
explicitly. As a result, the temperature dependent part of the propagator is
expressed through the scattering amplitudes. The obtained expression is
generalized for higher orders of perturbation theory. |
D0-Branes As Light-Front Confined Quarks: We argue that different aspects of Light-Front QCD at confined phase can be
recovered by the Matrix Quantum Mechanics of D0-branes. The concerning Matrix
Quantum Mechanics is obtained from dimensional reduction of pure Yang-Mills
theory to 0+1 dimension. The aspects of QCD dynamics which are studied in
correspondence with D0-branes are: 1) phenomenological inter-quark potentials,
2) whiteness of hadrons and 3) scattering amplitudes. In addition, some other
issues such as the large-N behavior, the gravity--gauge theory relation and
also a possible justification for involving ``non-commutative coordinates'' in
a study of QCD bound-states are discussed. | Exact inhomogeneous Einstein-Maxwell-Dilaton cosmologies: We present solution generating techniques which permit to construct exact
inhomogeneous and anisotropic cosmological solutions to a four-dimensional low
energy limit of string theory containing non-minimally interacting
electromagnetic and dilaton fields. Some explicit homogeneous and inhomogeneous
cosmological solutions are constructed. For example, inhomogeneous exact
solutions presenting Gowdy - type EMD universe are obtained. The asymptotic
behaviour of the solutions is investigated. The asymptotic form of the metric
near the initial singularity has a spatially varying Kasner form. The character
of the space-time singularities is discussed. The late evolution of the
solutions is described by a background homogeneous and anisotropic universe
filled with weakly interacting gravitational, dilatonic and electromagnetic
waves. |
Bulk Dynamics in Confining Gauge Theories: We consider gauge/string duality (in the supergravity approximation) for
confining gauge theories. The system under scrutiny is a 5-dimensional
consistent truncation of type IIB supergravity obtained using the
Papadopoulos-Tseytlin ansatz with boundary momentum added. We develop a
gauge-invariant and sigma-model-covariant approach to the dynamics of
5-dimensional bulk fluctuations. For the Maldacena-Nunez subsystem, we study
glueball mass spectra. For the Klebanov-Strassler subsystem, we compute the
linearized equations of motion for the 7-scalar system, and show that a
3-scalar sector containing the scalar dual to the gluino bilinear decouples in
the UV. We solve the fluctuation equations exactly in the "moderate UV"
approximation and check this approximation numerically. Our results demonstrate
the feasibility of analyzing the generally coupled equations for scalar bulk
fluctuations, and constitute a step on the way towards computing correlators in
confining gauge theories. | An Alternative to Collective Coordinates: Collective coordinates provide a powerful tool for separating collective and
elementary excitations, allowing both to be treated in the full quantum theory.
The price is a canonical transformation which leads to a complicated starting
point for subsequent calculations. Sometimes the collective behavior of a
soliton is simple but nontrivial, and one is interested in the elementary
excitations. We show that in this case an alternative prescription suffices, in
which the canonical transformation is not necessary. The use of a
nonperturbative operator which creates a soliton state allows the theory to be
constructed perturbatively in terms of the soliton normal modes. We show how
translation invariance may be perturbatively imposed. We apply this to
construct the two-loop ground state of an arbitrary scalar kink. |
Comparison of renormalization group schemes for sine-Gordon type models: The scheme-dependence of the renormalization group (RG) flow has been
investigated in the local potential approximation for two-dimensional periodic,
sine-Gordon type field-theoric models discussing the applicability of various
functional RG methods in detail. It was shown that scheme-independent
determination of such physical parameters is possible as the critical frequency
(temperature) at which Kosterlitz-Thouless-Berezinskii type phase transition
takes place in the sine-Gordon and the layered sine-Gordon models, and the
critical ratio characterizing the Ising type phase transition of the massive
sine-Gordon model. For the latter case the Maxwell construction represents a
strong constraint on the RG flow which results in a scheme-independent infrared
value for the critical ratio. For the massive sine-Gordon model also the
shrinking of the domain of the phase with spontaneously broken periodicity is
shown to take place due to the quantum fluctuations. | Explorations in Scalar Fermion Theories: $β$-functions,
Supersymmetry and Fixed Points: Results for $\beta$-functions and anomalous dimensions in general scalar
fermion theories are presented to three loops. Various constraints on the
individual coefficients for each diagram following from supersymmetry are
analysed. The results are used to discuss potential fixed points in the
$\varepsilon$-expansion for scalar fermion theories, with arbitrary numbers of
scalar fields, and where there are just two scalar couplings and one Yukawa
coupling. For different examples the fixed points follow a similar pattern as
the numbers of fermions is varied. For diagrams with subdivergences there are
extensive consistency constraints arising from the existence of a perturbative
$a$-function and these are analysed in detail. Further arbitrary scheme
variations which preserve the form of $\beta$ functions and anomalous
dimensions in terms of 1PI diagrams are also discussed. The existence of linear
and quadratic scheme invariants is demonstrated and the consistency condition
are shown to be expressible in terms of these invariants. |
A Discussion on Massive Gravitons and Propagating Torsion in Arbitrary
Dimensions: In this paper, we reassess a particular $R^{2}$-type gravity action in D
dimensions, recently studied by Nakasone and Oda, taking now torsion effects
into account. Considering that the vielbein and the spin connection carry
independent propagating degrees of freedom, we conclude that ghosts and
tachyons are absent only if torsion is non-propagating, and we also conclude
that there is no room for massive gravitons. To include these excitations, we
understand how to enlarge Nakasone-Oda's model by means of explicit torsion
terms in the action and we discuss the unitarity of the enlarged model for
arbitrary dimensions. | Brane bending and monopole moduli: We study intersecting brane systems that realize a class of singular monopole
configurations in four-dimensional Yang-Mills-Higgs theory. Singular monopoles
are solutions to the Bogomolny equation on R^3 with a prescribed number of
singularities corresponding to the insertion of 't Hooft defects. We use the
brane construction to motivate a recent conjecture on the conditions for which
the moduli space of solutions is non-empty. We also show how branes provide
physical intuition for various aspects of the dimension formula derived in
{arXiv:1404.5616}, including the contribution to the dimension from the defects
and its invariance under Weyl reflections of the 't Hooft charges. Along the
way we uncover and illustrate new dynamical phenomena for the brane systems,
including a description of smooth monopole extraction and bubbling from 't
Hooft defects. |
Effective field theory for hydrodynamics without boosts: We formulate the Schwinger-Keldysh effective field theory of hydrodynamics
without boost symmetry. This includes a spacetime covariant formulation of
classical hydrodynamics without boosts with an additional conserved
particle/charge current coupled to Aristotelian background sources. We find
that, up to first order in derivatives, the theory is characterised by the
thermodynamic equation of state and a total of 29 independent transport
coefficients, in particular, 3 hydrostatic, 9 non-hydrostatic non-dissipative,
and 17 dissipative. Furthermore, we study the spectrum of linearised
fluctuations around anisotropic equilibrium states with non-vanishing fluid
velocity. This analysis reveals a pair of sound modes that propagate at
different speeds along and opposite to the fluid flow, one charge diffusion
mode, and two distinct shear modes along and perpendicular to the fluid
velocity. We present these results in a new hydrodynamic frame that is linearly
stable irrespective of the boost symmetry in place. This provides a unified
covariant stable approach for simultaneously treating Lorentzian, Galilean, and
Lifshitz fluids within an effective field theory framework and sets the stage
for future studies of non-relativistic intertwined patterns of symmetry
breaking. | Probabilities in the landscape: I review recent progress in defining probability distributions in the
inflationary multiverse. |
Quantum chaos in the sparse SYK model: The Sachdev-Ye-Kitaev (SYK) model is a system of $N$ Majorana fermions with
random interactions and strongly chaotic dynamics, which at low energy admits a
holographically dual description as two-dimensional Jackiw-Teitelboim gravity.
