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p-brane Taxonomy: We review an approach to the construction and classification of p-brane
solitons in arbitrary dimensions, with an emphasis on those that arise in
toroidally-compactified M-theory. Procedures for constructing the low-energy
supergravity limits in arbitrary dimensions, and for studying the supersymmetry
properties of the solitons are presented. Wide classes of p-brane solutions are
obtained, and their properties and classification in terms of bound states and
intersections of M-branes are described. (Based on lectures presented at the
Summer School in High-Energy Physics and Cosmology, Trieste, Italy, 10 Jun - 26
Jul 1996.)
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Fermions in Geodesic Witten Diagrams: We develop the embedding formalism for odd dimensional Dirac spinors in AdS
and apply it to the (geodesic) Witten diagrams including fermionic degrees of
freedom. We first show that the geodesic Witten diagram (GWD) with fermion
exchange is equivalent to the conformal partial waves associated with the spin
one-half primary field. Then, we explicitly demonstrate the GWD decomposition
of the Witten diagram including the fermion exchange with the aid of the split
representation. The geodesic representation of CPW indeed gives the useful
basis for computing the Witten diagrams.
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Conformally invariant off-shell string physics: Using recent advances in the understanding of non-critical strings, we
construct a unique, conformally invariant continuation to off-shell momenta of
Polyakov amplitudes in critical string theory. Three-point amplitudes are
explicitly calculated. These off-shell amplitudes possess some unusual,
apparently stringy, characteristics, which are unlikely to be reproduced in a
string field theory. Thus our results may be an indication that some
fundamentally new formulation, other than string field theory, will be required
to extend our understanding of critical strings beyond the Polyakov path
integral.
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Stability of the Travelling Front of a Decaying Brane: The dynamics (in light-cone time) of the tachyon on an unstable brane in the
background of a dilaton linear along a null coordinate is a non-local
reaction-diffusion type equation, which admits a travelling front solution. We
analyze the (in-)stability of this solution using linearized perturbation
theory. We find that the front solution obtained in singular perturbation
method is stable. However, these inhomogenous solutions (unlike the homogenous
solution) also have Lyapunov exponents corresponding to unstable modes around
the (meta-)stable vacuum.
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Exactly solvable potentials of Calogero type for q-deformed Coxeter
groups: We establish that by parameterizing the configuration space of a
one-dimensional quantum system by polynomial invariants of q-deformed Coxeter
groups it is possible to construct exactly solvable models of Calogero type. We
adopt the previously introduced notion of solvability which consists of
relating the Hamiltonian to finite dimensional representation spaces of a Lie
algebra. We present explicitly the $G_2^q $-case for which we construct the
potentials by means of suitable gauge transformations.
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Energy loss in a strongly coupled anisotropic plasma: We study the energy loss of a rotating infinitely massive quark moving, at
constant velocity, through an anisotropic strongly-coupled N=4 plasma from
holography. It is shown that, similar to the isotropic plasma, the energy loss
of the rotating quark is due to either the drag force or radiation with a
continuous crossover from drag-dominated regime to the radiation dominated
regime. We find that the anisotropy has a significant effect on the energy loss
of the heavy quark, specially in the crossover regime. We argue that the energy
loss due to radiation in anisotropic media is less than the isotropic case.
Interestingly this is similar to analogous calculations for the energy loss in
weakly coupled anisotropic plasma.
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Background field method, Batalin-Vilkovisky formalism and parametric
completeness of renormalization: We investigate the background field method with the Batalin-Vilkovisky
formalism, to generalize known results, study parametric completeness and
achieve a better understanding of several properties. In particular, we study
renormalization and gauge dependence to all orders. Switching between the
background field approach and the usual approach by means of canonical
transformations, we prove parametric completeness without making use of
cohomological theorems, namely show that if the starting classical action is
sufficiently general all divergences can be subtracted by means of parameter
redefinitions and canonical transformations. Our approach applies to
renormalizable and non-renormalizable theories that are manifestly free of
gauge anomalies and satisfy the following assumptions: the gauge algebra is
irreducible and closes off shell, the gauge transformations are linear
functions of the fields, and closure is field-independent. Yang-Mills theories
and quantum gravity in arbitrary dimensions are included, as well as effective
and higher-derivative versions of them, but several other theories, such as
supergravity, are left out.
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Supergravity background of lambda-deformed model for AdS2 x S2
supercoset: Starting with the F/G supercoset model corresponding to the AdS_n x S^n
superstring one can define the lambda-model of arXiv:1409.1538 either as a
deformation of the F/F gauged WZW model or as an integrable one-parameter
generalization of the non-abelian T-dual of the AdS_n x S^n superstring sigma
model with respect to the whole supergroup F. Here we consider the case of n=2
and find the explicit form of the 4d target space background for the
lambda-model for the PSU(1,1|2)/[SO(1,1) x SO(2)] supercoset. We show that this
background represents a solution of type IIB 10d supergravity compactified on a
6-torus with only metric, dilaton Phi and the RR 5-form (represented by a
2-form F in 4d) being non-trivial. This implies that the lambda-model is Weyl
invariant at the quantum level and thus defines a consistent superstring sigma
model. The supergravity solution we find is different from the one in
arXiv:1410.1886 which should correspond to a version of the lambda-model where
only the bosonic subgroup of F is gauged. Still, the two solutions have
equivalent scaling limit of arXiv:1504.07213 leading to the isometric
background for the metric and e^Phi F which is related to the eta-deformed
AdS_2 x S^2 sigma model of arXiv:1309.5850. Similar results are expected in the
AdS_3 x S^3 and AdS_5 x S^5 cases.
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Duality and gauge invariance of noncommutative spacetime Podolsky
electromagnetic theory: The interest in higher derivatives field theories has its origin mainly in
their influence concerning the renormalization properties of physical models
and to remove ultraviolet divergences. In this letter we have introduced the
noncommutative (NC) version of the Podolsky theory and we investigated the
effect of the noncommutativity over its original gauge invariance property. We
have demonstrated precisely that the noncommutativity spoiled the gauge
invariance of the original action. After that we have used the Noether
dualization technique to obtain a dual and gauge invariant action. More than to
obtain the NC Podolsky theory, we have another motivation in this work, which
is to show that, although the introduction of noncommutativity spoils the gauge
invariance, it is possible to recover this property using a standard
dualization method which did not need any modification due to any NC effect in
the original theory, by the way
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BRST quantization of Yang-Mills theory: A purely Hamiltonian approach on
Fock space: We develop the basic ideas and equations for the BRST quantization of
Yang-Mills theories in an explicit Hamiltonian approach, without any reference
to the Lagrangian approach at any stage of the development. We present a new
representation of ghost fields that combines desirable self-adjointness
properties with canonical anticommutation relations for ghost creation and
annihilation operators, thus enabling us to characterize the physical states on
a well-defined Fock space. The Hamiltonian is constructed by piecing together
simple BRST invariant operators to obtain a minimal invariant extension of the
free theory. It is verified that the evolution equations implied by the
resulting minimal Hamiltonian provide a quantum version of the classical
Yang-Mills equations. The modifications and requirements for the inclusion of
matter are discussed in detail.
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Charge screening and confinement in the massive Schwinger model: Within the framework of Euclidean path integral and mass perturbation theory
we compute the Wilson loop of widely separated external charges for the massive
Schwinger model. From this result we show for arbitrary order mass perturbation
theory that integer external charges are completely screened, whereas for
noninteger charges a constant long-range force remains.
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Finite N analysis of matrix models for n-Ising spin on a random surface: The saddle point equation described by the eigenvalues of N by N Hermitian
matrices is analized for a finite N case and the scaling relation for the large
N is considered. The critical point and the critical exponents of matrix model
are obtained by the finite N scaling. One matrix model and two matrix model are
studied in detail. Small N behavior for n-Ising model on a random surface is
investigated.
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A Topological Field Theory for the triple Milnor linking coefficient: The subject of this work is a three-dimensional topological field theory with
a non-semisimple group of gauge symmetry with observables consisting in the
holonomies of connections around three closed loops. The connections are a
linear combination of gauge potentials with coefficients containing a set of
one-dimensional scalar fields. It is checked that these observables are both
metric independent and gauge invariant. The gauge invariance is achieved by
requiring non-trivial gauge transformations in the scalar field sector. This
topological field theory is solvable and has only a relevant amplitude which
has been computed exactly. From this amplitude it is possible to isolate a
topological invariant which is Milnor's triple linking invariant. The
topological invariant obtained in this way is in the form of a sum of multiple
contour integrals. The contours coincide with the trajectories of the three
loops mentioned before. The introduction of the one-dimensional scalar field is
necessary in order to reproduce correctly the particular path ordering of the
integration over the contours which is present in the triple Milnor linking
coefficient. This is the first example of a local topological gauge field
theory that is solvable and can be associated to a topological invariant of the
complexity of the triple Milnor linking coefficient.
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3d-3d correspondence for mapping tori: One of the main challenges in 3d-3d correspondence is that no existent
approach offers a complete description of 3d $N=2$ SCFT $T[M_3]$ --- or,
rather, a "collection of SCFTs" as we refer to it in the paper --- for all
types of 3-manifolds that include, for example, a 3-torus, Brieskorn spheres,
and hyperbolic surgeries on knots. The goal of this paper is to overcome this
challenge by a more systematic study of 3d-3d correspondence that, first of
all, does not rely heavily on any geometric structure on $M_3$ and, secondly,
is not limited to a particular supersymmetric partition function of $T[M_3]$.
In particular, we propose to describe such "collection of SCFTs" in terms of 3d
$N=2$ gauge theories with "non-linear matter'' fields valued in complex group
manifolds. As a result, we are able to recover familiar 3-manifold invariants,
such as Turaev torsion and WRT invariants, from twisted indices and
half-indices of $T[M_3]$, and propose new tools to compute more recent
$q$-series invariants $\hat Z (M_3)$ in the case of manifolds with $b_1 > 0$.
Although we use genus-1 mapping tori as our "case study," many results and
techniques readily apply to more general 3-manifolds, as we illustrate
throughout the paper.
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$R^4$ corrections to holographic Schwinger effect: We consider $R^4$ corrections to the holographic Schwinger effect in an AdS
black hole background and a confining D3-brane background. The potential
between a test particle pair are performed for both backgrounds. We find there
is no potential barrier in the critical electric field, which means that the
system becomes catastrophically unstable. It is shown that for both backgrounds
increasing the inverse 't Hooft coupling parameter $1/\lambda$ enhances the
Schwinger effect. We also discuss the possible relation between the Schwinger
effect and the viscosity-entropy ratio $\eta/s$ in strong coupling.
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Infrared resummation for derivative interactions in de Sitter space: In de Sitter space, scale invariant fluctuations give rise to infrared
logarithmic corrections to physical quantities, which eventually spoil
perturbation theories. For models without derivative interactions, it has been
known that the field equation reduces to a Langevin equation with white noise
in the leading logarithm approximation. The stochastic equation allows us to
evaluate the infrared effects nonperturbatively. We extend the resummation
formula so that it is applicable to models with derivative interactions. We
first consider the nonlinear sigma model and next consider a more general model
which consists of a noncanonical kinetic term and a potential term. The
stochastic equations derived from the infrared resummation in these models can
be understood as generalizations of the standard one to curved target spaces.
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Multi-charge accelerating black holes and spinning spindles: We construct a family of multi-dyonically charged and rotating supersymmetric
AdS$_2\times \Sigma$ solutions of $D=4$, $\mathcal{N}=4$ gauged supergravity,
where $\Sigma$ is a sphere with two conical singularities known as a spindle.
We argue that these arise as near horizon limits of extremal dyonically charged
rotating and accelerating supersymmetric black holes in AdS$_4$, that we
conjecture to exist. We demonstrate this in the non-rotating limit,
constructing the accelerating black hole solutions and showing that the
non-spinning spindle solutions arise as the near horizon limit of the
supersymmetric and extremal sub-class of these black holes. From the near
horizon solutions we compute the Bekenstein-Hawking entropy of the black holes
as a function of the conserved charges, and show that this may equivalently be
obtained by extremizing a simple entropy function. For appropriately quantized
magnetic fluxes, the solutions uplift on $S^7$, or its ${\cal N}=4$ orbifolds
$S^7/\Gamma$, to smooth supersymmetric solutions to $D=11$ supergravity, where
the entropy is expected to count microstates of the theory on $N$ M2-branes
wrapped on a spinning spindle, in the large $N$ limit.
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Koebe 1/4-Theorem and Inequalities in N=2 Super-QCD: The critical curve ${\cal C}$ on which ${\rm Im}\,\hat\tau =0$,
$\hat\tau=a_D/a$, determines hyperbolic domains whose Poincar\'e metric is
constructed in terms of $a_D$ and $a$. We describe ${\cal C}$ in a parametric
form related to a Schwarzian equation and prove new relations for $N=2$ Super
$SU(2)$ Yang-Mills. In particular, using the Koebe 1/4-theorem and Schwarz's
lemma, we obtain inequalities involving $u$, $a_D$ and $a$, which seem related
to the Renormalization Group. Furthermore, we obtain a closed form for the
prepotential as function of $a$. Finally, we show that $\partial_{\hat\tau}
\langle {\rm tr}\,\phi^2\rangle_{\hat \tau}={1\over 8\pi i b_1}\langle
\phi\rangle_{\hat\tau}^2$, where $b_1$ is the one-loop coefficient of the beta
function.
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Quantum Berezinskii-Kosterlitz-Thouless transition in the
superconducting phase of (2+1)-dimensional quantum chromodynamics: We study superconductivity in the hadron-quark mixed phase of planar quantum
chromodynamics (QCD) within the large $N$ limit of a Gross-Neveu model modified
by a repulsive vector term. At high densities, the combination of scalar
attraction and repulsive space-like part of the vector interaction squeezes
quarks into baryonic composite states, i.e., Dirac fermions with even numbers
of bosonic vortices attached. The time-like vector component induces Cooper
pairing between these Fermi surface modes. Remarkably, at zero temperature,
competition between the quark density and mass destroys superconductivity via a
Berezinskii-Kosterlitz-Thouless (BKT) phase transition driven by diverging
chiral quantum fluctuations near criticality. Dissolution of logarithmically
bound singlet diquarks is catalyzed by in-plane chiral mixing associated with
$\mathbb{Z}_2 \otimes \mathbb{Z}_2 \to \mathbb{Z}_2$ chiral symmetry breaking
of the Fermi surface into a transverse spin-polarized triplet ground state. We
calculate the QCD phase diagram for quark chemical potential above the baryon
mass based purely on Fermi surface considerations and find good agreement with
results obtained by other methods. We address similarities between our quantum
BKT transition and those found using holographic techniques.
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Sphaleron solutions of the Skyrme model from Yang-Mills holonomy: We discuss how an approximation to the axially symmetric sphalerons in the
Skyrme model can be constructed from the holonomy of a non-BPS Yang-Mills
calorons. These configurations, both in the Skyrme model and in the Euclidean
Yang-Mills theory, are characterized by two integers n and m, where n are the
winding numbers of the constituents and the second integer m defines type of
the solution, it has zero topological charge for even m and for odd values of m
the corresponding chain has total topological charge n. It is found numerically
that the holonomy of the chains of interpolating calorons--anticalorons
provides a reasonably good approximation to the corresponding
Skyrmion--antiSkyrmion chains when the topological charge of the Skyrmion
constitutents is two times more than the Chern-Pontryagin index of the caloron.
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Field Theory Supertubes: Starting with intersecting M2-branes in M-theory, the IIA supertube can be
found by compactification with a boost to the speed of light in the compact
dimension. A similar procedure applied to Donaldson-Uhlenbeck-Yau instantons on
$\bC^3$, viewed as intersecting membranes of 7D supersymmetric Yang-Mills (SYM)
theory, yields (for finite boost) a new set of 1/4 BPS equations for 6D
SYM-Higgs theory, and (for infinite boost) a generalization of the dyonic
instanton equations of 5D SYM-Higgs theory, solutions of which are interpreted
as Yang-Mills supertubes and realized as configurations of IIB string theory.