Hence the SYK model provides a toy model of quantum gravity that might be
feasible to simulate with near-term quantum hardware. Motivated by the goal of
reducing the resources needed for such a simulation, we study a sparsified
version of the SYK model, in which interaction terms are deleted with
probability $1{-p}$. Specifically, we compute numerically the spectral form
factor (SFF, the Fourier transform of the Hamiltonian's eigenvalue pair
correlation function) and the nearest-neighbor eigenvalue gap ratio $r$
(characterizing the distribution of gaps between consecutive eigenvalues). We
find that when $p$ is greater than a transition value $p_1$, which scales as
$1/N^3$, both the SFF and $r$ match the values attained by the full
unsparsified model and with expectations from random matrix theory (RMT). But
for $p<p_1$, deviations from unsparsified SYK and RMT occur, indicating a
breakdown of holography in the highly sparsified regime. Below an even smaller
value $p_2$, which also scales as $1/N^3$, even the spacing of consecutive
eigenvalues differs from RMT values, signaling a complete breakdown of spectral
rigidity. Our results cast doubt on the holographic interpretation of very
highly sparsified SYK models obtained via machine learning using teleportation
infidelity as a loss function. | Generalised vielbeins and non-linear realisations: We briefly review why the non-linear realisation of the semi-direct product
of a group with one of its representations leads to a field theory defined on a
generalised space-time equipped with a generalised vielbein. We give formulae,
which only involve matrix multiplication, for the generalised vielbein, the
Cartan forms and their transformations. We consider the generalised space-time
introduced in 2003 in the context of the non-linear realisation of the
semi-direct product of E(11) and its first fundamental representation. For this
latter theory we give explicit expressions for the generalised vielbein up to
and including the levels associated with the dual graviton in four, five and
eleven dimensions and for the IIB theory in ten dimensions. We also compute the
generalised vielbein, up to the analogous level, for the non-linear realisation
of the semi-direct product of very extended SL(2) with its first fundamental
representation, which is a theory associated with gravity in four dimensions. |
On the Landau-Ginzburg description of $(A_1^{(1)})^{\oplus N}$
invariants: We search for a \Lg\ interpretation of non-diagonal modular invariants of
tensor products of minimal $n=2$ superconformal models, looking in particular
at automorphism invariants and at some exceptional cases. For the former we
find a simple description as \lgo s, which reproduce the correct chiral rings
as well as the spectra of various Gepner--type models and orbifolds thereof. On
the other hand, we are able to prove for one of the exceptional cases that this
conformal field theory cannot be described by an orbifold of a \Lg\ model with
respect to a manifest linear symmetry of its potential. | Massive Gravity with Anisotropic Scaling: We study a massive gravity theory which is Lorentz violating all the way from
ultraviolet to infrared energy scales. At short distances the theory breaks
diffeomorphism invariance and time and space scale differently. Dynamical
metric fields are introduced which upon linearization over a Minkowski
background correspond to Lorentz violating mass terms at large distances. We
perform a scalar perturbation analysis and we show that with an appropriate
choice of parameters the theory is healthy without ghosts, tachyons, strong
coupling problems and instabilities |
Hall Viscosity in a Strongly Coupled Magnetized Plasma: We show how a Hall viscosity induced by a magnetic field can be generated in
strongly coupled theories with a holographic dual. This is achieved by
considering parity-breaking higher derivative terms in the gravity dual. These
terms couple the Riemann curvature tensor to the field strength of a gauge
field dual to the charge current, and have an analog in the field theory side
as a coupling between the "Euler current" and the electromagnetic field. As a
concrete example, we study the effect of the new terms in the thermodynamic and
transport properties of a strongly coupled magnetized plasma dual to a dyonic
black hole in $AdS_4$. As a new property of the holographic model, we find that
for a state that is initially neutral at zero magnetic field, a charge density
and non-dissipative Hall transport are present when the magnetic field is
turned on. Remarkably, we also observe that the results from the holographic
model are consistent with hydrodynamics even at magnetic fields much larger
than temperature. | Colliding localized, lumpy holographic shocks with a granular nuclear
structure: We apply a recent and simple technique which speeds up the calculation of
localized collisions in holography to study more realistic models of heavy ion
collisions via the gauge/gravity duality. The initial data takes into account
the lumpy nuclear structure of real heavy ions and the projectiles' aspect
ratio mimics the Lorentz contraction of nuclei during RHIC collisions. At the
hydrodynamization time of the central region of the quark gluon plasma
developed during the collision, we find that most of the vorticity three
vector's absolute value is deposited far away from the hydrodynamized part of
the plasma. Only the relativistic corrections to the thermal vorticity in the
hydrodynamized region are non-negligible. We compare the transverse flow after
the collision determined in this work with previous results, without granular
initial conditions and determine the proper energy density and fluid velocity
in a hydrodynamized subregion of the plasma. |
Chern-Simons Terms on Noncommutative Branes: We write down couplings of the fields on a single BPS Dp-brane with
noncommutative world-volume coordinates to the RR-forms in type II theories, in
a manifestly background independent way. This generalises the usual
Chern-Simons action for a commutative Dp-brane. We show that the noncommutative
Chern-Simons terms can be mapped to Myers terms on a collection of infinitely
many D-instantons. We also propose Chern-Simons couplings for unstable non-BPS
branes, and show that condensation of noncommutative tachyons on these branes
leads to the correct Myers terms on the decay products. | Mirror Symmetry, D-Branes and Counting Holomorphic Discs: We consider a class of special Lagrangian subspaces of Calabi-Yau manifolds
and identify their mirrors, using the recent derivation of mirror symmetry, as
certain holomorphic varieties of the mirror geometry. This transforms the
counting of holomorphic disc instantons ending on the Lagrangian submanifold to
the classical Abel-Jacobi map on the mirror. We recover some results already
anticipated as well as obtain some highly non-trivial new predictions. |
A Realization of Slow Roll Inflation and the MSSM in Supergravity
Theories with New Fayet-Iliopoulos Terms: A new supergravity D-term, not associated to gauged R-symmetry, was recently
discovered and used to construct new supergravity models. In this paper we use
a generalization of the new D-term that we used in previous works, to construct
a supergravity model of slow-roll inflation with the observable sector of the
minimal supersymmetric standard model. Supersymmetry is broken at a high scale
in the hidden sector and communicated to the observable sector by gravity
mediation. The new D-term contains free parameters that can give large masses
to scalar superpartners of quarks and leptons and to the higgsinos while
holding the masses of observed particles fixed. Gauginos receive a mass from a
non-canonical kinetic term for the vector supermultiplets. We also present a
simple argument proving in full generality that the cutoff $\Lambda$ of
effective theories containing new D-terms can never exceed the supersymmetry
breaking scale. In our theory, the relation between D-term and the Hubble
constant during inflation also implies the universal relation $\Lambda \lesssim
\sqrt{H M_{Pl}}$. | Black holes in braneworld models: In this review, we summarize current understandings of black hole solutions
in various braneworld models, including the Arkani-Hamed-Dimopoulos-Dvali
model, the Randall-Sundrum (RS) models, the Karch-Randall (KR) model and the
Dvali-Gabadadze-Porrati model. After illustrating basic properties of each
braneworld model, we introduce the bulk/brane correspondence in the RS and KR
braneworld models, adding supporting evidence for it. We then summarize the
studies on braneworld black hole solutions, which consist of constructing exact
or approximate solutions and investigating the phase diagram of solutions. In
the study of phase diagram, we will also expound the implications of the
bulk/brane correspondence to the braneworld black holes. |
Parity-Odd 3-Point Functions from CFT in Momentum Space and the Chiral
Anomaly: We illustrate how the Conformal Ward Identities (CWI) in momentum space for
parity-odd correlators determine the structure of a chiral anomaly interaction,
taking the example of the VVA (vector/vector/axial-vector) and AAA correlators
in momentum space. Only the conservation and the anomalous WIs, together with
the Bose symmetry, are imposed from the outset for the determination of the
correlators. We use a longitudinal/transverse decomposition of tensor
structures and form factors. The longitudinal (L) component is fixed by the
anomaly content and the anomaly pole, while in the transverse (T) sector we
define a new parameterization. We relate the latter both to the Rosenberg
original representation of the VVA and to the longitudinal/transverse (L/T)
one, first introduced in the analysis of $g-2$ of the muon in the investigation
of the diagram in the chiral limit of QCD. The correlators are completely
identified by the conformal constraints whose solutions are fixed only by the
anomaly coefficient, the residue of the anomaly pole. In both cases, our CFT
result matches the one-loop perturbative expression, as expected. The CWIs for
correlators of mixed chirality $J_L J J_R$ generate solutions in agreement with
the all-orders nonrenormalization theorems of perturbative QCD and in the
chiral limit. | Universal behaviour, transients and attractors in supersymmetric
Yang-Mills plasma: Numerical simulations of expanding plasma based on the AdS/CFT correspondence
as well as kinetic theory and hydrodynamic models strongly suggest that some
observables exhibit universal behaviour even when the system is not close to
local equilibrium. This leading behaviour is expected to be corrected by
transient, exponentially decaying contributions which carry information about
the initial state. Focusing on late times, when the system is already in the
hydrodynamic regime, we analyse numerical solutions describing expanding plasma
of strongly coupled N=4 supersymmetric Yang-Mills theory and identify these
transient effects, matching them in a quantitative way to leading trans-series
corrections corresponding to least-damped quasinormal modes of AdS black
branes. In the process we offer additional evidence supporting the recent
identification of the Borel sum of the hydrodynamic gradient expansion with the
far-from-equilibrium attractor in this system. |
Canonical Quantization of The Dissipative Hofstadter Model: We perform canonical quantization of the dissipative Hofstadter model, which
has a wide range of applications in condensed matter physics and string theory.