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Response of a uniformly accelerated Unruh-DeWitt detector in polymer
quantization: If an Unruh-DeWitt detector moves with a uniform acceleration in Fock-space
vacuum, then the transition rate of the detector is proportional to the thermal
spectrum. It is well known that the transition rate of the detector crucially
depends on the two-point function along the detectors trajectory and in order
to compute it the standard "$i \epsilon$" regularization is used for Fock
space. Numerically, we show here that the regulator $\epsilon$ is generic in
polymer quantization, the quantization method used in \emph{loop quantum
gravity} with a finite value $\epsilon \approx 2.16$, which leads to
non-thermal spectrum for the uniformly accelerated detector. We also discuss
the response of a spatially smeared detector.
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Integrable Classical and Quantum Gravity: In these lectures we report recent work on the exact quantization of
dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space
sigma-models coupled to gravity and a dilaton. Using methods developed in the
context of flat space integrable systems, the Wheeler-DeWitt equations for
these models can be reduced to a modified version of the Knizhnik-Zamolodchikov
equations from conformal field theory, the insertions given by singularities in
the spectral parameter plane. This basic result in principle permits the
explicit construction of solutions, i.e. physical states of the quantized
theory. In this way, we arrive at integrable models of quantum gravity with
infinitely many self-interacting propagating degrees of freedom.
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On the Solution of Topological Landau-Ginzburg Models with $c=3$: The solution is given for the $c=3$ topological matter model whose underlying
conformal theory has Landau-Ginzburg model $W=-\qa (x^4 +y^4)+\af x^2y^2$.
While consistency conditions are used to solve it, this model is probably at
the limit of such techniques. By using the flatness of the metric of the space
of coupling constants I rederive the differential equation that relates the
parameter \af\ to the flat coordinate $t$. This simpler method is also applied
to the $x^3+y^6$-model.
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Quantum evolution of the Hawking state for black holes: We give a general description of the evolving quantum state of a
Schwarzschild black hole, in the quantum field theory approximation. Such a
time-dependent description is based on introducing a choice of time slices. We
in particular consider slices that smoothly cross the horizon, and introduction
of "stationary" such slices simplifies the analysis. This analysis goes beyond
standard derivations of Hawking radiation that focus on asymptotic excitations,
and in particular gives an evolving state that is regular at the horizon, with
no explicit transplanckian dependence, and that can in principle be generalized
to incorporate interacting fields. It is also expected to be useful in
connecting to information-theoretic investigation of black hole evolution. The
description of the evolving state depends on the choice of slices as well as
coordinates on the slices and mode bases; these choices give different
"pictures" analogous to that of Schr\"odinger. Evolution does have a simpler
appearance in an energy eigenbasis, but such a basis is also singular at the
horizon; evolution of regular modes has a more complicated appearance, whose
properties may be inferred by comparing with the energy eigenbasis. In a
regular description, Hawking quanta are produced in a black hole atmosphere, at
scales comparable to the horizon size. This approach is also argued to extend
to more general asymptotics, such as that of anti de Sitter space. In the
latter context, this analysis provides a description of the hamiltonian and
evolution of a black hole that may be compared to the large-$N$ dynamics of the
proposed dual CFT.
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Hyper-Kahler manifolds and multiply-intersecting branes: Generalized membrane solutions of D=11 supergravity, for which the transverse
space is a toric hyper-K{\" a}hler manifold, are shown to have IIB duals
representing the intersection of parallel 3-branes with 5-branes whose
orientations are determined by their $Sl(2;\bZ)$ charge vectors. These IIB
solutions, which generically preserve 3/16 of the supersymmetry, can be further
mapped to solutions of D=11 supergravity representing the intersection of
parallel membranes with any number of fivebranes at arbitrary angles.
Alternatively, a subclass (corresponding to non-singular D=11 solutions) can be
mapped to solutions representing the intersection on a string of any number of
D-5-branes at arbitrary angles, again preserving 3/16 supersymmetry, as we
verify in a special case by a quaternionic extension of the analysis of
Berkooz, Douglas and Leigh. We also use similar methods to find new 1/8
supersymmetric solutions of orthogonally intersecting branes.
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A Dark Energy Model Characterized by the Age of the Universe: Quantum mechanics together with general relativity leads to the
K\'arolyh\'azy relation and a corresponding energy density of quantum
fluctuations of space-time. Based on the energy density we propose a dark
energy model, in which the age of the universe is introduced as the length
measure. This dark energy is consistent with astronomical data if the unique
numerical parameter in the dark energy model is taken to be a number of order
one. The dark energy behaves like a cosmological constant at early time and
drives the universe to an eternally accelerated expansion with power-law form
at late time. In addition, we point out a subtlety in this kind of dark energy
model.
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Chern-Simons theory in 11 dimensions as a non-perturbative phase of M
theory: A Chern-Simons theory in 11 dimensions, which is a piece of the 11
dimensional supergravity action, is considered as a quantum field theory in its
own right. We conjecture that it defines a non-perturbative phase of M theory
in which the metric and gravitino vanish. The theory is diffeomorphism
invariant but not topological in that there are local degrees of freedom.
Nevertheless, there are a countable number of momentum variables associated
with relative cobordism classes of embeddings of seven dimensional manifolds in
ten dimensional space. The canonical theory is developed in terms of an algebra
of gauge invariant observables. We find a sector of the theory corresponding to
a topological compactification in which the geometry of the compactified
directions is coded in an algebra of functions on the base manifold. The
diffeomorphism invariant quantum theory associated to this sector is
constructed, and is found to describe diffeomorphism classes of excitations of
three surfaces wrapping homology classes of the compactified dimensions.
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A matrix-model approach to integrated correlators in a $\mathcal{N}=2$
SYM theory: In a $\mathcal{N}=2$ superconformal gauge theory with matter hypermultiplets
transforming in the symmetric and anti-symmetric representations of SU($N$), we
study the integrated correlators of two Coulomb-branch operators and two
moment-map operators using localization. In the corresponding matrix model we
identify the operator associated with the integrated insertions of moment-map
operators and provide for it an exact expression valid for all values of the
coupling constant in the planar limit. This allows us to study the integrated
correlators at strong-coupling where we show that they behave as the 2-point
functions of the Coulomb-branch operators, up to an overall constant dependent
only on the conformal dimensions of the latter. The strong-coupling relation
between integrated correlators and 2-point functions turns out to be the same
as in $\mathcal{N}=4$ SYM at large $N$, despite the reduced amount of
supersymmetry in our theory.
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Domain Walls in Extended Lovelock Gravity: We derive a BPS-like first order system of equations for a family of flat
static domain walls (DWs) of dimensionally extended cubic Lovelock Gravity
coupled to massive scalar self-interacting matter. The explicit construction of
such DWs is achieved by introducing of an appropriate matter superpotential. We
further analyse the dependence of the geometric properties of the
asymptotically AdSd space-times representing distinct DWs on the shape of the
matter potential, on the values of the Lovelock couplings and on the scalar
field boundary conditions. Few explicit examples of Lovelock DWs interpolating
between AdS-type vacua of different cosmological constants are presented. In
five dimensions our method provides interesting solutions of the Myers-Robinson
Quasi-topological Gravity in the presence of matter important for the
description of the specific renormalization group flows in its holographic dual
four-dimensional CFT perturbed by relevant operators.
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Gravity Waves from Soft Theorem in General Dimensions: Classical limit of multiple soft graviton theorem can be used to compute the
angular power spectrum of long wavelength gravitational radiation in classical
scattering provided the total energy carried away by the radiation is small
compared to the energies of the scatterers. We could ensure this either by
taking the limit in which the impact parameter is large compared to the
Schwarzschild radii of the scatterers, or by taking the probe limit where one
object (the probe) has mass much smaller than the other object (the scatterer).
We compute the results to subsubleading order in soft momentum and test them
using explicit examples involving classical scattering. Our analysis also
generalizes to the case where there are multiple objects involved in the
scattering and the objects exchange mass, fragment or fuse into each other
during the scattering. A similar analysis can be carried out for soft photons
to subleading order, reproducing standard textbook results. We also discuss the
modification of soft expansion in four dimensions beyond the leading order due
to infrared divergences.
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Surface Casimir densities on a spherical brane in Rindler-like
spacetimes: The vacuum expectation value of the surface energy-momentum tensor is
evaluated for a scalar field obeying Robin boundary condition on a spherical
brane in (D+1)-dimensional spacetime $Ri\times S^{D-1}$, where $Ri$ is a
two-dimensional Rindler spacetime. The generalized zeta function technique is
used in combination with the contour integral representation. The surface
energies on separate sides of the brane contain pole and finite contributions.
Analytic expressions for both these contributions are derived. For an
infinitely thin brane in odd spatial dimensions, the pole parts cancel and the
total surface energy, evaluated as the sum of the energies on separate sides,
is finite. For a minimally coupled scalar field the surface energy-momentum
tensor corresponds to the source of the cosmological constant type.
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Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and
NLSM: The tree-level S-matrix of Einstein's theory is known to have a
representation as an integral over the moduli space of punctured spheres
localized to the solutions of the scattering equations. In this paper we
introduce three operations that can be applied on the integrand in order to
produce other theories. Starting in $d+M$ dimensions we use dimensional
reduction to construct Einstein-Maxwell with gauge group $U(1)^M$. The second
operation turns gravitons into gluons and we call it "squeezing". This gives
rise to a formula for all multi-trace mixed amplitudes in Einstein-Yang-Mills.
Dimensionally reducing Yang-Mills we find the S-matrix of a special
Yang-Mills-Scalar (YMS) theory, and by the squeezing operation we find that of
a YMS theory with an additional cubic scalar vertex. A corollary of the YMS
formula gives one for a single massless scalar with a $\phi^4$ interaction.
Starting again from Einstein's theory but in $d+d$ dimensions we introduce a
"generalized dimensional reduction" that produces the Born-Infeld theory or a
special Galileon theory in $d$ dimensions depending on how it is applied. An
extension of Born-Infeld formula leads to one for the Dirac-Born-Infeld (DBI)
theory. By applying the same operation to Yang-Mills we obtain the $U(N)$
non-linear sigma model (NLSM). Finally, we show how the Kawai-Lewellen-Tye
relations naturally follow from our formulation and provide additional
connections among these theories. One such relation constructs DBI from YMS and
NLSM.
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Aspects of Diffeomorphism and Conformal invariance in classical
Liouville theory: The interplay between the diffeomorphism and conformal symmetries (a feature
common in quantum field theories) is shown to be exhibited for the case of
black holes in two dimensional classical Liouville theory. We show that
although the theory is conformally invariant in the near horizon limit, there
is a breaking of the diffeomorphism symmetry at the classical level. On the
other hand, in the region away from the horizon, the conformal symmetry of the
theory gets broken with the diffeomorphism symmetry remaining intact.
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The M-Theory S-Matrix From ABJM: Beyond 11D Supergravity: We show that by studying the flat spacetime limit of the Mellin amplitude
associated with the four-point correlation function of scalar operators in the
stress tensor multiplet of ABJM theory, one can produce the momentum expansion
of the M-theory four-graviton S-matrix elements. Using CFT data previously
obtained from the supersymmetric localization method, we carry out this
procedure explicitly to the second nontrivial order in the momentum expansion,
and recover precisely the known $R^4$ contribution to the scattering amplitude
of super-gravitons in M-theory in eleven dimensions.
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Euclidean field theory and singular classical field configurations: Euclidean field theory on 4-dimensional sphere is suggested for the study of
high energy multiparticle production. The singular classical field
configurations are found in scalar and SU(2)-gauge theories and the cross
section of 2->n processes is calculated. It is shown,that the cross section has
a maximum at the energy compared to the sphaleron mass.
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Black holes, information, and locality: Thirty years of a deepening information paradox suggest the need to revise
our basic physical framework. Multiple indicators point toward reassessment of
the principle of locality: lack of a precise definition in quantum gravity,
behavior of high-energy scattering, hints from strings and AdS/CFT, conundrums
of quantum cosmology, and finally lack of good alternative resolutions of the
paradox. A plausible conjecture states that the non-perturbative dynamics of
gravity is unitary but nonlocal. String theory may directly address these
issues but so far important aspects remain elusive. If this viewpoint is
correct, critical questions are to understand the "correspondence" limit where
nonlocal physics reduces to local quantum field theory, and beyond, to unveil
principles of an underlying nonlocal theory.
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The algebraic structure of geometric flows in two dimensions: There is a common description of different intrinsic geometric flows in two
dimensions using Toda field equations associated to continual Lie algebras that
incorporate the deformation variable t into their system. The Ricci flow admits
zero curvature formulation in terms of an infinite dimensional algebra with
Cartan operator d/dt. Likewise, the Calabi flow arises as Toda field equation
associated to a supercontinual algebra with odd Cartan operator d/d \theta -
\theta d/dt. Thus, taking the square root of the Cartan operator allows to
connect the two distinct classes of geometric deformations of second and fourth
order, respectively. The algebra is also used to construct formal solutions of
the Calabi flow in terms of free fields by Backlund transformations, as for the
Ricci flow. Some applications of the present framework to the general class of
Robinson-Trautman metrics that describe spherical gravitational radiation in
vacuum in four space-time dimensions are also discussed. Further iteration of
the algorithm allows to construct an infinite hierarchy of higher order
geometric flows, which are integrable in two dimensions and they admit
immediate generalization to Kahler manifolds in all dimensions. These flows
provide examples of more general deformations introduced by Calabi that
preserve the Kahler class and minimize the quadratic curvature functional for
extremal metrics.
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Classical/quantum integrability in non-compact sector of AdS/CFT: We discuss non-compact SL(2,R) sectors in N=4 SYM and in AdS string theory
and compare their integrable structures. We formulate and solve the
Riemann-Hilbert problem for the finite gap solutions of the classical sigma
model and show that at one loop it is identical to the classical limit of Bethe
equations of the spin (-1/2) chain for the dilatation operator of SYM.
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Non-supersymmetric Orientifolds of Gepner Models: Starting from a previously collected set of tachyon-free closed strings, we
search for N=2 minimal model orientifold spectra which contain the standard
model and are free of tachyons and tadpoles at lowest order. For each class of
tachyon-free closed strings -- bulk supersymmetry, automorphism invariants or
Klein bottle projection -- we do indeed find non-supersymmetric and tachyon
free chiral brane configurations that contain the standard model. However, a
tadpole-cancelling hidden sector could only be found in the case of bulk
supersymmetry. Although about half of the examples we have found make use of
branes that break the bulk space-time supersymmetry, the resulting massless
open string spectra are nevertheless supersymmetric in all cases. Dropping the
requirement that the standard model be contained in the spectrum, we find
chiral tachyon and tadpole-free solutions in all three cases, although in the
case of bulk supersymmetry all massless spectra are supersymmetric. In the
other two cases we find truly non-supersymmetric spectra, but a large fraction
of them are nevertheless partly or fully supersymmetric at the massless level.
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String and Fivebrane Solitons: Singular or Non-singular?: We ask whether the recently discovered superstring and superfivebrane
solutions of D=10 supergravity admit the interpretation of non-singular
solitons even though, in the absence of Yang-Mills fields, they exhibit
curvature singularities at the origin. We answer the question using a test
probe/source approach, and find that the nature of the singularity is
probe-dependent. If the test probe and source are both superstrings or both
superfivebranes, one falls into the other in a finite proper time and the
singularity is real, whereas if one is a superstring and the other a
superfivebrane it takes an infinite proper time (the force is repulsive!) and
the singularity is harmless. Black strings and fivebranes, on the other hand,
always display real singularities.