The target space duality and the non-commutative algebra developed in string
theory are discussed for the model. We show that the target space duality
transformation of closed string theory, $O(2,2;R)$, removes the interaction
with a uniform magnetic field. The $O(2,2;R)$ dual transformation changes the
basis of oscillator operators so that the algebra of the string coordinate
operators at the boundary become non-commutative. In the zero temperature
limit, the non-commutative algebra of open string theory emerges. We also
developed the boundary state formulation for the dissipative Hofstadter model. | Six-loop $\varepsilon$ expansion of three-dimensional $\text{U}(n)\times
\text{U}(m)$ models: We analyze the Landau-Wilson field theory with $\text{U}(n)\times\text{U}(m)$
symmetry which describes the finite-temperature phase transition in QCD in the
limit of vanishing quark masses with $n=m=N_f$ flavors and unbroken anomaly at
the critical temperature. The six-loop expansions of the renormalization group
functions are calculated within the Minimal Subtraction scheme in $4 -
\varepsilon$ dimensions. The $\varepsilon$ series for the upper marginal
dimensionality $n^{+}(m,4-\varepsilon)$ -- the key quantity of the theory --
are obtained and resummed by means of different approaches. The numbers found
are compared with their counterparts obtained earlier within lower perturbative
orders and the pseudo-$\varepsilon$ analysis of massive six-loop
three-dimensional expansions. In particular, using an increase in the accuracy
of numerical results for $n^{+}(m,3)$ by one order of magnitude, we strengthen
the conclusions obtained within previous order in perturbation theory about
fairness of the inequality $n^{+}(m,3)>m$. This, in turn, indicates the absence
of a stable three-dimensional fixed point for $n=m$, and as a consequence a
first-order kind of finite-temperature phase transition in light QCD. |
Decoupling and Reduction in Chern-Simons Modified Gravity: We show that for four-dimensional spacetimes with a non-null hypersurface
orthogonal Killing vector and for a Chern-Simons (CS) background
(non-dynamical) scalar field, which is constant along the Killing vector, the
source-free equations of CS modified gravity decouple into their Einstein and
Cotton constituents. Thus, the model supports only general relativity
solutions. We also show that, when the cosmological constant vanishes and the
gradient of the CS scalar field is parallel to the non-null hypersurface
orthogonal Killing vector of constant length, CS modified gravity reduces to
topologically massive gravity in three dimensions. Meanwhile, with the
cosmological constant such a reduction requires an appropriate source term for
CS modified gravity. | Faddeev-Popov determinant in 2-dimensional Regge gravity.: By regularizing the singularities appearing in the two dimensional Regge
calculus by means of a segment of a sphere or pseudo-sphere and then taking the
regulator to zero, we obtain a simple formula for the gauge volume which
appears in the functional integral. Such a formula is an analytic function of
the opening of the conic singularity in the interval from $\pi$ to $4\pi$ and
in the continuum limit it goes over to the correct result. |
Alternativity and reciprocity in the Cayley-Dickson algebra: We calculate the eigenvalue \rho of the multiplication mapping R on the
Cayley-Dickson algebra A_n. If the element in A_n is composed of a pair of
alternative elements in A_{n-1}, half the eigenvectors of R in A_n are still
eigenvectors in the subspace which is isomorphic to A_{n-1}.
The invariant under the reciprocal transformation A_n \times A_{n} \ni (x,y)
-> (-y,x) plays a fundamental role in simplifying the functional form of \rho.
If some physical field can be identified with the eigenspace of R, with an
injective map from the field to a scalar quantity (such as a mass) m, then
there is a one-to-one map \pi: m \mapsto \rho. As an example, the electro-weak
gauge field can be regarded as the eigenspace of R, where \pi implies that the
W-boson mass is less than the Z-boson mass, as in the standard model. | Chiral vortical effect in pionic superfluid vs spin alignment of baryons: We consider chiral fluids, with (nearly) massless fermionic constituents, in
the confining phase. Chiral vortical effect (CVE) is the flow of axial current
along the axis of rotation of the fluid while the spin alignment is a
non-vanishing correlation of polarizations of baryons with the axis of
rotation. As the theoretical framework we use the model of pionic superfluidity
induced by a non-vanishing isotopic chemical potential. We note that the
average value of spin of virtual baryons reproduces the CVE. The role of
defects, or vortices is crucial. The model does not apply directly to the
quark-gluon plasma but might indicate existence of a mechanism to produce
baryons with relatively large polarization in heavy-ion collisions. |
Nonlinear field theory with topological solitons: Skyrme models: In this talk, we give new insight into one of the best-known nonlinear field
theories, the Skyrme model. We present some exact relevant solutions coming
from different new versions (gauged BPS baby as well as vector BPS Skyrme
models) giving rise to topological solitons, and highlighting the BPS character
of the theory. | Refining G-structure classifications: Using G-structure language, a systematic, iterative formalism for computing
neccessary and sufficient conditions for the existence of N arbitrary linearly
independent Killing spinors is presented. The key organisational tool is the
common isotropy group of the Killing spinors. The formalism is illustrated for
configurations in gauged SU(2) supergravity in seven dimensions admitting at
least one null Killing spinor, and the possible isotropy groups are shown to be
$(SU(2)\ltimes\mathbb{R}^4)\times\mathbb{R}$, SU(2), $\mathbb{R}^5$, or the
identity. The constraints associated with the existence of certain additional
Killing spinors are computed, and used to derive numerous solutions. A
discussion of the relevance of the formalism to the complete classification of
all supersymmetric configurations in d=11 is given. |
The Spectrum in the Sachdev-Ye-Kitaev Model: The SYK model consists of $N\gg 1$ fermions in $0+1$ dimensions with a
random, all-to-all quartic interaction. Recently, Kitaev has found that the SYK
model is maximally chaotic and has proposed it as a model of holography. We
solve the Schwinger-Dyson equation and compute the spectrum of two-particle
states in SYK, finding both a continuous and discrete tower. The four-point
function is expressed as a sum over the spectrum. The sum over the discrete
tower is evaluated. | Physical Combinatorics and Quasiparticles: We consider the physical combinatorics of critical lattice models and their
associated conformal field theories arising in the continuum scaling limit. As
examples, we consider A-type unitary minimal models and the level-1 sl(2)
Wess-Zumino-Witten (WZW) model. The Hamiltonian of the WZW model is the
$U_q(sl(2))$ invariant XXX spin chain. For simplicity, we consider these
theories only in their vacuum sectors on the strip. Combinatorially, fermionic
particles are introduced as certain features of RSOS paths. They are composites
of dual-particles and exhibit the properties of quasiparticles. The particles
and dual-particles are identified, through an energy preserving bijection, with
patterns of zeros of the eigenvalues of the fused transfer matrices in their
analyticity strips. The associated (m,n) systems arise as geometric packing
constraints on the particles. The analyticity encoded in the patterns of zeros
is the key to the analytic calculation of the excitation energies through the
Thermodynamic Bethe Ansatz (TBA). As a by-product of our study, in the case of
the WZW or XXX model, we find a relation between the location of the Bethe root
strings and the location of the transfer matrix 2-strings. |
Exploring the ground state spectrum of gamma-deformed N=4 SYM: We study the gamma-deformation of the planar N=4 super Yang-Mills theory