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Finite-size effects on the phase transition in a four- and six-fermion
interaction model: We consider four- and six-fermion interacting models at finite temperature
and density. We construct the corresponding free energies and investigate the
appearance of first- and second-order phase transitions. Finite-size effects on
the phase structure are investigated using methods of quantum field theory on
toroidal topologies
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Note On The Dilaton Effective Action And Entanglement Entropy: In this note we do the analysis of entanglement entropy more carefully when
the non-conformal theory flows to a non-trivial IR fixed point. In particular
we emphasize the role of the trace of the energy-momentum tensor in these
calculations. We also compare the current technique for evaluating the
entanglement entropy, particularly the Green's function method for gaussian
theories, with the dilaton effective action approach and show that they compute
identical quantities. As a result of this, the dilaton effective action
approach can be thought of as an extension of Green's function technique to
interacting theories.
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Nonlocal multi-trace sources and bulk entanglement in holographic
conformal field theories: We consider CFT states defined by adding nonlocal multi-trace sources to the
Euclidean path integral defining the vacuum state. For holographic theories, we
argue that these states correspond to states in the gravitational theory with a
good semiclassical description but with a more general structure of bulk
entanglement than states defined from single-trace sources. We show that at
leading order in large N, the entanglement entropies for any such state are
precisely the same as those of another state defined by appropriate
single-trace effective sources; thus, if the leading order entanglement
entropies are geometrical for the single-trace states of a CFT, they are
geometrical for all the multi-trace states as well. Next, we consider the
perturbative calculation of 1/N corrections to the CFT entanglement entropies,
demonstrating that these show qualitatively different features, including
non-analyticity in the sources and/or divergences in the naive perturbative
expansion. These features are consistent with the expectation that the 1/N
corrections include contributions from bulk entanglement on the gravity side.
Finally, we investigate the dynamical constraints on the bulk geometry and the
quantum state of the bulk fields which must be satisfied so that the entropies
can be reproduced via the quantum-corrected Ryu-Takayanagi formula.
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Trans-Planckian Dark Energy?: It has recently been proposed by Mersini et al. 01, Bastero-Gil and Mersini
02 that the dark energy could be attributed to the cosmological properties of a
scalar field with a non-standard dispersion relation that decreases
exponentially at wave-numbers larger than Planck scale (k_phys > M_Planck). In
this scenario, the energy density stored in the modes of trans-Planckian
wave-numbers but sub-Hubble frequencies produced by amplification of the vacuum
quantum fluctuations would account naturally for the dark energy. The present
article examines this model in detail and shows step by step that it does not
work. In particular, we show that this model cannot make definite predictions
since there is no well-defined vacuum state in the region of wave-numbers
considered, hence the initial data cannot be specified unambiguously. We also
show that for most choices of initial data this scenario implies the production
of a large amount of energy density (of order M_Planck^4) for modes with
momenta of order M_Planck, far in excess of the background energy density. We
evaluate the amount of fine-tuning in the initial data necessary to avoid this
back-reaction problem and find it is of order H/M_Planck. We also argue that
the equation of state of the trans-Planckian modes is not vacuum-like.
Therefore this model does not provide a suitable explanation for the dark
energy.
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Covariant Quantization of d=4 Brink-Schwarz Superparticle with Lorentz
Harmonics: Covariant first and second quantization of the free d=4 massless
superparticle are implemented with the introduction of purely gauge auxiliary
spinor Lorentz harmonics. It is shown that the general solution of the
condition of maslessness is a sum of two independent chiral superfields with
each of them corresponding to finite superspin. A translationally covariant, in
general bijective correspondence between harmonic and massless superfields is
constructed. By calculation of the commutation function it is shown that in the
considered approach only harmonic fields with correct connection between spin
and statistics and with integer negative homogeneity index satisfy the
microcausality condition. It is emphasized that harmonic fields that arise are
reducible at integer points. The index spinor technique is used to describe
infinite-component fields of finite spin; the equations of motion of such
fields are obtained, and for them Weinberg's theorem on the connection between
massless helicity particles and the type of nongauge field that describes them
is generalized.
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Theory of Superselection Sectors for Generalized Ising models: We apply the theory of superselection sectors in the same way as done by
G.Mack and V.Schomerus for the Ising model to generalizations of this model
described by J.Fr\"{o}hlich and T.Kerler.
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Noncommutative geometry and the classical orbits of particles in a
central force potential: We investigate the effect of the noncommutative geometry on the classical
orbits of particles in a central force potential. The relation is implemented
through the modified commutation relations $[x_i, x_j]=i \theta_{ij} $.
Comparison with observation places severe constraints on the value of the
noncommutativity parameter.
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The effective action of a BPS Alice string: Recently a BPS Alice string has been found in a $U(1)\times SU(2)$ gauge
theory coupled with a charged complex adjoint scalar field arXiv:1703.08971. It
is a half BPS state preserving a half of supercharges when embedded into a
supersymmetric gauge theory. In this paper, we study zero modes of a BPS Alice
string. After presenting $U(1)$ and translational zero modes, we construct the
effective action of these modes. In contrast to previous analysis of the
conventional Alice string for which only large distance behaviors are known, we
can perform calculation exactly in the full space thanks to BPS properties.
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Observations on the Space of Four Dimensional String and $M$ theory
Vacua: The space of four dimensional string and $M$ theory vacua with non-Abelian
gauge symmetry, chiral fermions and unbroken supersymmetry beyond the
electroweak scale appears to be a disconnected space whose different components
represent distinct universality classes of vacua. Calculating statistical
distributions of physical observables a la Douglas therefore requires that the
distinct components are carefully accounted for. We highlight some classes of
vacua which deserve further study and suggest an argument which may serve to
rule out vacua which are small perturbations of supersymmetric $AdS_4$.
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String Cosmology with a Time-Dependent Antisymmetric Tensor Potential: We present a class of exact solutions for homogeneous, anisotropic
cosmologies in four dimensions derived from the low-energy string effective
action including a homogeneous dilaton $\phi$ and antisymmetric tensor
potential $B_{\mu\nu}$. Making this potential time-dependent produces an
anisotropic energy-momentum tensor, and leads us to consider a Bianchi I
cosmology. The solution for the axion field must then only be a linear function
of one spatial coordinate. This in turn places an upper bound on the product of
the two scale factors evolving perpendicular to the gradient of the axion
field. The only late-time isotropic solution is then a {\em contracting}
universe.
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Microcausality of Dirac field on noncommutative spacetime: We study the microcausality of free Dirac field on noncommutative spacetime.
We calculate the vacuum and non-vacuum state expectation values for the Moyal
commutator $[\bar{\psi}_{\alpha}(x)\star\psi_{\beta}(x),\bar{\psi}_
{\sigma}(x^{\prime})\star\psi_{\tau}(x^{\prime})]_{\star}$ of Dirac field on
noncommutative spacetime. We find that they do not vanish for some cases of the
indexes for an arbitrary spacelike interval, no matter whether $\theta^{0i}=0$
or $\theta^{0i}\neq0$. However for the physical observable quantities of Dirac
field such as the Lorentz scalar $:\bar{\psi}(x)\star\psi(x):$ and the current
$j^{\mu}(x)=:\bar{\psi}(x)\gamma^{\mu}\star\psi(x):$ etc., we find that they
still satisfy the microcausality. Therefore microcausality is satisfied for
Dirac field on noncommutative spacetime.
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Defects composed of kinks and Q-balls: analytical solutions and
stability: In this paper all the defect-type solutions in a family of scalar field
theories with a real and a complex field in (1+1) dimensional Minkowski
spacetime have been analytically identified. Three types of solutions have been
found: (a) topological kinks without the presence of $Q$-balls, (b) defects
which consist of a topological kink coupled with a $Q$-ball and (c) a
one-parameter family of solutions where a $Q$-ball is combined with a
non-topological soliton. The properties of these solutions and its linear
stability are also discussed.
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Mode Interactions of the Tachyon Condensate in p-adic String Theory: We study the fluctuation modes for lump solutions of the tachyon effective
potential in p-adic open string theory. We find a discrete spectrum with
equally spaced mass squared levels. We also find that the interactions derived
from this field theory are consistent with p-adic string amplitudes for excited
string states.
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Fermions on one or fewer Kinks: We find the full spectrum of fermion bound states on a Z_2 kink. In addition
to the zero mode, there are int[2 m_f/m_s] bound states, where m_f is the
fermion and m_s the scalar mass. We also study fermion modes on the background
of a well-separated kink-antikink pair. Using a variational argument, we prove
that there is at least one bound state in this background, and that the energy
of this bound state goes to zero with increasing kink-antikink separation, 2L,
and faster than e^{-a2L} where a = min(m_s, 2 m_f). By numerical evaluation, we
find some of the low lying bound states explicitly.
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Anomaly analysis of Hawking radiation from 2+1 dimensional spinning
black hole: Considering gravitational and gauge anomalies at the horizon, a new
successful method that to derive Hawking radiations from black holes has been
developed recently by Wilczek et al.. By using the dimensional reduction
technique, we apply this method to a non-vacuum solution, the 2+1 dimensional
spinning black hole. The Hawking temperature and angular velocity on the
horizon are obtained. The results may partially imply that this method is
independent of the gravity theory, the dimension of spacetime and the
topological structure of the event horizon.
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Yangian symmetry in deformed WZNW models on squashed spheres: We introduce a deformation of the Wess-Zumino-Novikov-Witten model with
three-dimensional squashed sphere target space. We show how with an appropriate
choice of Wess--Zumino and boundary terms it is possible to construct an
infinite family of conserved charges realizing an SU(2) Yangian. Finally we
discuss the running of the squashing parameter under renormalization group
flow.
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On the Time Evolution of Holographic n-partite Information: We study various scaling behaviors of n-partite information during a process
of thermalization after a global quantum quench for n disjoint system
consisting of n parallel strips whose widths are much larger than the
separation between them. By making use of the holographic description for
entanglement entropy we explore holographic description of the n-partite
information by which we show that it has a definite sign: it is positive for
even n and negative for odd n. This might be thought of as an intrinsic
property of a field theory which has gravity dual.
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Phase Space Discretization and Moyal Quantization: The Moyal quantization is described as a discretization of the classical
phase space by using difference analogue of vector fields. Difference analogue
of Lie brackets plays the role of Heisenberg commutators.
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Slow-walking inflation: We propose a new model of slow-roll inflation in string cosmology, based on
warped throat supergravity solutions displaying `walking' dynamics, i.e. the
coupling constant of the dual gauge theory slowly varies over a range of energy
scales. The features of the throat geometry are sourced by a rich field
content, given by the dilaton and RR and NS fluxes. By considering the motion
of a D3-brane probe in this geometry, we are able to analytically calculate the
brane potential in a physically interesting regime. This potential has an
inflection point: in its proximity we realize a model of inflation lasting
sixty e-foldings, and whose robust predictions are in agreement with current
observations. We are also able to interpret some of the most interesting
aspects of this scenario in terms of the properties of the QFT dual theory.
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Charge Screening and Confinement in Hot 3-D QED: We examine the possibility of a confinement-deconfinement phase transition at
finite temperature in both parity invariant and topologically massive
three-dimensional quantum electrodynamics. We review an argument showing that
the Abelian version of the Polyakov loop operator is an order parameter for
confinement, even in the presence of dynamical electrons. We show that, in the
parity invariant case, where the tree-level Coulomb potential is logarithmic,
there is a Berezinskii-Kosterlitz-Thouless transition at a critical temperature
($T_c=e^2/8\pi+{\cal O}(e^4/m)$, when the ratio of the electromagnetic coupling
and the temperature to the electron mass is small). Above $T_c$ the electric
charge is not confined and the system is in a Debye plasma phase, whereas below
$T_c$ the electric charges are confined by a logarithmic Coulomb potential,
qualitatively described by the tree-level interaction. When there is a
topological mass, no matter how small, in a strict sense the theory is not
confining at any temperature; the model exhibits a screening phase, analogous
to that found in the Schwinger model and two-dimensional QCD with massless
adjoint matter. However, if the topological mass is much smaller than the other
dimensional parameters, there is a temperature for which the range of the
Coulomb interaction changes from the inverse topological mass to the inverse
electron mass. We speculate that this is a vestige of the BKT transition of the
parity-invariant system, separating regions with screening and deconfining
behavior.
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Krylov complexity in quantum field theory, and beyond: We study Krylov complexity in various models of quantum field theory: free
massive bosons and fermions on flat space and on spheres, holographic models,
and lattice models with the UV-cutoff. In certain cases we find asymptotic
behavior of Lanczos coefficients, which goes beyond previously observed
universality. We confirm that in all cases the exponential growth of Krylov
complexity satisfies the conjectural inequality, which generalizes the
Maldacena-Shenker-Stanford bound on chaos. We discuss temperature dependence of
Lanczos coefficients and note that the relation between the growth of Lanczos
coefficients and chaos may only hold for the sufficiently late, truly
asymptotic regime governed by the physics at the UV cutoff. Contrary to
previous suggestions, we show scenarios when Krylov complexity in quantum field
theory behaves qualitatively differently from the holographic complexity.
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Gauged N=4 supergravities: We present the gauged N=4 (half-maximal) supergravities in four and five
spacetime dimensions coupled to an arbitrary number of vector multiplets. The
gaugings are parameterized by a set of appropriately constrained constant
tensors, which transform covariantly under the global symmetry groups SL(2) x
SO(6,n) and SO(1,1) x SO(5,n), respectively. In terms of these tensors the
universal Lagrangian and the Killing Spinor equations are given. The known
gaugings, in particular those originating from flux compactifications, are
incorporated in the formulation, but also new classes of gaugings are found.
Finally, we present the embedding chain of the five dimensional into the four
dimensional into the three dimensional gaugings, thereby showing how the
deformation parameters organize under the respectively larger duality groups.
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Inflation coupled to a Gauss-Bonnet term: The newly released Planck CMB data place tight constraints on slow-roll
inflationary models. Some of commonly discussed inflationary potentials are
disfavored due mainly to the large tensor-to-scalar ratio. In this paper we
show that these potentials may be in good agreement with the Planck data when
the inflaton has a non-minimal coupling to the Gauss-Bonnet term. Moreover,
such a coupling violates the consistency relation between the tensor spectral
index and tensor-to-scalar ratio. If the tensor spectral index is allowed to
vary freely, the Planck constraints on the tensor-to-scalar ratio are slightly
improved.
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Operator Algebra in Logarithmic Conformal Field Theory: For some time now, conformal field theories in two dimensions have been
studied as integrable systems. Much of the success of these studies is related
to the existence of an operator algebra of the theory. In this paper, some of
the extensions of this machinery to the logarithmic case are studied, and used.
More precisely, from Mobius symmetry constraints, the generic three and four
point functions of logarithmic quasiprimary fields are calculated in closed
form for arbitrary Jordan rank. As an example, c=0 disordered systems with
non-degenerate vacua are studied. With the aid of two, three and four point
functions, the operator algebra is obtained and associativity of the algebra
studied.
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Constraints on Sequential Discontinuities from the Geometry of On-shell
Spaces: We present several classes of constraints on the discontinuities of Feynman
integrals that go beyond the Steinmann relations. These constraints follow from
a geometric formulation of the Landau equations that was advocated by Pham, in
which the singularities of Feynman integrals correspond to critical points of
maps between on-shell spaces. To establish our results, we review elements of
Picard-Lefschetz theory, which connect the homotopy properties of the space of
complexified external momenta to the homology of the combined space of on-shell
internal and external momenta. An important concept that emerges from this
analysis is the question of whether or not a pair of Landau singularities is
compatible-namely, whether or not the Landau equations for the two
singularities can be satisfied simultaneously. Under conditions we describe,
sequential discontinuities with respect to non-compatible Landau singularities
must vanish. Although we only rigorously prove results for Feynman integrals
with generic masses in this paper, we expect the geometric and algebraic
insights that we gain will also assist in the analysis of more general Feynman
integrals.