which breaks all supersymmetries but is expected to preserve integrability of
the model. We focus on the operator Tr$(\phi_1\phi_1)$ built from two scalars,
whose integrability description has been questioned before due to contributions
from double-trace counterterms. We show that despite these subtle effects, the
integrability-based Quantum Spectral Curve (QSC) framework works perfectly for
this state and in particular reproduces the known 1-loop prediction. This
resolves an earlier controversy concerning this operator and provides further
evidence that the gamma-deformed model is an integrable CFT at least in the
planar limit. We use the QSC to compute the first 5 weak coupling orders of the
anomalous dimension analytically, matching known results in the fishnet limit,
and also compute it numerically all the way from weak to strong coupling. We
also utilize this data to extract a new coefficient of the beta function of the
double-trace operator couplings. | Massive Three-Dimensional Supergravity From R+R^2 Action in Six
Dimensions: We obtain a three-parameter family of massive N=1 supergravities in three
dimensions from the 3-sphere reduction of an off-shell N=(1,0) six-dimensional
Poincare supergravity that includes a curvature squared invariant. The
three-dimensional theory contains an off-shell supergravity multiplet and an
on-shell scalar matter multiplet. We then generalise this in three dimensions
to an eight-parameter family of supergravities. We also find a duality
relationship between the six-dimensional theory and the N=(1,0) six-dimensional
theory obtained through a T^4 reduction of the heterotic string effective
action that includes the higher-order terms associated with the
supersymmetrisation of the anomaly-cancelling \tr(R\wedge R) term. |
N=4 SYM on R x S^3 and Theories with 16 Supercharges: We study N=4 SYM on R x S^3 and theories with 16 supercharges arising as its
consistent truncations. These theories include the plane wave matrix model, N=4
SYM on R x S^2 and N=4 SYM on R x S^3/Z_k, and their gravity duals were studied
by Lin and Maldacena. We make a harmonic expansion of the original N=4 SYM on R
x S^3 and obtain each of the truncated theories by keeping a part of the
Kaluza-Klein modes. This enables us to analyze all the theories in a unified
way. We explicitly construct some nontrivial vacua of N=4 SYM on R x S^2. We
perform 1-loop analysis of the original and truncated theories. In particular,
we examine states regarded as the integrable SO(6) spin chain and a
time-dependent BPS solution, which is considered to correspond to the AdS giant
graviton in the original theory. | S-matrix Unitarity and Renormalizability in Higher Derivative Theories: We investigate the relation between the $S$-matrix unitarity
($SS^{\dagger}=1$) and the renormalizability, in theories with negative norm
states. The relation has been confirmed in many theories, such as gauge
theories, Einstein gravity and Lifshitz-type non-relativistic theories by
analyzing the unitarity bound, which follows from the $S$-matrix unitarity and
the norm positivity. On the other hand, renormalizable theories with a higher
derivative kinetic term do not necessarily satisfy the unitarity bound
essentially because the unitarity bound does not hold due to the negative norm
states. In these theories, it is not clear if the $S$-matrix unitarity provides
a nontrivial constraint related to the renormalizability. In this paper we
introduce scalar field models with a higher derivative kinetic term and analyze
the $S$-matrix unitarity. We have positive results of the relation. |
Gravitational orbits, double-twist mirage, and many-body scars: We explore the implications of stable gravitational orbits around an AdS
black hole for the boundary conformal field theory. The orbits are long-lived
states that eventually decay due to gravitational radiation and tunneling. They
appear as narrow resonances in the heavy-light OPE when the spectrum becomes
effectively continuous due to the presence of the black hole horizon.
Alternatively, they can be identified with quasi-normal modes with small
imaginary part in the thermal two-point function. The two pictures are related
via the eigenstate thermalisation hypothesis. When the decay effects can be
neglected the orbits appear as a discrete family of double-twist operators. We
investigate the connection between orbits, quasi-normal modes, and double-twist
operators in detail. Using the corrected Bohr-Sommerfeld formula for
quasi-normal modes, we compute the anomalous dimension of double-twist
operators. We compare our results to the prediction of the light-cone
bootstrap, finding perfect agreement where the results overlap. We also compute
the orbit decay time due to scalar radiation and compare it to the tunneling
rate. Perturbatively in spin, in the light-cone bootstrap framework
double-twist operators appear as a small fraction of the Hilbert space which
violate the eigenstate thermalization hypothesis, a phenomenon known as
many-body scars. Nonperturbatively in spin, the double-twist operators become
long-lived states that eventually thermalize. We briefly discuss the connection
between perturbative scars in holographic theories and known examples of scars
in the condensed matter literature. | Inflation from D-\bar{D} brane annihilation: We demonstrate that the initial conditions for inflation are met when D5 and
\bar{D}5 branes annihilate. This scenario uses Sen's conjecture that a
co-dimension two vortex forms on the worldvolume of the annihilated 5-brane
system. Analogous to a "Big Bang", when the five branes annihilate, a vortex
localized on a 3-brane forms and its false vacuum energy generates an
inflationy space-time. We also provide a natural mechanism for ending inflation
via the motion of the vortex in the bulk due to its extrinsic curvature. We
also suggest a consistent way to end inflation and localize matter on our
space-time. |
Relativistic Particles on Quantum Space-time: We discuss alternatives to the usual quantization of relativistic particles
which result in discrete spectra for position and time operators. | Dualities and the SL(2,Z) Anomaly: The SL(2,Z) anomaly recently derived for type IIB supergravity in 10
dimensions is shown to be a consequence of T-duality with the type IIA string,
after compactification to 2 dimensions on an 8-fold. This explains the identity
of the gravitational 8-forms appearing in different contexts in the effective
actions of type IIA and IIB string theories. In this framework, constraints on
the compactification manifold arise from modular invariance of the 2d theory.
Related issues in 6 dimensions are examined, and it is argued that similar
anomalies are present on the worldvolumes of M-theory 5-branes and orientifold
5-planes. |
The Lion, the Witch, and the Wormhole: Ensemble averaging the symmetric
product orbifold: We consider the ensemble average of two dimensional symmetric product
orbifold CFTs $\text{Sym}^N(\mathbb{T}^D)$ over the Narain moduli space. We
argue for a bulk dual given by $N$ copies of an abelian Chern-Simons theory
coupled to topological gravity, endowed with a discrete gauge symmetry
exchanging the $N$ copies. As a check of this proposal, we calculate the
ensemble average of various partition and correlation functions of the
symmetric product orbifold theory and compare the resulting expressions to
gauge theory quantities in the bulk. We comment on the ensemble average of the
tensionless string partition function on $\text{AdS}_3 \times \text{S}^3 \times
\mathbb T^4$ by considering the specific case of $D=4$ with the addition of
supersymmetry. | SL(2,Z) duality of Born-Infeld theory from self-dual electrodynamics in
6 dimensions: We reformulate the Born-Infeld action, coupled to an axion and a dilaton in a
duality manifest way. This action is the generalization of the Schwarz-Sen
action for non-linear electrodynamics. We show that this action may be obtained
by dimensional reduction on a torus of a self-dual theory in 6 dimensions. The
dilaton-axion being identified with the complex structure of the torus.