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Nucleation at finite temperature beyond the superminispace model: The transition from the quantum to the classical regime of the nucleation of
the closed Robertson-Walker Universe with spacially homogeneous matter fields
is investigated with a perturbation expansion around the sphaleron
configuration. A criterion is derived for the occurrence of a first-order type
transition, and the related phase diagram for scalar and vector fields is
obtained. For scalar fields both the first and second order transitions can
occur depending on the shape of the potential barrier. For a vector field, here
that of an O(3) nonlinear $\sigma$-model, the transition is seen to be only of
the first order.
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N=(4,4), 2D supergravity in SU(2)xSU(2) harmonic superspace: We work out the basics of conformal $N=(4,4)$, 2D supergravity in the
$N=(4,4)$, 2D analytic harmonic superspace with two independent sets of
harmonic variables. We define the relevant most general analytic superspace
diffeomorphism group and show that in the flat limit it goes over into the
``large'' $N=(4,4)$, 2D superconformal group. The basic objects of the
supergravity considered are analytic vielbeins covariantizing two
analyticity-preserving harmonic derivatives. For self-consistency they should
be constrained in a certain way. We solve the constraints and show that the
remaining irreducible field content in a WZ gauge amounts to a new short
$N=(4,4)$ Weyl supermultiplet. As in the previously known cases, it involves no
auxiliary fields and the number of remaining components in it coincides with
the number of residual gauge invariances. We discuss various truncations of
this ``master'' conformal supergravity group and its compensations via
couplings to $N=(4,4)$ superconformal matter multiplets. Besides recovering the
standard minimal off-shell $N=(4,4)$ conformal and Poincar\'e supergravity
multiplets, we find, at the linearized level, several new off-shell gauge
representations.
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Black-Hole Solutions to Einstein's Equations in the Presence of Matter
and Modifications of Gravitation in Extra Dimensions: In this thesis, we wish to examine the black-hole solutions of modified
gravity theories inspired by String Theory or Cosmology. Namely, these
modifications will take the guise of additional gauge and scalar fields for the
so-called Einstein-Maxwell-Dilaton theories with an exponential Liouville
potential; and of extra spatial dimensions for Einstein-Gauss-Bonnet theories.
The black-hole solutions of EMD theories as well as their integrability are
reviewed. One of the main results is that a master equation is obtained in the
case of planar horizon topology, which allows to completely integrate the
problem for s special relationship between the couplings. We also classify
existing solutions. We move on to the study of Gauss-Bonnet black holes,
focusing on the six-dimensional case. It is found that the Gauss-Bonnet
coupling exposes the Weyl tensor of the horizon to the dynamics, severely
restricting the Einstein spaces admissible and effectively lifting some of the
degeneracy on the horizon topology. We then turn to the study of the
thermodynamic properties of black holes, in General Relativity as well as in
EMD theories. For the latter, phase transitions may be found in the canonical
ensemble, which resemble the phase transitions for Reissner-Nordstr\"om black
holes. Generically, we find that the thermodynamic properties (stability, order
of phase transitions) depend crucially on the values of the EMD coupling
constants. Finally, we interpret our planar EMD solutions holographically as
Infra-Red geometries through the AdS/CFT correspondence, taking into account
various validity constraints. We also compute AC and DC conductivities as
applications to Condensed Matter Systems, and find some properties
characteristic of strange metal behaviour.
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New higher-derivative invariants in N=2 supergravity and the
Gauss-Bonnet term: A new class of N=2 locally supersymmetric higher-derivative invariants is
constructed based on logarithms of conformal primary chiral superfields. They
characteristically involve a coupling to R_{\mu\nu}^2 - 1/3*R^2, which equals
the non-conformal part of the Gauss-Bonnet term. Upon combining one such
invariant with the known supersymmetric version of the square of the Weyl
tensor, one obtains the supersymmetric extension of the Gauss-Bonnet term. The
construction is carried out in the context of both conformal superspace and the
superconformal multiplet calculus. The new class of supersymmetric invariants
resolves two open questions. The first concerns the proper identification of
the 4D supersymmetric invariants that arise from dimensional reduction of the
5D mixed gauge-gravitational Chern-Simons term. The second is why the pure
Gauss-Bonnet term without supersymmetric completion has reproduced the correct
result in calculations of the BPS black hole entropy in certain models.
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Magnetic Monopoles Near the Black Hole Threshold: We present new analytic and numerical results for self-gravitating
SU(2)-Higgs magnetic monopoles approaching the black hole threshold. Our
investigation extends to large Higgs self-coupling, lambda, a regime heretofore
unexplored. When lambda is small, the critical solution where a horizon first
appears is extremal Reissner-Nordstrom outside the horizon but has a
nonsingular interior. When lambda is large, the critical solution is an
extremal black hole with non-Abelian hair and a mass less than the extremal
Reissner-Nordstrom value. The transition between these two regimes is
reminiscent of a first-order phase transition. We analyze in detail the
approach to these critical solutions as the Higgs expectation value is varied,
and compare this analysis with the numerical results.
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Non-perturbative N=1 strings from geometric singularities: The study of curved D-brane geometries in type II strings implies a general
relation between local singularities $\cx W$ of Calabi-Yau manifolds and
gravity free supersymmetric QFT's. The minimal supersymmetric case is described
by F-theory compactifications on $\cx W$ and can be used as a starting point to
define minimal supersymmetric heterotic string compactifications on compact
Calabi-Yau manifolds with holomorphic, stable gauge backgrounds. The geometric
construction generalizes to non-perturbative vacua with five-branes and
provides a framework to study non-perturbative dynamics of the heterotic
theory.
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Left Regular Representation of $sl_q(3)$: Reduction and Intertwiners: Reduction of the left regular representation of quantum algebra $sl_q(3)$ is
studied and ~$q$-difference intertwining operators are constructed. The
irreducible representations correspond to the spaces of local sections of
certain line bundles over the q-flag manifold.
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Traversable Casimir Wormholes in D Dimensions: Wormholes (WH) require negative energy, and therefore an exotic matter
source. Since Casimir energy is negative, it has been speculated as a good
candidate to source that objects a long time ago. However only very recently a
full solution for D = 4 has been found by Garattini [1], thus the Casimir
energy can be a source of traversable WHs. Soon later Alencar et al [2] have
shown, that this is not true in D = 3. In this paper, we show that Casimir
energy can be a source of the Morris-Thorne WH for all spacetime with D > 3.
Finally, we add the cosmological constant and find that for D = 3 Casimir WHs
are possible, however, the space must always being AdS. For D > 3, we show that
the cosmological constant invert the signal with increasing throat size.
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Constrained superfields from an anti-D3-brane in KKLT: The KKLT construction of dS vacua relies on an uplift term that arises from
an anti-D3-brane. It was argued by Kachru, Pearson and Verlinde that this
anti-D3-brane is an excited state in a supersymmetric theory since it can decay
to a supersymmetric ground state. Hence the anti-D3-brane breaks supersymmetry
spontaneously and one should be able to package all the world-volume fields on
the anti-D3-brane into a four dimensional $\cal{N}=1$ supersymmetric action.
Here we extend previous results and identify the constrained superfields that
correspond to all the degrees of freedom on the anti-D3-brane. In particular,
we show explicitly that the four 4D worldvolume spinors give rise to
constrained chiral multiplets $S$ and $Y^i$, $i=1,2,3$ that satisfy
$S^2=SY^i=0$. We also conjecture (and provide evidence in a forthcoming
publication) that the vector field $A_\mu$ and the three scalars $\phi^i$ give
rise to a field strength multiplet $W_\alpha$ and three chiral multiplets $H^i$
that satisfy the constraints $S W_\alpha= \bar{D}_{\dot \alpha} (S \bar
H^i)=0$. This is the first time that such constrained multiplets appear in
string theory constructions.
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Newtonian versus black-hole scattering: We discuss non-relativistic scattering by a Newtonian potential. We show that
the gray-body factors associated with scattering by a black hole exhibit the
same functional dependence as scattering amplitudes in the Newtonian limit,
which should be the weak-field limit of any quantum theory of gravity. This
behavior arises independently of the presence of supersymmetry. The connection
to two-dimensional conformal field theory is also discussed.
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Static Axisymmetric Vacuum Solutions and Non-Uniform Black Strings: We describe new numerical methods to solve the static axisymmetric vacuum
Einstein equations in more than four dimensions. As an illustration, we study
the compactified non-uniform black string phase connected to the uniform
strings at the Gregory-Laflamme critical point. We compute solutions with a
ratio of maximum to minimum horizon radius up to nine. For a fixed
compactification radius, the mass of these solutions is larger than the mass of
the classically unstable uniform strings. Thus they cannot be the end state of
the instability.
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Fundamental theories in a phantom universe: Starting with the holographic dark energy model of Li it is shown that the
holographic screen at the future event horizon is sent toward infinity in the
phantom energy case, so allowing for the existence of unique fundamental
theories which are mathematically consistent in phantom cosmologies.
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A Functional Approach to the Heat Kernel in Curved Space: The heat kernel $M_{xy} = <x\mid exp [ 1/\sqrt{g} \partial_\mu g^{\mu\nu}
\sqrt{g} \partial_\nu ]t \mid y>$ is of central importance when studying the
propagation of a scalar particle in curved space. It is quite convenient to
analyze this quantity in terms of classical variables by use of the quantum
mechanical path integral; regrettably it is not entirely clear how this path
integral can be mathematically well defined in curved space. An alternate
approach to studying the heat kernel in terms of classical variables was
introduced by Onofri. This technique is shown to be applicable to problems in
curved space; an unambiguous expression for $M_{xy}$ is obtained which involves
functional derivatives of a classical quantity. We illustrate how this can be
used by computing $M_{xx}$ to lowest order in the curvature scalar R.
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Quantum Gravity and Lorentz invariance violation in the Standard Model: The most important problem of fundamental Physics is the quantization of the
gravitational field. A main difficulty is the lack of available experimental
tests that discriminate among the theories proposed to quantize gravity.
Recently, Lorentz invariance violation by Quantum Gravity(QG) have been the
source of a growing interest. However, the predictions depend on ad-hoc
hypothesis and too many arbitrary parameters. Here we show that the Standard
Model(SM) itself contains tiny Lorentz invariance violation(LIV) terms coming
from QG. All terms depend on one arbitrary parameter $\alpha$ that set the
scale of QG effects. This parameter can be estimated using data from the Ultra
High Energy Cosmic Rays spectrum to be $|\alpha|<\sim 10^{-22}-10^{-23}$.
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Black Hole Entropy Function and the Attractor Mechanism in Higher
Derivative Gravity: We study extremal black hole solutions in D dimensions with near horizon
geometry AdS_2\times S^{D-2} in higher derivative gravity coupled to other
scalar, vector and anti-symmetric tensor fields. We define an entropy function
by integrating the Lagrangian density over S^{D-2} for a general AdS_2\times
S^{D-2} background, taking the Legendre transform of the resulting function
with respect to the parameters labelling the electric fields, and multiplying
the result by a factor of 2\pi. We show that the values of the scalar fields at
the horizon as well as the sizes of AdS_2 and S^{D-2} are determined by
extremizing this entropy function with respect to the corresponding parameters,
and the entropy of the black hole is given by the value of the entropy function
at this extremum. Our analysis relies on the analysis of the equations of
motion and does not directly make use of supersymmetry or specific structure of
the higher derivative terms.
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A Cosmological Super-Bounce: We study a model for a non-singular cosmic bounce in N=1 supergravity, based
on supergravity versions of the ghost condensate and cubic Galileon scalar
field theories. The bounce is preceded by an ekpyrotic contracting phase which
prevents the growth of anisotropies in the approach to the bounce, and allows
for the generation of scale-invariant density perturbations that carry over
into the expanding phase of the universe. We present the conditions required
for the bounce to be free of ghost excitations, as well as the tunings that are
necessary in order for the model to be in agreement with cosmological
observations. All of these conditions can be met. Our model thus provides a
proof-of-principle that non-singular bounces are viable in supergravity,
despite the fact that during the bounce the null energy condition is violated.
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BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and
new defect CFT data: We compute the expectation values of BPS Wilson loops in the mass-deformed
ABJM theory using the Fermi gas technique. We obtain explicit results in terms
of Airy functions, effectively resumming the full 1/N expansion up to
exponentially small terms. In the maximal supersymmetric case, these
expressions enable us to derive multi-point correlation functions for
topological operators belonging to the stress tensor multiplet, in the presence
of a 1/2--BPS Wilson line. From the one-point correlator, we recover the ABJM
Bremsstrahlung function, confirming nicely previous results obtained through
latitude Wilson loops. Likewise, higher point correlators can be used to
extract iteratively new defect CFT data for higher dimensional topological
operators. We present a detailed example of the dimension-two operator
appearing in the OPE of two stress tensor multiplets.
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Kinks bounded by fermions: We present and study new mechanism of interaction between the solitons based
on the exchange interaction mediated by the localized fermion states. As
particular examples, we consider solutions of simple 1+1 dimensional scalar
field theories with self-interaction potentials, including sine-Gordon model
and the polynomial $\phi^4$, $\phi^6$ models, coupled to the Dirac fermions
with back-reaction. We discover that there is an additional fermion exchange
interaction between the solitons, it leads to the formation of static
multi-soliton bound states. Further, we argue that similar mechanisms of
formation of stable coupled multi-soliton configurations can be observed for a
wide class of physical systems.
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Modular symmetry of massive free fermions: We construct an infinite set of conserved tensor currents of rank $2n$,
$n=1,2,\dots$, in the two-dimensional theory of free massive fermions, which
are bilinear in the fermionic fields. The one-point functions of these currents
on the torus depend on the modular parameter $\tau$ and spin structure
$(\alpha,\beta)$. We show that, upon scaling the mass $m$ so as to keep the
combination $m^2$Im($\tau$) invariant, the one-point functions are
non-holomorphic Jacobi forms of weights $(2n,0)$ or $(0,2n)$ and index 0, with
respect to the modular parameter $\tau$ and elliptic parameter
$z=\alpha\tau+\beta$. In particular, we express the one-point functions as
Kronecker-Eisenstein-type sums over the lattice $\mathbb{Z}\tau+\mathbb{Z}$,
which makes the modular symmetry manifest. We show that there is an action of
three differential operators on these Jacobi forms which form an
$\mathfrak{sl}_2(\mathbb{R})$ Lie algebra. Further we show that these Jacobi
forms obey three differential equations arising from the representation theory
of the Jacobi group.
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Spin(11,3), particles and octonions: The fermionic fields of one generation of the Standard Model, including the
Lorentz spinor degrees of freedom, can be identified with components of a
single real 64-dimensional semi-spinor representation S of the group
Spin(11,3). We describe an octonionic model for Spin(11,3) in which the
semi-spinor representation gets identified with S=OxO', where O,O' are the
usual and split octonions respectively. It is then well-known that choosing a
unit imaginary octonion u in Im(O) equips O with a complex structure J.
Similarly, choosing a unit imaginary split octonion u' in Im(O') equips O' with
a complex structure J', except that there are now two inequivalent complex
structures, one parametrised by a choice of a timelike and the other of a
spacelike unit u'. In either case, the identification S=OxO' implies that there
are two natural commuting complex structures J, J' on S. Our main new
observation is that the subgroup of Spin(11,3) that commutes with both J, J' on
S is the direct product Spin(6) x Spin(4) x Spin(1,3) of the Pati-Salam and
Lorentz groups, when u' is chosen to be timelike. The splitting of S into
eigenspaces of J corresponds to splitting into particles and anti-particles.
The splitting of S into eigenspaces of J' corresponds to splitting of Lorentz
Dirac spinors into two different chiralities. We also study the simplest
possible symmetry breaking scenario with the "Higgs" field taking values in the
representation that corresponds to 3-forms in R^{11,3}. We show that this Higgs
can be designed to transform as the bi-doublet of the left/right symmetric
extension of the SM, and thus breaks Spin(11,3) down to the product of the SM,
Lorentz and U(1)_{B-L} groups, with the last one remaining unbroken. This
3-form Higgs field also produces the Dirac mass terms for all the particles.