Applications to M-theory and the self-dual IIB three brane are investigated. |
Fermionic vacuum polarization by a magnetic tube in the cosmic string
spacetime: In this paper, we consider a charged massive fermionic quantum field in the
idealized cosmic string spacetime and in the presence of a magnetic field
confined in a cylindrical tube of finite radius. Three distinct configurations
for the magnetic fields are taken into account: (i) a cylindrical shell of
radius $a$, (ii) a magnetic field proportional to $1/r$ and (iii) a constant
magnetic field. In these three cases, the axis of the infinitely long tube of
radius $a$ coincides with the cosmic string. Our main objectives in this paper
are to analyze the fermionic condensat (FC) e and the vacuum expectation value
(VEV) of the fermionic energy-momentum tensor. In order to do that, we
explicitly construct the complete set of normalized wave-functions for each
configuration of magnetic field. We show that in the region outside the tube,
the FC and the VEV of the energy-momentum tensor are decomposed into two parts:
the first ones correspond to the zero-thickness magnetic flux contributions,
and the seconds are induced by the non-trivial structure of the magnetic field,
named core-induced contributions. The latter present specific forms depending
on the magnetic field configuration considered. We also show that the VEV of
the energy-momentum tensor is diagonal, obeys the conservation condition and
its trace is expressed in terms of the fermionic condensate. The zero-thickness
contributions to the FC and VEV of the energy-momentum tensor, depend only on
the fractional part of the ration of the magnetic flux inside the tube by the
quantum one. As to the core-induced contributions they depend on the total
magnetic flux inside the tube, and consequently, in general, are not a periodic
function of the magnetic flux. | Black Hole Motion in Entropic Reformulation of General Relativity: We consider a system of black holes -- a simplest substitute of a system of
point particles in the mechanics of general relativity -- and try to describe
their motion with the help of entropic action: a sum of the areas of black hole
horizons. We demonstrate that such description is indeed consistent with the
Newton's laws of motion and gravity, modulo numerical coefficients, which
coincide but seem different from unity. Since a large part of the modern
discussion of entropic reformulation of general relativity is actually based on
dimensional considerations, for making a next step it is crucially important to
modify the argument, so that these dimensionless parameters acquire correct
values. |
The Kerr/CFT Correspondence: Quantum gravity in the region very near the horizon of an extreme Kerr black
hole (whose angular momentum and mass are related by J=GM^2) is considered. It
is shown that consistent boundary conditions exist, for which the asymptotic
symmetry generators form one copy of the Virasoro algebra with central charge
c_L=12J / \hbar. This implies that the near-horizon quantum states can be
identified with those of (a chiral half of) a two-dimensional conformal field
theory (CFT). Moreover, in the extreme limit, the Frolov-Thorne vacuum state
reduces to a thermal density matrix with dimensionless temperature T_L=1/2\pi
and conjugate energy given by the zero mode generator, L_0, of the Virasoro
algebra. Assuming unitarity, the Cardy formula then gives a microscopic entropy
S_{micro}=2\pi J / \hbar for the CFT, which reproduces the macroscopic
Bekenstein-Hawking entropy S_{macro}=Area / 4\hbar G. The results apply to any
consistent unitary quantum theory of gravity with a Kerr solution. We
accordingly conjecture that extreme Kerr black holes are holographically dual
to a chiral two-dimensional conformal field theory with central charge c_L=12J
/ \hbar, and in particular that the near-extreme black hole GRS 1915+105 is
approximately dual to a CFT with c_L \sim 2 \times 10^{79}. | Symmetry breaking and RG flows with higher dimensional operators: We discuss the role of higher dimensional operators in the spontaneous
breaking of internal symmetry and scale invariance, in the context of the
Lorentz invariant scalar field theory. Using the $\varepsilon$-expansion we
determine phase diagrams and demonstrate that (un)stable RG flows computed with
a certain basis of dimension 6 operators in the Lagrangian, map to (un)stable
RG flows of another basis related to the first by field redefinitions. Crucial
is the presence of reparametrization ghosts if Ostrogradsky ghosts appear. |
On Relativistic Models in the Equilibrium Statistical Mechanics: Relativistic effects in the thermodynamical properties of interacting
particle systems are investigated within the framework of the relativistic
direct interaction theory in various forms of dynamics. In the front form of
relativistic dynamics an exactly solvable model of a one-dimensional hard
spheres gas is formulated and an equation of state and thermodynamical
potentials for such a gas are found. Weakly-relativistic corrections to the
thermodynamical functions of the dilute gas with short-range interactions are
discussed on the basis of the approximately relativistic Hamiltonian function
in the instant form of dynamics. | Algebra of chiral currents on the physical surface: Using a particular structure for the Lagrangian action in a one-dimensional
Thirring model and performing the Dirac's procedure, we are able to obtain the
algebra for chiral currents which is entirely defied on the constraint surface
in the corresponding hamiltonian description of the theory. |
Entropic Accelerating Universe: To accommodate the observed accelerated expansion of the universe, one
popular idea is to invoke a driving term in the Friedmann-Lemaitre equation of
dark energy which must then comprise 70% of the present cosmological energy
density. We propose an alternative interpretation which takes into account the
entropy and temperature intrinsic to the horizon of the universe due to the
information holographically stored there. Dark energy is thereby obviated and
the acceleration is due to an entropic force naturally arising from the
information storage on the horizon surface screen. We consider an additional
quantitative approach inspired by surface terms in general relativity and show
that this leads to the entropic accelerating universe. | Quantizing non-Lagrangian gauge theories: an augmentation method: We discuss a recently proposed method of quantizing general non-Lagrangian
gauge theories. The method can be implemented in many different ways, in
particular, it can employ a conversion procedure that turns an original
non-Lagrangian field theory in $d$ dimensions into an equivalent Lagrangian
topological field theory in $d+1$ dimensions. The method involves, besides the
classical equations of motion, one more geometric ingredient called the
Lagrange anchor. Different Lagrange anchors result in different quantizations
of one and the same classical theory. Given the classical equations of motion
and Lagrange anchor as input data, a new procedure, called the augmentation, is
proposed to quantize non-Lagrangian dynamics. Within the augmentation
procedure, the originally non-Lagrangian theory is absorbed by a wider
Lagrangian theory on the same space-time manifold. The augmented theory is not
generally equivalent to the original one as it has more physical degrees of
freedom than the original theory. However, the extra degrees of freedom are
factorized out in a certain regular way both at classical and quantum levels.
The general techniques are exemplified by quantizing two non-Lagrangian models
of physical interest. |
Branes at angles and calibrated geometry: In a recent paper, Ohta and Townsend studied the conditions which must be
satisfied for a configuration of two intersecting M5-branes at angles to be
supersymmetric. In this paper we extend this result to any number of M5-branes
or any number of M2-branes. This is accomplished by interpreting their results
in terms of calibrated geometry, which is of independent interest. | Generalized Rogers Ramanujan Expressions for Some Non--Singlet Twisted
Affine Algebras: Hatayama et al. described generalized Rogers--Ramanujan (GRR) expressions for
the string functions of the singlet representation of twisted affine algebras.
We give here such GRR expressions for some non-singlet string functions. In the
case of the algebra $A_2^{(2)}$ this gives all the string functions. We verify
these expressions using Freudenthal--Kac formula. |
Understanding Something About Nothing: Radiation Zeros: Radiation symmetry is briefly reviewed, along with its historical,
experimental, computational, and theoretical relevance. A sketch of the proof
of a theorem for radiation zeros is used to highlight the connection between
gauge-boson couplings and Poincare transformations. It is emphasized that while
mostly bad things happen to good zeros, the weak-boson self-couplings continue
to be intimately tied to the best examples of exact or approximate zeros. | A natural cosmological constant from chameleons: We present a simple model where the effective cosmological constant appears
from chameleon scalar fields. For a Kachru-Kallosh-Linde-Trivedi
(KKLT)-inspired form of the potential and a particular chameleon coupling to
the local density, patches of approximately constant scalar field potential
cluster around regions of matter with density above a certain value, generating
the effect of a cosmological constant on large scales. This construction
addresses both the cosmological constant problem (why $\Lambda$ is so small,
yet nonzero) and the coincidence problem (why $\Lambda$ is comparable to the
matter density now). |
Self-dual Continuous Series of Representations for U_q(sl(2)) and
U_q(osp(1|2)): We determine the Clebsch-Gordan and Racah-Wigner coefficients for continuous
series of representations of the quantum deformed algebras U_q(sl(2)) and
U_q(osp(1|2)). While our results for the former algebra reproduce formulas by
Ponsot and Teschner, the expressions for the orthosymplectic algebra are new.
Up to some normalization factors, the associated Racah-Wigner coefficients are
shown to agree with the fusing matrix in the Neveu-Schwarz sector of N=1
supersymmetric Liouville field theory. | Integrability of Supergravity Black Holes and New Tensor Classifiers of
Regular and Nilpotent Orbits: In this paper we apply in a systematic way a previously developed integration
algorithm of the relevant Lax equation to the construction of spherical
symmetric, asymptotically flat black hole solutions of N=2 supergravities with
symmetric Special Geometry. Our main goal is the classification of these
black-holes according to the H*-orbits in which the space of possible Lax
operators decomposes, H* being the isotropy group of scalar manifold
originating from time-like dimensional reduction of supergravity from D=4 to
D=3 dimensions. The main result of our investigation is the construction of
three universal tensors, extracted from quadratic and quartic powers of the Lax
operator, that are capable of classifying both regular and nilpotent H* orbits
of Lax operators. Our tensor based classification is compared, in the case of
the simple one-field model S^3, to the algebraic classification of nilpotent
orbits and it is shown to provide a simple and practical discriminating method.
We present a detailed analysis of the S^3 model and its black hole solutions,
discussing the Liouville integrability of the corresponding dynamical system.
By means of the Kostant-representation of a generic Lie algebra element, we
were able to develop an algorithm which produces the necessary number of
hamiltonians in involution required by Liouville integrability of generic
orbits. The degenerate orbits correspond to extremal black-holes and are
nilpotent. We analyze these orbits in some detail working out different
representatives thereof and showing that the relation between H* orbits and
critical points of the geodesic potential is not one-to-one. Finally we present
the conjecture that our newly identified tensor classifiers are universal and
able to label all regular and nilpotent orbits in all homogeneous symmetric
Special Geometries. |
On Low-Energy Effective Action of Noncommutative Hypermultiplet Model: We consider the noncommutative hypermultiplet model within harmonic
superspace approach. The 1-loop four-point contributions to the effective
action of selfinteracting q-hypermultiplet are computed. This model has two
coupling constants instead of a single one in commutative case. It is shown
that both these coupling constants are generated by 1-loop quantum corrections
in the model of q-hypermultiplet interacting with vector multiplet. The
holomorphic effective action of q-hypermultiplet in external gauge superfield
is calculated. For the fundamental representation there is no UV/IR-mixing and
the holomorphic potential is a star-product generalization of a standard
commutative one. For the adjoint representation of U(N) gauge group the leading
contributions to the holomorphic effective action are given by the terms
respecting for the UV/IR-mixing which are related to U(1) phase of U(N) group. | Asymptotic critical behavior of holographic phase transition at finite
topological charge -- the spectrum of excited states becomes continuous at
$T=0$: Within the framework of AdS/CFT duality, excited states of the conformal
field living at the global AdS boundary of a four-dimensional spacetime
Einstein gravity are investigated analytically in the probe limit where the
field equations are linearized. At asymptotically large values, the threshold
chemical potential for the appearance of excited condensate states are
discrete, equal spacing, with the gap approaches zero logarithmically in the
limit $T\rightarrow 0$. Remarkably, numerical results show that, this behavior
applies even for states as low as for the first or the second excited state of
the condensate. This is especially significant on the liquid side of the black
hole van der Waals - like phase transition (small or zero topological charge)
where there seems to be no gap between the ground state and the first excited
state at zero temperature. We postulate that, at the exact limit $T = 0$ where
the gap is zero, the spectrum of threshold chemical potentials becomes
continuous, all excited states of the condensate are activated above a finite
chemical potential, suggesting a new quantum phase transition as a function of
the chemical potential. Previous studies have largely missed this continuous
spectrum of excited states in the $T\rightarrow 0$ limit. This fact should be
taken into account carefully in AdS/CFT duality studies. |