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Warped AdS_3 Black Holes: Three dimensional topologically massive gravity (TMG) with a negative
cosmological constant -\ell^{-2} and positive Newton constant G admits an AdS_3
vacuum solution for any value of the graviton mass \mu. These are all known to
be perturbatively unstable except at the recently explored chiral point
\mu\ell=1. However we show herein that for every value of \mu\ell< 3 there are
two other (potentially stable) vacuum solutions given by SL(2,R)x
U(1)-invariant warped AdS_3 geometries, with a timelike or spacelike U(1)
isometry.
Critical behavior occurs at \mu\ell=3, where the warping transitions from a
stretching to a squashing, and there are a pair of warped solutions with a null
U(1) isometry. For \mu\ell>3, there are known warped black hole solutions which
are asymptotic to warped AdS_3. We show that these black holes are discrete
quotients of warped AdS_3 just as BTZ black holes are discrete quotients of
ordinary AdS_3. Moreover new solutions of this type, relevant to any theory
with warped AdS_3 solutions, are exhibited. Finally we note that the black hole
thermodynamics is consistent with the hypothesis that, for \mu\ell>3, the
warped AdS_3 ground state of TMG is holographically dual to a 2D boundary CFT
with central charges c_R={15(\mu\ell)^2+81\over G\mu((\mu\ell)^2+27)} and
c_L={12 \mu\ell^2\over G((\mu\ell)^2+27)}.
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The Born-Infeld Sphaleron: We study the SU(2) electroweak model in which the standard Yang-Mills
coupling is supplemented by a Born-Infeld term. The deformation of the
sphaleron and bisphaleron solutions due to the Born-Infeld term is investigated
and new branches of solutions are exhibited. Especially, we find a new branch
of solutions connecting the Born-Infeld sphaleron to the first solution of the
Kerner-Gal'tsov series.
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Yukawa Couplings for Bosonic $Z_N$ Orbifolds: Their Moduli and Twisted
Sector Dependence: The three point correlation functions with twist fields are determined for
bosonic $Z_N$ orbifolds. Both the choice of the modular background (compatible
with the twist) and of the (higher) twisted sectors involved are fully general.
We point out a necessary restriction on the set of instantons contributing to
twist field correlation functions not obtained in previous calculations. Our
results show that the theory is target space duality invariant.
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Detuning the BSW Effect with Longitudinal String Spreading: Black holes are interesting astrophysical objects that have been studied as
systems sensitive to quantum gravitational data. The accelerated geometry in
the exterior of extremal black holes can induce large center-of-mass energies
between particles with particular momenta at the horizon. This is known as the
Ba\~nados-Silk-West (BSW) effect. For point particles, the BSW effect requires
tuning to have the collision coincide with the horizon. However, this tuning is
relaxed for string-theoretic objects. String scattering amplitudes are large in
the Regge limit, occurring at large center-of-mass energies and shallow
scattering angles, parametrically surpassing quantum field theoretic
amplitudes. In this limit, longitudinal string spreading is induced between
strings with a large difference in light-cone momenta, and this spread can be
used to 'detune' the BSW effect. With this in mind, quantum gravitational data,
as described by string theory, may play an important role in near horizon
dynamics of extremal Kerr black holes. Further, though it may be hard to
realize astrophysically, this system acts as a natural particle accelerator for
probing the nature of small-scale physics at Planckian energies.
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Courant sigma model and $L_\infty$-algebras: The Courant sigma model is a 3-dimensional topological sigma model of AKSZ
type which has been used for the systematic description of closed strings in
non-geometric flux backgrounds. In particular, the expression for the fluxes
and their Bianchi identities coincide with the local form of the axioms of a
Courant algebroid. On the other hand, the axioms of a Courant algebroid also
coincide with the conditions for gauge invariance of the Courant sigma model.
In this paper we embed this interplay between background fluxes of closed
strings, gauge (or more precisely BRST) symmetries of the Courant sigma model
and axioms of a Courant algebroid into an $L_\infty$-algebra structure. We show
how the complete BV-BRST formulation of the Courant sigma model is described in
terms of $L_\infty$-algebras. Moreover, the morphism between the
$L_\infty$-algebra for a Courant algebroid and the one for the corresponding
sigma model is constructed.
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Holographic entanglement beyond classical gravity: The Renyi entropies and entanglement entropy of 1+1 CFTs with gravity duals
can be computed by explicit construction of the bulk spacetimes dual to
branched covers of the boundary geometry. At the classical level in the bulk
this has recently been shown to reproduce the conjectured Ryu-Takayanagi
formula for the holographic entanglement entropy. We study the one-loop bulk
corrections to this formula. The functional determinants in the bulk geometries
are given by a sum over certain words of generators of the Schottky group of
the branched cover. For the case of two disjoint intervals on a line we obtain
analytic answers for the one-loop entanglement entropy in an expansion in small
cross-ratio. These reproduce and go beyond anticipated universal terms that are
not visible classically in the bulk. We also consider the case of a single
interval on a circle at finite temperature. At high temperatures we show that
the one-loop contributions introduce expected finite size corrections to the
entanglement entropy that are not present classically. At low temperatures, the
one-loop corrections capture the mixed nature of the density matrix, also not
visible classically below the Hawking-Page temperature.
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Nonlinear QED Effects in Strong-Field Magnetohydrodynamics: We examine wave propagation and the formation of shocks in strongly
magnetized plasmas by applying a variational technique and the method of
characteristics to the coupled magnetohydrodynamic (MHD) and
quantum-electrodynamic (QED) equations of motion. In sufficiently strong
magnetic fields such as those found near neutron stars, not only is the plasma
extremely relativistic but the effects of QED must be included to understand
processes in the magnetosphere. As Thompson & Blaes [1] find, the fundamental
modes in the extreme relativistic limit of MHD coupled with QED are two
oppositely directed Alfv\'{e}n modes and the fast mode. QED introduces
nonlinear couplings which affect the propagation of the fast mode such that
waves traveling in the fast mode evolve as vacuum electromagnetic ones do in
the presence of an external magnetic field [2] (Heyl & Hernquist 1998). The
propagation of a single Alfv\'{e}n mode is unaffected but QED does alter the
coupling between the Alfv\'{e}n modes.
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G2 Hitchin functionals at one loop: We consider the quantization of the effective target space description of
topological M-theory in terms of the Hitchin functional whose critical points
describe seven-manifolds with G2 structure. The one-loop partition function for
this theory is calculated and an extended version of it, that is related to
generalized G2 geometry, is compared with the topological G2 string. We relate
the reduction of the effective action for the extended G2 theory to the Hitchin
functional description of the topological string in six dimensions. The
dependence of the partition functions on the choice of background G2 metric is
also determined.
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The Seiberg-Witten Differential From M-Theory: The form of the Seiberg-Witten differential is derived from the M-theory
approach to N=2 supersymmetric Yang-Mills theories by directly imposing the BPS
condition for twobranes ending on fivebranes. The BPS condition also implies
that the pullback of the Kahler form onto the space part of the twobrane
world-volume vanishes.
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Faddeev-Jackiw Quantization of the Gauge Invariant Self-dual Fields
Relative to String Theory: We obtain a new symplectic Lagrangian density and deduce Faddeev-Jackiw (FJ)
generalized brackets of the gauge invariant self-dual fields interacting with
gauge fields. We further give FJ quantization of this system. Furthermore, the
FJ method is compared with Dirac method, the results show the two methods are
equivalent in the quantization of this system. And by the practical research in
this letter, it can be found that the FJ method is really simpler than the
Dirac method, namely, the FJ method obviates the need to distinguish primary
and secondary constraints and first- and second-class constraints. Therefore,
the FJ method is a more economical and effective method of quantization.
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Non-Supersymmetric F-Theory Compactifications on Spin(7) Manifolds: We propose a novel approach to obtain non-supersymmetric four-dimensional
effective actions by considering F-theory on manifolds with special holonomy
Spin(7). To perform such studies we suggest that a duality relating M-theory on
a certain class of Spin(7) manifolds with F-theory on the same manifolds times
an interval exists. The Spin(7) geometries under consideration are constructed
as quotients of elliptically fibered Calabi-Yau fourfolds by an
anti-holomorphic and isometric involution. The three-dimensional minimally
supersymmetric effective action of M-theory on a general Spin(7) manifold with
fluxes is determined and specialized to the aforementioned geometries. This
effective theory is compared with an interval Kaluza-Klein reduction of a
non-supersymmetric four-dimensional theory with definite boundary conditions
for all fields. Using this strategy a minimal set of couplings of the
four-dimensional low-energy effective actions is obtained in terms of the
Spin(7) geometric data. We also discuss briefly the string interpretation in
the Type IIB weak coupling limit.
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Collaborating with David Gross; Descendants of the Chiral Anomaly: I recall my collaboration with David Gross. A result about descendants of the
chiral anomaly is presented: Chern-Simons terms can be written as total
derivatives.
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The Berry Phase and Monopoles in Non-Abelian Gauge Theories: We consider the quantum mechanical notion of the geometrical (Berry) phase in
SU(2) gauge theory, both in the continuum and on the lattice. It is shown that
in the coherent state basis eigenvalues of the Wilson loop operator naturally
decompose into the geometrical and dynamical phase factors. Moreover, for each
Wilson loop there is a unique choice of U(1) gauge rotations which do not
change the value of the Berry phase. Determining this U(1) locally in terms of
infinitesimal Wilson loops we define monopole-like defects and study their
properties in numerical simulations on the lattice. The construction is gauge
dependent, as is common for all known definitions of monopoles. We argue that
for physical applications the use of the Lorenz gauge is most appropriate. And,
indeed, the constructed monopoles have the correct continuum limit in this
gauge. Physical consequences are briefly discussed.
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The Spinning Particles as a Nonlinear Realizations of the Superworldline
Reparametrization Invariance: The superdiffeomorphisms invariant description of $N$ - extended spinning
particle is constructed in the framework of nonlinear realizations approach.
The action is universal for all values of $N$ and describes the time evolution
of $D+2$ different group elements of the superdiffeomorphisms group of the
$(1,N)$ superspace. The form of this action coincides with the one-dimensional
version of the gravity action, analogous to Trautman's one.
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Pseudomoduli Dark Matter and Quiver Gauge Theories: We investigate supersymmetric models for dark matter which is represented by
pseudomoduli in weakly coupled hidden sectors. We propose a scheme to add a
dark matter sector to quiver gauge theories with metastable supersymmetry
breaking. We discuss the embedding of such scheme in string theory and we
describe the dark matter sector in terms of D7 flavour branes. We explore the
phenomenology in various regions of the parameters.
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Entropy formula in Einstein-Maxwell-Dilaton theory and its validity for
black strings: We consider near horizon fall-off conditions of stationary black holes in
Einstein-Maxwell-Dilaton theory and find conserved charge conjugate to symmetry
generator that preserves near horizon fall-off conditions. Subsequently, we
find supertranslation, superrotation and multiple-charge modes. We apply the
obtained results on a typical static dilaton black hole and on a charged
rotating black string, as examples. In this case, supertranslation
double-zero-mode charge $\mathcal{T}_{(0,0)}$ is not equal to black hole
entropy times Hawking temperature. This may be seen as a problem but it is not,
because, in Einstein-Maxwell-Dilaton theory, we have a U(1) gauge freedom and
we use an appropriate gauge fixing to fix that problem. We show that new
entropy formula $4 \pi \hat{J}^{+}_{0} \hat{J}^{-}_{0}$, proposed in \cite{17},
is valid for black strings as well as black holes.
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How does Casimir energy fall? IV. Gravitational interaction of
regularized quantum vacuum energy: Several years ago we demonstrated that the Casimir energy for perfectly
reflecting and imperfectly reflecting parallel plates gravitated normally, that
is, obeyed the equivalence principle. At that time the divergences in the
theory were treated only formally, without proper regularization, and the
coupling to gravity was limited to the canonical energy-momentum-stress tensor.
Here we strengthen the result by removing both of those limitations. We
consider, as a toy model, massless scalar fields interacting with
semitransparent ($\delta$-function) potentials defining parallel plates, which
become Dirichlet plates for strong coupling. We insert space and time
point-split regulation parameters, and obtain well-defined contributions to the
self- energy of each plate, and the interaction energy between the plates.
(This self-energy does not vanish even in the conformally-coupled,
strong-coupled limit.) We also compute the local energy density, which requires
regularization near the plates. In general, the energy density includes a
surface energy that resides precisely on the boundaries. This energy is also
regulated. The gravitational interaction of this well-defined system is then
investigated, and it is verified that the equivalence principle is satisfied.
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Unruh thermal hadronization and the cosmological constant: We use black holes with a negative cosmological constant to investigate
aspects of the freeze-out temperature for hadron production in high energy
heavy-ion collisions. The two black hole solutions present in the anti-de
Sitter geometry have different mass and are compared to the data showing that
the small black hole solution is in good agreement. This is a new feature in
the literature since the small black hole in general relativity has different
thermodynamic behavior from that of the large black hole solution. We find that
the inclusion of the cosmological constant (which can be interpreted as the
plasma pressure) leads to a lowering of the temperature of the freeze-out curve
as a function of the baryochemical potential, improving the description
previously suggested by Castorina, Kharzeev, and Satz.
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Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N
Four-Point Functions: We introduce the impact-parameter representation for conformal field theory
correlators of the form A ~ < O_1 O_2 O_1 O_2 >. This representation is
appropriate in the eikonal kinematical regime, and approximates the conformal
partial-wave decomposition in the limit of large spin and dimension of the
exchanged primary. Using recent results on the two-point function < O_1 O_1
>_{shock} in the presence of a shock wave in Anti-de Sitter, and its relation
to the discontinuity of the four-point amplitude A across a kinematical
branch-cut, we find the high spin and dimension conformal partial- wave
decomposition of all tree-level Anti-de Sitter Witten diagrams. We show that,
as in flat space, the eikonal kinematical regime is dominated by the T-channel
exchange of the massless particle with highest spin (graviton dominance). We
also compute the anomalous dimensions of the high-spin O_1 O_2 composites.
Finally, we conjecture a formula re-summing crossed-ladder Witten diagrams to
all orders in the gravitational coupling.
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Unitary evolution of perturbations of a two-dimensional black hole: We discuss massive scalar perturbations of a two-dimensional dilaton black
hole. We employ a Pauli-Villars reqularization scheme to calculate the effect
of the scalar perturbation on the Bekenstein-Hawking entropy. By concentrating
on the dynamics of the scalar field near the horizon, we argue that quantum
effects alter the effective potential. We calculate the two-point function
explicitly and show that it exhibits Poincare recurrences.
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A note on W symmetry of N=2 gauge theory: The AGT correspondence indicates $\mathcal{N}=2$ gauge theory possesses of W
algebra symmetry. We study how the conformal block of Toda CFT gives the
expectation value of Casimir operators of gauge theory. The $A_2$ Toda CFT with
$W_3$ symmetry is taken as the main example.
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The Quantum Affine Origin of the AdS/CFT Secret Symmetry: We find a new quantum affine symmetry of the S-matrix of the one-dimensional
Hubbard chain. We show that this symmetry originates from the quantum affine
superalgebra U_q(gl(2|2)), and in the rational limit exactly reproduces the
secret symmetry of the AdS/CFT worldsheet S-matrix.
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Explore the Origin of Spontaneous Symmetry Breaking from Adaptive
Perturbation Method: Spontaneous symmetry breaking occurs when the underlying laws of a physical
system are symmetric, but the vacuum state chosen by the system is not. The
(3+1)d $\phi^4$ theory is relatively simple compared to other more complex
theories, making it a good starting point for investigating the origin of
non-trivial vacua. The adaptive perturbation method is a technique used to
handle strongly coupled systems. The study of strongly correlated systems is
useful in testing holography. It has been successful in strongly coupled QM and
is being generalized to scalar field theory to analyze the system in the
strong-coupling regime. The unperturbed Hamiltonian does not commute with the
usual number operator. However, the quantized scalar field admits a plane-wave
expansion when acting on the vacuum. While quantizing the scalar field theory,
the field can be expanded into plane-wave modes, making the calculations more
tractable. However, the Lorentz symmetry, which describes how physical laws
remain the same under certain spacetime transformations, might not be manifest
in this approach. The proposed elegant resummation of Feynman diagrams aims to
restore the Lorentz symmetry in the calculations. The results obtained using
this method are compared with numerical solutions for specific values of the
coupling constant $\lambda = 1, 2, 4, 8, 16$. Finally, we find evidence for
quantum triviality, where self-consistency of the theory in the UV requires
$\lambda = 0$. This result implies that the $\phi^4$ theory alone does not
experience SSB, and the $\langle \phi\rangle = 0$ phase is protected under the
RG-flow by a boundary of Gaussian fixed-points.
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The action principle and the supersymmetrisation of Chern-Simons terms
in eleven-dimensional supergravity: We develop computational tools for calculating supersymmetric higher-order
derivative corrections to eleven-dimensional supergravity using the action
principle approach. We show that, provided the superspace Bianchi identities
admit a perturbative solution in the derivative expansion, there are at least
two independent superinvariants at the eight-derivative order of
eleven-dimensional supergravity. Assuming the twelve-superforms associated to
certain anomalous Chern-Simons terms are Weil-trivial, there will be a third
independent superinvariant at this order. Under certain conditions, at least
two superinvariants will survive to all orders in the derivative expansion.
However only one of them will be present in the quantum theory: the
supersymmetrization of the Chern-Simons terms of eleven dimensional
supergravity required for the cancellation of the M5-brane gravitational
anomaly by inflow. This superinvariant can be shown to be unique at the
eight-derivative order, assuming it is quartic in the fields. On the other
hand, a necessary condition for the superinvariant to be quartic is the
exactness, in tau-cohomology, of X0,8 -the purely spinorial component of the
eight-superform related by descent to the M5-brane anomaly polynomial. In that
case it can also be shown that the solution of the Weil-triviality condition of
the corresponding twelve-form, which is a prerequisite for the explicit
construction of the superinvariant, is guaranteed to exist. We prove that
certain highly non-trivial necessary conditions for the tau-exactness of X0,8
are satisfied. Moreover any potential superinvariant associated to anomalous
Chern-Simons terms at the eight-derivative order must necessarily contain terms
cubic or lower in the fields.
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The Distribution of Ground State Energies in JT Gravity: It is shown that the distribution of the lowest energy eigenvalue of the
quantum completions of Jackiw-Teitelboim gravity is completely described by a
non-linear ordinary differential equation (ODE) arising from a non-perturbative
treatment of a special random Hermitian matrix model. Its solution matches the
result recently obtained by computing a Fredholm determinant using quadrature
methods. The new ODE approach allows for analytical expressions for the
asymptotic behaviour to be extracted. The results are highly analogous to the
well-known Tracy-Widom distribution for the lowest eigenvalue of Gaussian
random Hermitian matrices, which appears in a very diverse set of physical and
mathematical contexts. Similarly, it is expected that the new distribution
characterizes a type of universality that can arise in various gravity
settings, including black hole physics in various dimensions, and perhaps
beyond. It has an association to a special multicritical generalization of the
Gross-Witten-Wadia phase transition.
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Three Dimensional Black Hole Coupled to the Born-Infeld Electrodynamics: A nonlinear charged version of the (2+1)-anti de Sitter black hole solution
is derived. The source to the Einstein equations is a Born-Infeld
electromagnetic field, which in the weak field limit becomes the (2+1)-Maxwell
field. The obtained Einstein-Born-Infeld solution for certain range of the
parameters (mass, charge, cosmological and Born-Infeld constants) represent a
static circularly symmetric black hole. Although the covariant metric
components and the electric field do not exhibit a singular behavior at r=0 the
curvature invariants are singular at that point.
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A Rational Logarithmic Conformal Field Theory: We analyse the fusion of representations of the triplet algebra, the
maximally extended symmetry algebra of the Virasoro algebra at c=-2. It is
shown that there exists a finite number of representations which are closed
under fusion. These include all irreducible representations, but also some
reducible representations which appear as indecomposable components in fusion
products.
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On Massive Mixed Symmetry Tensor Fields in Minkowski Space and (A)dS: In this paper we give explicit gauge invariant Lagrangian formulation for
massive theories based on mixed symmetry tensors \Phi_{[\mu\nu],\alpha},
T_{[\mu\nu\alpha],\beta} and R_{[\mu\nu],[\alpha\beta]} both in Minkowski as
well as in (Anti) de Sitter spaces. In particular, we study all possible
massless and partially massless limits for such theories in (A)dS.
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The Chern-Simons term in a dual Josephson junction: A dual Josephson junction corresponding to a (2+1)-dimensional
non-superconducting layer sandwiched between two (3+1)-dimensional dual
superconducting regions constitutes a model of localization of a U(1) gauge
field within the layer. Monopole tunneling currents flow from one dual
superconducting region to another due to a phase difference between the wave
functions of the monopole condensate below and above the non-superconducting
layer when there is an electromagnetic field within the layer. These magnetic
currents appear within the (2+1)-dimensional layer as a gas of magnetic
instanton events and a weak electric charge confinement is expected to take
place at very long distances within the layer. In the present work, we consider
what happens when one introduces fermions in this physical scenario. Due to the
dual Meissner effect featured in the dual superconducting bulk, it is argued
that unconfined fermions would be localized within the (2+1)-dimensional layer,
where their quantum fluctuations radiatively induce a Chern-Simons term, which
is known to destroy the electric charge confinement and to promote the
confinement of the magnetic instantons.
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Gauge Invariances and Phases of Massive Higher Spins in (A)dS: The (m^2,\Lambda) plane of spin s>1 massive fields in (A)dS backgrounds is
shown to consist of separate phases, divided by lines of novel ``partially
massless'' gauge theories that successively remove helicities, starting from
the lowest, 0 or +/-(1/2). The norms of the excluded states flip as the gauge
lines are crossed and only the region containing the massive Minkowski theory
is unitary. The partially massless gauge theories are unitary or not, depending
on the ordering of the gauge lines. This ``level splitting'' of massless
Minkowski gauge theories is specific to non-zero \Lambda.
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Two-dimensional topological field theories as taffy: In this paper we use trivial defects to define global taffy-like operations
on string worldsheets, which preserve the field theory. We fold open and closed
strings on a space X into open strings on products of multiple copies of X, and
perform checks that the "taffy-folded" worldsheets have the same massless
spectra and other properties as the original worldsheets. Such folding tricks
are a standard method in the defects community; the novelty of this paper lies
in deriving mathematical identities to check that e.g. massless spectra are
invariant in topological field theories. We discuss the case of the B model
extensively, and also derive the same identities for string topology, where
they become statements of homotopy invariance. We outline analogous results in
the A model, B-twisted Landau-Ginzburg models, and physical strings. We also
discuss the understanding of the closed string states as the Hochschild
homology of the open string algebra, and outline possible applications to
elliptic genera.
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On the constrained KP hierarchy II, An additional remark: This is an additional remark to the paper (hep-th 9411005) concerning a
Hamiltonian structure of suggested there system of equations. The remark is
inspired by a letter from L. Feher and I. Marshall.
|
On unique parametrization of the linear group GL(4.C) and its subgroups
by using the Dirac matrix algebra basis: A unifying overview of the ways to parameterize the linear group GL(4.C) and
its subgroups is given. As parameters for this group there are taken 16
coefficients G = G(A,B,A_{k}, B_{k}, F_{kl}) in resolving matrix G in terms of
16 basic elements of the Dirac matrix algebra. Alternatively to the use of 16
tensor quantities, the possibility to parameterize the group GL(4.C) with the
help of four 4-dimensional complex vectors (k, m, n, l) is investigated. The
multiplication rules G'G are formulated in the form of a bilinear function of
two sets of 16 variables. The detailed investigation is restricted to
6-parameter case G(A, B, F_{kl}), which provides us with spinor covering for
the complex orthogonal group SO(3.1.C). The complex Euler's angles
parametrization for the last group is also given. Many different
parametrizations of the group based on the curvilinear coordinates for complex
extension of the 3-space of constant curvature are discussed. The use of the
Newmann-Penrose formalism and applying quaternion techniques in the theory of
complex Lorentz group are considered. Connections between
Einstein-Mayer study on semi-vectors and Fedorov's treatment of the Lorentz
group theory are stated in detail. Classification of fermions in intrinsic
parities is given on the base of the theory of representations for spinor
covering of the complex Lorentz group.
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Effective Superstrings: We generalize the method of quantizing effective strings proposed by
Polchinski and Strominger to superstrings. The Ramond-Neveu-Schwarz string is
different from the Green-Schwarz string in non-critical dimensions. Both are
anomaly-free and Poincare invariant. Some implications of the results are
discussed. The formal analogy with 4D (super)gravity is pointed out.
|
Worldsheet computation of heavy-light correlators: We compute a large collection of string worldsheet correlators describing
light probes interacting with heavy black hole microstates. The heavy states
consist of NS5 branes carrying momentum and/or fundamental string charge. In
the fivebrane decoupling limit, worldsheet string theory on a family of such
backgrounds is given by exactly solvable null-gauged WZW models. We construct
physical vertex operators in these cosets, including all massless fluctuations.
We first compute a large class of novel heavy-light-light-heavy correlators in
the AdS$_3$ limit, where the light operators include those dual to chiral
primaries of the holographically dual CFT. We compare a subset of these
correlators to the holographic CFT at the symmetric product orbifold point, and
find precise agreement in all cases, including for light operators in twisted
sectors of the orbifold CFT. The agreement is highly non-trivial, and includes
amplitudes that describe the analogue of Hawking radiation for these
microstates. We further derive a formula for worldsheet correlators consisting
of $n$ light insertions on these backgrounds, and discuss which subset of these
correlators are likely to be protected. As a test, we compute a heavy-light
five-point function, obtaining precisely the same result both from the
worldsheet and the symmetric orbifold CFT. This paper is a companion to and
extension of [arXiv:2203.13828].
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Dressing Symmetries of Holomorphic BF Theories: We consider holomorphic BF theories, their solutions and symmetries. The
equivalence of Cech and Dolbeault descriptions of holomorphic bundles is used
to develop a method for calculating hidden (nonlocal) symmetries of holomorphic
BF theories. A special cohomological symmetry group and its action on the
solution space are described.
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On Dynamics of Strings and Branes: We study Nambu-Goto strings and branes. It is shown that they can be
considered as continuous limits of ordered discrete sets of relativistic
particles for which the tangential velocities are excluded from the action. The
linear in unphysical momenta constraints are found. It allows to derive the
evolution operators for the objects under consideration from the "first
principles".
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$\mathcal N=3$ four dimensional field theories: We briefly review a class of four dimensional $\mathcal N=3$ field theories
constructed by taking a quotient of $\mathcal N=4$ SYM with gauge group $U(N)$.
The quotient involves a discrete symmetry that only exists for specific, order
one, values of the coupling constant, so the resulting theories are
intrinsically strongly coupled. These theories admit a simple realization in
string theory as the worldvolume theory of a stack of D3 branes probing a
generalized orientifold plane, or S-fold. Their holographic dual is given by a
non-trivial F-theory fibration over $AdS_5 \times S^5/\mathbb Z_k$ which is
weakly curved but with the string coupling frozen at an order one value.
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Exciting LLM Geometries: We study excitations of LLM geometries. These geometries arise from the
backreaction of a condensate of giant gravitons. Excitations of the condensed
branes are open strings, which give rise to an emergent Yang-Mills theory at
low energy. We study the dynamics of the planar limit of these emergent gauge
theories, accumulating evidence that they are planar ${\cal N}=4$ super
Yang-Mills. There are three observations supporting this conclusion: (i) we
argue for an isomorphism between the planar Hilbert space of the original
${\cal N}=4$ super Yang-Mills and the planar Hilbert space of the emergent
gauge theory, (ii) we argue that the OPE coefficients of the planar limit of
the emergent gauge theory vanish and (iii) we argue that the planar spectrum of
anomalous dimensions of the emergent gauge theory is that of planar ${\cal
N}=4$ super Yang-Mills. Despite the fact that the planar limit of the emergent
gauge theory is planar ${\cal N}=4$ super Yang-Mills, we explain why the
emergent gauge theory is not ${\cal N}=4$ super Yang-Mills theory.
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Rigid nongeometric orientifolds and the swampland: Nongeometric flux compactifications with frozen complex structure moduli have
been recently studied for several phenomenological purposes. In this context,
we analyze the possibility of realizing de-Sitter solutions in the context of
${\cal N} =1$ type II nongeometric flux compactifications using the ${\mathbb
T}^6/({\mathbb Z}_3 \times {\mathbb Z}_3)$ toroidal orientifolds. For the type
IIB case, we observe that the Bianchi identities are too strong to
simultaneously allow both the NS-NS three-form flux ($H_3$) and the
nongeometric ($Q$) flux to take non-zero values, which makes this model
irrelevant for phenomenology due to the no-scale structure. For the type IIA
case, we find that all the (nongeometric) flux solutions satisfying the Bianchi
identities result in de-Sitter no-go scenarios except for one case in which the
no-go condition can be evaded. However for this case also, in our (limited)
numerical investigation we do not find any de-Sitter vacua using the integer
fluxes satisfying all the Bianchi identities.
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Yang-Mills Instantons from Gravitational Instantons: We show that every gravitational instantons are SU(2) Yang-Mills instantons
on a Ricci-flat four manifold although the reverse is not necessarily true. It
is shown that gravitational instantons satisfy exactly the same self-duality
equation of SU(2) Yang-Mills instantons on the Ricci-flat manifold determined
by the gravitational instantons themselves. We explicitly check the
correspondence with several examples and discuss their topological properties.
|
Holographic Subregion Complexity in Einstein-Born-Infeld theory: We numerically investigate the evolution of the holographic subregion
complexity during a quench process in Einstein-Born-Infeld theory. Based on the
subregion CV conjecture, we argue that the subregion complexity can be treated
as a probe to explore the interior of the black hole. The effects of the
nonlinear parameter and the charge on the evolution of the holographic
subregion complexity are also investigated. When the charge is sufficiently
large, it not only changes the evolution pattern of the subregion complexity,
but also washes out the second stage featured by linear growth.
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The $1/N$ expansion of the symmetric traceless and the antisymmetric
tensor models in rank three: We prove rigorously that the symmetric traceless and the antisymmetric tensor
models in rank three with tetrahedral interaction admit a $1/N$ expansion, and
that at leading order they are dominated by melon diagrams. This proves the
recent conjecture of I. Klebanov and G. Tarnopolsky in JHEP 10 (2017) 037
[arXiv:1706.00839], which they checked numerically up to 8th order in the
coupling constant.
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The continuum limit of the conformal sector at second order in
perturbation theory: Recently a novel perturbative continuum limit for quantum gravity has been
proposed and demonstrated to work at first order. Every interaction monomial
$\sigma$ is dressed with a coefficient function $f^\sigma_\Lambda(\varphi)$ of
the conformal factor field, $\varphi$. Each coefficient function is
parametrised by an infinite number of underlying couplings, and decays at large
$\varphi$ with a characteristic amplitude suppression scale which can be chosen
to be at a common value, $\Lambda_\text{p}$. Although the theory is
perturbative in couplings it is non-perturbative in $\hbar$. At second order in
perturbation theory, one must sum over all melonic Feynman diagrams to obtain
the particular integral. We show that it leads to a well defined renormalized
trajectory and thus continuum limit, provided it is solved by starting at an
arbitrary cutoff scale $\Lambda=\mu$ which lies in the range
$0<\mu<a\Lambda_\text{p}$ ($a$ some non-universal number). If $\mu$ lies above
this range the resulting coefficient functions become singular, and the flow
ceases to exist, before the physical limit is reached. To this one must add a
well-behaved complementary solution, containing irrelevant couplings determined
uniquely by the first-order interactions, and renormalized relevant couplings.