Spontaneous Lorentz Violation, Nambu-Goldstone Modes, and Massive Modes: In any theory with spontaneous symmetry breaking, it is important to account
for the massless Nambu-Goldstone and massive Higgs modes. In this short review,
the fate of these modes is examined for the case of a bumblebee model, in which
Lorentz symmetry is spontaneously broken. | Embedding Feynman Integral (Calabi-Yau) Geometries in Weighted
Projective Space: It has recently been demonstrated that Feynman integrals relevant to a wide
range of perturbative quantum field theories involve periods of Calabi-Yaus of
arbitrarily large dimension. While the number of Calabi-Yau manifolds of
dimension three or higher is considerable (if not infinite), those relevant to
most known examples come from a very simple class: degree-$2k$ hypersurfaces in
$k$-dimensional weighted projective space $\mathbb{WP}^{1,\ldots,1,k}$. In this
work, we describe some of the basic properties of these spaces and identify
additional examples of Feynman integrals that give rise to hypersurfaces of
this type. Details of these examples at three and four loops are included as
ancillary files to this work. |
Geometric twist decomposition off the light--cone for nonlocal QCD
operators: A general procedure is introduced allowing for the infinite decomposition of
nonlocal operators off the light--cone into operators of definite geometric
twist. | Large $N$ analytical functional bootstrap I: 1D CFTs and total
positivity: We initiate the analytical functional bootstrap study of conformal field
theories with large $N$ limits. In this first paper we particularly focus on
the 1D $O(N)$ vector bootstrap. We obtain a remarkably simple bootstrap
equation from the $O(N)$ vector crossing equations in the large $N$ limit. The
bootstrap bound is saturated by the generalized free field theory. We study the
analytical extremal functionals of this crossing equation, for which the total
positivity of the $SL(2,\mathbb{R})$ conformal block plays a critical role. We
prove the $SL(2,\mathbb{R})$ conformal block is totally positive for large
scaling dimension $\Delta$ and show that the total positivity is violated below
a critical value $\Delta_{\textrm{TP}}^*\approx 0.32315626$. The conformal
block forms a surprisingly sophisticated mathematical structure, which for
instance can violate total positivity at the order $10^{-5654}$ for a normal
value $\Delta=0.1627$! We construct a series of analytical functionals
$\{\alpha_M\}$ which satisfy the bootstrap positive conditions up to a range
$\Delta\leqslant \Lambda_M$. The functionals $\{\alpha_M\}$ have a trivial
large $M$ limit. Surprisingly, due to total positivity, they can approach the
large $M$ limit in a way consistent with the bootstrap positive conditions for
arbitrarily high $\Lambda_M$, therefore proving the bootstrap bound
analytically. Our result provides a concrete example to illustrate how the
analytical properties of the conformal block lead to nontrivial bootstrap
bounds. We expect this work paves the way for large $N$ analytical functional
bootstrap in higher dimensions. |
4D Effective Theory and Geometrical Approach: We consider the 4D effective theory for the light Kaluza-Klein (KK) modes.
The heavy KK mode contribution is generally needed to reproduce the correct
physical predictions: an equivalence, between the effective theory and the
D-dimensional (or geometrical) approach to spontaneous symmetry breaking (SSB),
emerges only if the heavy mode contribution is taken into account. This happens
even if the heavy mode masses are at the Planck scale. In particular, we
analyze a 6D Einstein-Maxwell model coupled to a charged scalar and fermions.
Moreover, we briefly review non-Abelian and supersymmetric extensions of this
theory. | The Holographic Dual of the $Ω$-background: We find an explicit supergravity background dual to the $\Omega$-deformation
of a four-dimensional $\mathcal{N}=2$ SCFT on $\mathbb{R}^4$. The solution can
be constructed in the five-dimensional ${\cal N}=4^+$ gauged supergravity and
has a nontrivial self-dual 2-form. When uplifted to type IIB supergravity the
background is a deformation of AdS$_5\times S^5$ which preserves 16
supercharges. We also discuss generalizations of this solution corresponding to
turning on a vacuum expectation value for a scalar operator in the dual SCFT. |
Triangle Anomalies from Einstein Manifolds: The triangle anomalies in conformal field theory, which can be used to
determine the central charge a, correspond to the Chern-Simons couplings of
gauge fields in AdS under the gauge/gravity correspondence. We present a simple
geometrical formula for the Chern-Simons couplings in the case of type IIB
supergravity compactified on a five-dimensional Einstein manifold X. When X is
a circle bundle over del Pezzo surfaces or a toric Sasaki-Einstein manifold, we
show that the gravity result is in perfect agreement with the corresponding
quiver gauge theory. Our analysis reveals an interesting connection with the
condensation of giant gravitons or dibaryon operators which effectively induces
a rolling among Sasaki-Einstein vacua. | Strings, Branes and Two-Time Physics: We generalize the ideas and formalism of Two-Time Physics from particle
dynamics to some specific examples of string and p-brane (p >= 1) dynamics. The
two-time string or p-brane action can be gauge fixed to produce various
one-time string or p-brane actions that are dual to each other under gauge
transformations. We discuss the particular gauges that correspond to
tensionless strings and p-branes in flat (d-1)+1 spacetime, rigid strings and
p-branes in flat (d-1)+1 spacetime, and tensionless strings and p-branes
propagating in the AdS_{d-n} x S^n backgrounds. |
Galileon accretion: We study steady-state spherically symmetric accretion of a galileon field
onto a Schwarzschild black hole in the test fluid approximation. The galileon
is assumed to undergo a stage of cosmological evolution, thus setting a
non-trivial boundary condition at spatial infinity. The critical flow is found
for some parameters of the theory. There is a range of parameters when the
critical flow exists, but the solution is unstable. It is also shown that for a
certain range of parameters the critical flow solution does not exist.
Depending on the model the sound horizon of the flow can be either outside or
inside of the Schwarzschild horizon. The latter property may make it
problematic to embed the galileon theory in the standard black hole
thermodynamics. | Anomaly candidates and invariants of D=4, N=1 supergravity theories: All anomaly candidates and the form of the most general invariant local
action are given for old and new minimal supergravity, including the cases
where additional Yang--Mills and chiral matter multiplets are present.
Furthermore nonminimal supergravity is discussed. In this case local
supersymmetry itself may be anomalous and some of the corresponding anomaly
candidates are given explicitly. The results are obtained by solving the
descent equations which contain the consistency equation satisfied by
integrands of anomalies and invariant actions. |
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