Even though some irrelevant couplings diverge in the limit
$\Lambda_\text{p}\to\infty$, domains for the underlying relevant couplings can
be chosen such that diffeomorphism invariance will be recovered in this limit,
and where the underlying couplings disappear to be replaced by effective
diffeomorphism invariant couplings.
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Natural Inflation and Quantum Gravity: Cosmic Inflation provides an attractive framework for understanding the early
universe and the cosmic microwave background. It can readily involve energies
close to the scale at which Quantum Gravity effects become important. General
considerations of black hole quantum mechanics suggest nontrivial constraints
on any effective field theory model of inflation that emerges as a low-energy
limit of quantum gravity, in particular the constraint of the Weak Gravity
Conjecture. We show that higher-dimensional gauge and gravitational dynamics
can elegantly satisfy these constraints and lead to a viable,
theoretically-controlled and predictive class of Natural Inflation models.
|
Bigravity and Lorentz-violating Massive Gravity: Bigravity is a natural arena where a non-linear theory of massive gravity can
be formulated. If the interaction between the metrics $f$ and $g$ is
non-derivative, spherically symmetric exact solutions can be found. At large
distances from the origin, these are generically Lorentz-breaking bi-flat
solutions (provided that the corresponding vacuum energies are adjusted
appropriately). The spectrum of linearized perturbations around such
backgrounds contains a massless as well as a massive graviton, with {\em two}
physical polarizations each. There are no propagating vectors or scalars, and
the theory is ghost free (as happens with certain massive gravities with
explicit breaking of Lorentz invariance). At the linearized level, corrections
to GR are proportional to the square of the graviton mass, and so there is no
vDVZ discontinuity. Surprisingly, the solution of linear theory for a static
spherically symmetric source does {\em not} agree with the linearization of any
of the known exact solutions. The latter coincide with the standard
Schwarzschild-(A)dS solutions of General Relativity, with no corrections at
all. Another interesting class of solutions is obtained where $f$ and $g$ are
proportional to each other. The case of bi-de Sitter solutions is analyzed in
some detail.
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On the Entropy of Quantum Fields in Black Hole Backgrounds: We show that the partition function for a scalar field in a static spacetime
background can be expressed as a functional integral in the corresponding
optical space, and point out that the difference between this and the
functional integral in the original metric is a Liouville type action. A
general formula for the free energy is derived in the high temperature
approximation and applied to various cases. In particular we find that
thermodynamics in the extremal Reissner-Nordstr\"om space has extra
singularities that make it ill-defined.
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The 't Hooft-Polyakov Monopole in the Presence of a 't Hooft Operator: We present explicit BPS field configurations representing one nonabelian
monopole with one minimal weight 't Hooft operator insertion. We explore the
SO(3) and SU(2) gauge groups. In the case of SU(2) gauge group the minimal 't
Hooft operator can be completely screened by the monopole. If the gauge group
is SO(3), however, such screening is impossible. In the latter case we observe
a different effect of the gauge symmetry enhancement in the vicinity of the 't
Hooft operator.
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Five-dimensional topologically twisted maximally supersymmetric
Yang-Mills theory: Herein, we consider a topologically twisted version of maximally
supersymmetric Yang-Mills theory in five dimensions which was introduced by
Witten in 2011. We consider this theory on a five manifold of the form M_4 x I
for M_4 an oriented Riemannian four manifold. The complete and unique action of
the theory in bulk is written down and is shown to be invariant under two
scalar supersymmetries.
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On D-branes in the Nappi-Witten and GMM gauged WZW models: We construct D-branes in the Nappi-Witten (NW) and
Guadagnini-Martellini-Mintchev (GMM) gauged WZW models. For the $SL(2,R)\times
SU(2)/U(1)\times U(1)$ NW and $SU(2)\times SU(2)/U(1)$ GMM models we present
the explicit equations describing the D-brane hypersurfaces in their target
spaces. In the latter case we show that the D-branes are classified according
to the Cardy theorem. We also present the semiclassical mass computation and
find its agreement with the CFT predictions.
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Linearized Gravity in Brane Backgrounds: A treatment of linearized gravity is given in the Randall-Sundrum background.
The graviton propagator is found in terms of the scalar propagator, for which
an explicit integral expression is provided. This reduces to the
four-dimensional propagator at long distances along the brane, and provides
estimates of subleading corrections. Asymptotics of the propagator off the
brane yields exponential falloff of gravitational fields due to matter on the
brane. This implies that black holes bound to the brane have a "pancake"-like
shape in the extra dimension, and indicates validity of a perturbative
treatment off the brane. Some connections with the AdS/CFT correspondence are
described.
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Evolution equations beyond one loop from conformal symmetry: We study implications of exact conformal invariance of scalar quantum field
theories at the critical point in non-integer dimensions for the evolution
kernels of the light-ray operators in physical (integer) dimensions. We
demonstrate that all constraints due the conformal symmetry are encoded in the
form of the generators of the collinear sl(2) subgroup. Two of them, S_- and
S_0, can be fixed at all loops in terms of the evolution kernel, while the
generator of special conformal transformations, S_+, receives nontrivial
corrections which can be calculated order by order in perturbation theory.
Provided that the generator S_+ is known at the k-1 loop order, one can fix the
evolution kernel in physical dimension to the k-loop accuracy up to terms that
are invariant with respect to the tree-level generators. The invariant parts
can easily be restored from the anomalous dimensions. The method is illustrated
on two examples: The O(n)-symmetric phi^4 theory in d=4 to the three-loop
accuracy, and the su(n) matrix phi^3 theory in d=6 to the two-loop accuracy. We
expect that the same technique can be used in gauge theories e.g. in QCD.
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On Maximal Massive 3D Supergravity: We construct, at the linearized level, the three-dimensional (3D) N = 4
supersymmetric "general massive supergravity" and the maximally supersymmetric
N = 8 "new massive supergravity". We also construct the maximally
supersymmetric linearized N = 7 topologically massive supergravity, although we
expect N = 6 to be maximal at the non-linear level.
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An Itzykson-Zuber-like Integral and Diffusion for Complex Ordinary and
Supermatrices: We compute an analogue of the Itzykson-Zuber integral for the case of
arbitrary complex matrices. The calculation is done for both ordinary and
supermatrices by transferring the Itzykson-Zuber diffusion equation method to
the space of arbitrary complex matrices. The integral is of interest for
applications in Quantum Chromodynamics and the theory of two-dimensional
Quantum Gravity.
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Nilpotent Symmetries and Curci-Ferrari Type Restrictions in 2D
Non-Abelian Gauge Theory: Superfield Approach: We derive the off-shell nilpotent symmetries of the two (1+1)-dimensional
(2D) non-Abelian 1-form gauge theory by using the theoretical techniques of the
geometrical superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism.
For this purpose, we exploit the augmented version of superfield approach
(AVSA) and derive theoretically useful nilpotent (anti-)BRST, (anti-)co-BRST
symmetries and Curci-Ferrari (CF) type restrictions for the self-interacting 2D
non-Abelian 1-form gauge theory (where there is no interaction with matter
fields). The derivation of the (anti-)co-BRST symmetries and all possible
CF-type restrictions are completely novel results within the framework of AVSA
to BRST formalism where the ordinary 2D non-Abelian theory is generalized onto
an appropriately chosen (2, 2)-dimensional supermanifold. The latter is
parameterized by the superspace coordinates Z^{M} = (x^{\mu}, \theta,
\bar\theta) where x^{\mu } (with \mu = 0,1) are the bosonic coordinates and a
pair of Grassmannian variables (\theta, \bar\theta) obey the relationships:
\theta^{2} = \bar\theta^{2} = 0, \theta\bar\theta + \bar\theta\theta = 0.
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Fusion in Fractional Level sl^(2)-Theories with k=-1/2: The fusion rules of conformal field theories admitting an sl^(2)-symmetry at
level k=-1/2 are studied. It is shown that the fusion closes on the set of
irreducible highest weight modules and their images under spectral flow, but
not when "highest weight" is replaced with "relaxed highest weight". The fusion
of the relaxed modules, necessary for a well-defined u^(1)-coset, gives two
families of indecomposable modules on which the Virasoro zero-mode acts
non-diagonalisably. This confirms the logarithmic nature of the associated
theories. The structures of the indecomposable modules are completely
determined as staggered modules and it is shown that there are no logarithmic
couplings (beta-invariants). The relation to the fusion ring of the c=-2
triplet model and the implications for the beta gamma ghost system are briefly
discussed.
|
String Effective Actions and Cosmological Stability of Scalar Potentials: The cosmology of the string effective action, including one loop string
threshold corrections, is analyzed for static compactifications. The stability
of the minima of a general supersymmetry breaking potential is studied in the
presence of radiation. In particular, it is shown that the radiation bath makes
the minima with negative cosmological constant unstable.
|
Consequences of 't Hooft's Equivalence Class Theory and Symmetry by
Large Coarse Graining: According to 't Hooft (Class.Quantum.Grav. 16 (1999), 3263), quantum gravity
can be postulated as a dissipative deterministic system, where quantum states
at the ``atomic scale''can be understood as equivalence classes of primordial
states governed by a dissipative deterministic dynamics law at the ``Planck
scale''. In this paper, it is shown that for a quantum system to have an
underlying deterministic dissipative dynamics, the time variable should be
discrete if the continuity of its temporal evolution is required. Besides, the
underlying deterministic theory also imposes restrictions on the energy
spectrum of the quantum system. It is also found that quantum symmetry at the
``atomic scale'' can be induced from 't Hooft's Coarse Graining classification
of primordial states at the "Planck scale".
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From Rigid Supersymmetry to Twisted Holomorphic Theories: We study N=1 field theories with a U(1)_R symmetry on compact four-manifolds
M. Supersymmetry requires M to be a complex manifold. The supersymmetric theory
on M can be described in terms of conventional fields coupled to background
supergravity, or in terms of twisted fields adapted to the complex geometry of
M. Many properties of the theory that are difficult to see in one formulation
are simpler in the other one. We use the twisted description to study the
dependence of the partition function Z_M on the geometry of M, as well as
coupling constants and background gauge fields, recovering and extending
previous results. We also indicate how to generalize our analysis to
three-dimensional N=2 theories with a U(1)_R symmetry. In this case
supersymmetry requires M to carry a transversely holomorphic foliation, which
endows it with a near-perfect analogue of complex geometry. Finally, we present
new explicit formulas for the dependence of Z_M on the choice of U(1)_R
symmetry in four and three dimensions, and illustrate them for complex
manifolds diffeomorphic to S^3 x S^1, as well as general squashed
three-spheres.
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Rindler Fluid with Weak Momentum Relaxation: We realize the weak momentum relaxation in Rindler fluid, which lives on the
time-like cutoff surface in an accelerating frame of flat spacetime. The
translational invariance is broken by massless scalar fields with weak
strength. Both of the Ward identity and the momentum relaxation rate of Rindler
fluid are obtained, with higher order correction in terms of the strength of
momentum relaxation. The Rindler fluid with momentum relaxation could also be
approached through the near horizon limit of cutoff AdS fluid with momentum
relaxation, which lives on a finite time-like cutoff surface in Anti-de
Sitter(AdS) spacetime, and further could be connected with the holographic
conformal fluid living on AdS boundary at infinity. Thus, in the holographic
Wilson renormalization group flow of the fluid/gravity correspondence with
momentum relaxation, the Rindler fluid can be considered as the Infrared
Radiation(IR) fixed point, and the holographic conformal fluid plays the role
of the ultraviolet(UV) fixed point.
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One-Instanton Tests of the Exact Results in N=2 Supersymmetric QCD: We use the microscopic instanton calculus to determine the one-instanton
contribution to the quantum modulus u_3=<Tr(\phi^3)> in N=2 SU(N_c)
supersymmetric QCD with N_f<2N_c fundamental flavors. This is compared with the
corresponding prediction of the hyperelliptic curves which are expected to give
exact solutions in this theory. The results agree up to certain regular terms
which appear when N_f\geq 2N_c-3. The curve prediction for these terms depends
upon the curve parameterization which is generically ambiguous when N_f\geq
N_c. In SU(3) theory our instanton calculation of the regular terms is found to
disagree with the predictions of all of the suggested curves. For this theory
we employ our results as input to improve the curve parameterization for
N_f=3,4,5.
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The S-Matrix of 2D Type 0B String Theory Part 1: Perturbation Theory
Revisited: We study the perturbative S-matrix of closed strings in the two-dimensional
type 0B string theory from the worldsheet perspective, by directly integrating
correlation functions of ${\cal N}=1$ Liouville theory. The latter is computed
numerically using recurrence relations for super-Virasoro conformal blocks. We
show that the tree level 3- and 4-point amplitudes are in agreement with the
proposed dual matrix quantum mechanics. The non-perturbative aspects of the
duality will be analyzed in a companion paper.
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Binding energy of a holographic deuteron and tritium in anti-de-Sitter
space/conformal field theory (AdS/CFT): In the large 't Hooft coupling limit, the hadronic size of baryon is small
and nucleon-nucleon potential is obtained from massless pseudo-scalar exchanges
and an infinite tower of spin one mesons exchanges. In this paper we use the
holographic nucleon-nucleon interaction and obtain the corresponding potential
and binding energy for deuteron and tritium nuclei. The obtained potentials are
repulsive at short distances and clearly become zero by increasing distance as
we expected.
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A study of the zero modes of the Faddeev-Popov operator in Euclidean
Yang-Mills theories in the Landau gauge in d=2,3,4 dimensions: Examples of normalizable zero modes of the Faddeev-Popov operator in SU(2)
Euclidean Yang-Mills theories in the Landau gauge are constructed in d=2,3,4
dimensions.
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Classical Gauged Massless Rarita-Schwinger Fields: We show that, in contrast to known results in the massive case, a minimally
gauged massless Rarita-Schwinger field yields a consistent classical theory,
with a generalized fermionic gauge invariance realized as a canonical
transformation. To simplify the algebra, we study a two-component left chiral
reduction of the massless theory. We formulate the classical theory in both
Lagrangian and Hamiltonian form for a general non-Abelian gauging, and analyze
the constraints and the Rarita-Schwinger gauge invariance of the action. An
explicit wave front calculation for Abelian gauge fields shows that wave-like
modes do not propagate with superluminal velocities. An analysis of
Rarita-Schwinger spinor scattering from gauge fields shows that adiabatic
decoupling fails in the limit of zero gauge field amplitude, invalidating
various "no-go" theorems based on "on-shell" methods that claim to show the
impossibility of gauging Rarita-Schwinger fields. Quantization of
Rarita-Schwinger fields, using many formulas from this paper, is taken up in
the following paper.
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An Integration Formula for the Moment Maps of Circle Actions: The integration of the exponential of the square of the moment map of the
circle action is studied by a direct stationary phase computation and by
applying the Duistermaat-Heckman formula. Both methods yield two distinct
formulas expressing the integral in terms of contributions from the critical
set of the square of the moment map. The cohomological pairings on the
symplectic quotient, including its volume (which was known to be a piecewise
polynomial), are computed explicitly using the asymptotic behavior of the two
formulas.
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New Massive Gravity Holography: We investigate the holographic renormalization group flows and the classical
phase transitions that occur in two dimensional QFT model dual to the New
Massive 3D Gravity coupled to scalar matter. Specific matter self-interactions
generated by quadratic superpotential are considered. The off-critical
$AdS_3/CFT_2$ correspondence determines the exact form of the $ QFT_2$ 's
$\beta$ -function and the singular part of the reduced free energy. The
corresponding scaling laws and critical exponents characterizing the RG fixed
points as well as the values of the mass gaps in the massive phases are
obtained.
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Stable and Unstable Circular Strings in Inflationary Universes: It was shown by Garriga and Vilenkin that the circular shape of nucleated
cosmic strings, of zero loop-energy in de Sitter space, is stable in the sense
that the ratio of the mean fluctuation amplitude to the loop radius is
constant. This result can be generalized to all expanding strings (of non-zero
loop-energy) in de Sitter space. In other curved spacetimes the situation,
however, may be different.
In this paper we develop a general formalism treating fluctuations around
circular strings embedded in arbitrary spatially flat FRW spacetimes. As
examples we consider Minkowski space, de Sitter space and power law expanding
universes. In the special case of power law inflation we find that in certain
cases the fluctuations grow much slower that the radius of the underlying
unperturbed circular string. The inflation of the universe thus tends to wash
out the fluctuations and to stabilize these strings.
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N=2 Conformal Superspace in Four Dimensions: We develop the geometry of four dimensional N=2 superspace where the entire
conformal algebra of SU(2,2|2) is realized linearly in the structure group
rather than just the SL(2,C) x U(2)_R subgroup of Lorentz and R-symmetries,
extending to N=2 our prior result for N=1 superspace. This formulation
explicitly lifts to superspace the existing methods of the N=2 superconformal
tensor calculus; at the same time the geometry, when degauged to SL(2,C) x
U(2)_R, reproduces the existing formulation of N=2 conformal supergravity
constructed by Howe.
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Debye screening in strongly coupled N=4 supersymmetric Yang-Mills plasma: Using the AdS/CFT correspondence, we examine the behavior of correlators of
Polyakov loops and other operators in N=4 supersymmetric Yang-Mills theory at
non-zero temperature. The implications for Debye screening in this strongly
coupled non-Abelian plasma, and comparisons with available results for thermal
QCD, are discussed.
|
Gauged permutation invariant matrix quantum mechanics: Path Integrals: We give a path integral construction of the quantum mechanical partition
function for gauged finite groups. Our construction gives the quantization of a
system of $d$, $N\times N$ matrices invariant under the adjoint action of the
symmetric group $S_N$. The approach is general to any discrete group. For a
system of harmonic oscillators, i.e. for the non-interacting case, the
partition function is given by the Molien-Weyl formula times the zero-point
energy contribution. We further generalise the result to a system of non-square
and complex matrices transforming under arbitrary representations of the gauge
group.
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Duality and bosonization in Schwinger-Keldysh formulation: We present a path-integral bosonization approach for systems out of
equilibrium based on a duality transformation of the original Dirac fermion
theory combined with the Schwinger-Keldysh time closed contour technique, to
handle the non-equilibrium situation. The duality approach to bosonization that
we present is valid for $D \geq 2$ space-time dimensions leading for $D=2$ to
exact results. In this last case we present the bosonization rules for fermion
currents, calculate current-current correlation functions and establish the
connection between the fermionic and bosonic distribution functions in a
generic, nonequilibrium situation.
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Revisiting the classifications of 6d SCFTs and LSTs: Gauge-theoretic anomaly cancellation predicts the existence of many 6d SCFTs
and little string theories (LSTs) that have not been given a string theory
construction so far. In this paper, we provide an explicit construction of all
such "missing" 6d SCFTs and LSTs by using the frozen phase of F-theory. We
conjecture that the full set of 6d SCFTs and LSTs is obtained by combining the
set of theories constructed in this paper with the set of theories that have
been constructed in earlier literature using the unfrozen phase of F-theory.
Along the way, we demonstrate that there exist SCFTs that do not descend from
LSTs via an RG flow.
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Unitarity, Crossing Symmetry and Duality in the scattering of ${\cal
N}=1$ Susy Matter Chern-Simons theories: We study the most general renormalizable ${\cal N}=1$ $U(N)$ Chern-Simons
gauge theory coupled to a single (generically massive) fundamental matter
multiplet. At leading order in the 't Hooft large $N$ limit we present
computations and conjectures for the $2 \times 2$ $S$ matrix in these theories;
our results apply at all orders in the 't Hooft coupling and the matter self
interaction. Our $S$ matrices are in perfect agreement with the recently
conjectured strong weak coupling self duality of this class of theories. The
consistency of our results with unitarity requires a modification of the usual
rules of crossing symmetry in precisely the manner anticipated in
arXiv:1404.6373, lending substantial support to the conjectures of that paper.
In a certain range of coupling constants our $S$ matrices have a pole whose
mass vanishes on a self dual codimension one surface in the space of couplings.
|
Analog model for quantum gravity effects: phonons in random fluids: We describe an analog model for quantum gravity effects in condensed matter
physics. The situation discussed is that of phonons propagating in a fluid with
a random velocity wave equation. We consider that there are random fluctuations
in the reciprocal of the bulk modulus of the system and study free phonons in
the presence of Gaussian colored noise with zero mean. We show that in this
model, after performing the random averages over the noise function a free
conventional scalar quantum field theory describing free phonons becomes a
self-interacting model.
|
Anisotropic homogeneous string cosmology with two-loop corrections: The two-loop (order $\alpha'$) $\beta$-function equations, which are
equivalent to the equations of motion of $\alpha'$-corrected string effective
action, are considered for anisotropic homogeneous space-times. These equations
are solved for all Bianchi-type models in two schemes of effective action,
namely $R^2$ and Gauss-Bonnet schemes with zero cosmological constant and then
the metric, dilaton and $B$-field are found at $\alpha'$ perturbative
corrections.
|
On the Behavior of Superconductors of High Critical Temperatures Outside
Schwarzchild Black Holes in AdS Space: The physical analysis of condensed matter systems can be difficult due to
strong coupling, but the mathematical context of the AdS/CFT correspondence
enables non-perturbative descriptions in terms of dual weakly coupled systems.
This brief review explores the holographic condensed matter applications of
AdS/CFT, particularly through the lens of a high-$T_c$ superconductor outside a
Schwarzchild black hole in Anti-de Sitter space. A simple two-dimensional
electron condensate Lagrangian is examined first, as employed by G. T.
Horowitz, later used to calculate a frequency-dependent conductivity and a free
energy analysis; the asymptotics of both in this procedure, as examined by P.
S\"aterskog, are also reviewed. An extended Lagrangian with a higher order
Maxwell term is assessed thereafter, with a conductivity peak obtained at low
frequencies described well by the Drude model in certain limits. The behavior
of Drude model parameters in these limits is also investigated.
|
SUSY Enhancements in (0,4) Deformations of AdS_3/CFT_2: We discuss a marginal deformation of the SL(2,R) x SU(2) x U(1)^4 WZW model,
which describes string theory on AdS_3 x S^3 x T^4, that corresponds to warping
the S^3 factor. This deformation breaks part of the N=(4,4) supersymmetry of
the undeformed dual CFT to N=(0,4) supersymmetry. In the spirit of work by
Giveon, Kutasov, and Seiberg, we construct the asymptotic spacetime symmetry
algebra from worldsheet operators and find a restoration of (4,4) supersymmetry
at discrete values of the deformation parameter. We explain this result from
various perspectives: the worldsheet, supergravity, and from the singular D1-D5
CFT. The supergravity analysis includes an asymptotic symmetry computation of
the level of the affine SU(2) R-symmetry, which arises purely from B-field
contributions.
|
Non-local Field Theory from Matrix Models: We show that a class of matrix theories can be understood as an extension of
quantum field theory which has non-local interactions. This reformulation is
based on the Wigner-Weyl transformation, and the interactions take the form of
Moyal product on a doubled geometry. We recover local dynamics on the spacetime
as a low-energy limit. This framework opens up the possibility for studying
novel high-energy phenomena, including the unification of gauge and geometric
symmetries in a gauge theory.
|
The Two-Dimensional String as a Topological Field Theory: A certain topological field theory is shown to be equivalent to the
compactified c=1 string. This theory is described in both Kazama-Suzuki coset
and Landau-Ginzburg formulations. The genus-g partition function and genus-0
multi-tachyon correlators of the c=1 string are shown to be calculable in this
approach. The KPZ formulation of non-critical string theory has a natural
relation to this topological model. (Talk given at the Nato Advanced Research
Workshop on `New Developments in String Theory, Conformal Models and
Topological Field Theory', Cargese, May 12-21 1993.)
|
Exactly Solvable Vacuum Decays with Gravity: Using a new approach to the analysis of false vacuum decay based on the
so-called tunneling potential, we develop a general method to find scalar
potentials with a false vacuum with exactly solvable decay at the
semi-classical level, including gravitational corrections. We examine in
particular the decays of de Sitter vacua providing concrete examples that allow
to explore analytically the transition between the Coleman-De Luccia and
Hawking-Moss regimes.
|
A Holographic Bound on Cosmic Magnetic Fields: Magnetic fields large enough to be observable are ubiquitous in astrophysics,
even at extremely large length scales. This has led to the suggestion that such
fields are seeded at very early (inflationary) times, and subsequently
amplified by various processes involving, for example, dynamo effects. Many
such mechanisms give rise to extremely large magnetic fields at the end of
inflationary reheating, and therefore also during the quark-gluon plasma epoch
of the early universe. Such plasmas have a well-known holographic description
in terms of a thermal asymptotically AdS black hole. We show that holography
imposes an upper bound on the intensity of magnetic fields ($\approx \; 3.6
\times 10^{18}\;\; \text{gauss}$ at the hadronization temperature) in these
circumstances; this is above, but not far above, the values expected in some
models of cosmic magnetogenesis.
|
Regularization schemes and the multiplicative anomaly: Elizalde, Vanzo, and Zerbini have shown that the effective action of two free
Euclidean scalar fields in flat space contains a `multiplicative anomaly' when
zeta-function regularization is used. This is related to the Wodzicki residue.
I show that there is no anomaly when using a wide range of other regularization
schemes and further that this anomaly can be removed by an unusual choice of
renormalisation scales. I define new types of anomalies and show that they have
similar properties. Thus multiplicative anomalies encode no novel physics. They
merely illustrate some dangerous aspects of zeta-function and Schwinger proper
time regularization schemes.
|
Renormalization in Wavelet basis: Discrete wavelet-based methods promise to emerge as an excellent framework
for the non-perturbative analysis of quantum field theories. In this work, we
investigate aspects of renormalization in theories analyzed using wavelet-based
methods. We demonstrate the non-perturbative approach of regularization,
renormalization, and the emergence of flowing coupling constant within the
context of these methods. This is tested on a model of the particle in an
attractive Dirac delta function potential in two spatial dimensions, which is
known to demonstrate quintessential features found in a typical relativistic
quantum field theory.
|
Topological Modes in Dual Lattice Models: Lattice gauge theory with gauge group $Z_{P}$ is reconsidered in four
dimensions on a simplicial complex $K$. One finds that the dual theory,
formulated on the dual block complex $\hat{K}$, contains topological modes
which are in correspondence with the cohomology group $H^{2}(\hat{K},Z_{P})$,
in addition to the usual dynamical link variables. This is a general phenomenon
in all models with single plaquette based actions; the action of the dual
theory becomes twisted with a field representing the above cohomology class. A
similar observation is made about the dual version of the three dimensional
Ising model. The importance of distinct topological sectors is confirmed
numerically in the two dimensional Ising model where they are parameterized by
$H^{1}(\hat{K},Z_{2})$.
|
Effective Interactions of Planar Fermions in a Strong Magnetic Field-the
Effect of Landau Level Mixing: We obtain expressions for the current operator in the lowest Landau level
(L.L.L.) field theory, where higher Landau level mixing due to various external
and interparticle interactions is sytematically taken into account. We consider
the current operators in the presence of electromagnetic interactions, both
Coulomb and time-dependent, as well as local four-fermi interactions. The
importance of Landau level mixing for long-range interactions is especially
emphasized. We also calculate the edge-current for a finite sample.
|
Quantum-corrected black holes and naked singularities in
(2+1)-dimensions: We analytically investigate the pertubative effects of a quantum
conformally-coupled scalar field on rotating (2+1)-dimensional black holes and
naked singularities. In both cases we obtain the quantum-backreacted metric
analytically. In the black hole case, we explore the quantum corrections on
different regions of relevance for a rotating black hole geometry. We find that
the quantum effects lead to a growth of both the event horizon and the
ergosphere, as well as to a reduction of the angular velocity compared to their
corresponding unperturbed values. Quantum corrections also give rise to the
formation of a curvature singularity at the Cauchy horizon and show no evidence
of the appearance of a superradiant instability. In the naked singularity case,
quantum effects lead to the formation of a horizon that hides the conical
defect, thus turning it into a black hole. The fact that these effects occur
not only for static but also for spinning geometries makes a strong case for
the r\^ole of quantum mechanics as a cosmic censor in Nature.
|
A Note on Mirror Symmetry for Manifolds with Spin(7) Holonomy: Starting from the superconformal algebras associated with $G_2$ manifolds, I
extend the algebra to the manifolds with spin(7) holonomy. I show how the
mirror symmetry in manifolds with spin(7) holonomy arises as the automorphism
in the extended sperconformal algebra. The automorphism is realized as 14 kinds
of T-dualities on the supersymmetric $T^4$ toroidal fibrations. One class of
Joyce's orbifolds are pairwise identified under the symmetry.
|
Simplicial quantum dynamics: Present-day quantum field theory can be regularized by a decomposition into
quantum simplices. This replaces the infinite-dimensional Hilbert space by a
high-dimensional spinor space and singular canonical Lie groups by regular spin
groups. It radically changes the uncertainty principle for small distances.
Gaugeons, including the gravitational, are represented as bound fermion-pairs,
and space-time curvature as a singular organized limit of quantum
non-commutativity.
Keywords: Quantum logic, quantum set theory, quantum gravity, quantum
topology, simplicial quantization.
|
Leading Nonlinear Tidal Effects and Scattering Amplitudes: We present the two-body Hamiltonian and associated eikonal phase, to leading
post-Minkowskian order, for infinitely many tidal deformations described by
operators with arbitrary powers of the curvature tensor. Scattering amplitudes
in momentum and position space provide systematic complementary approaches. For
the tidal operators quadratic in curvature, which describe the linear response
to an external gravitational field, we work out the leading post-Minkowskian
contributions using a basis of operators with arbitrary numbers of derivatives
which are in one-to-one correspondence with the worldline multipole operators.
Explicit examples are used to show that the same techniques apply to both
bodies interacting tidally with a spinning particle, for which we find the
leading contributions from quadratic in curvature tidal operators with an
arbitrary number of derivatives, and to effective field theory extensions of
general relativity. We also note that the leading post-Minkowskian order
contributions from higher-dimension operators manifest double-copy relations.
Finally, we comment on the structure of higher-order corrections.
|
Coarse-Graining the Lin-Maldacena Geometries: The Lin-Maldacena geometries are nonsingular gravity duals to degenerate
vacuum states of a family of field theories with SU(2|4) supersymmetry. In this
note, we show that at large N, where the number of vacuum states is large,
there is a natural `macroscopic' description of typical states, giving rise to
a set of coarse-grained geometries. For a given coarse-grained state, we can
associate an entropy related to the number of underlying microstates. We find a
simple formula for this entropy in terms of the data that specify the geometry.
We see that this entropy function is zero for the original microstate
geometries and maximized for a certain ``typical state'' geometry, which we
argue is the gravity dual to the zero-temperature limit of the thermal state of
the corresponding field theory. Finally, we note that the coarse-grained
geometries are singular if and only if the entropy function is non-zero.
|
Aspects of Symmetry in Sine-Gordon Theory: As a prototype of powerful non-abelian symmetry in an Integrable System, I
will show the appearance of a Witt algebra of vector fields in the SG theory.
This symmetry does not share anything with the well-known Virasoro algebra of
the conformal $c=1$ unperturbed limit. Although it is quasi-local in the SG
field theory, nevertheless it gives rise to a local action on $N$-soliton
solution variables. I will explicitly write the action on special variables,
which possess a beautiful geometrical meaning and enter the Form Factor
expressions of quantum theory. At the end, I will also give some preliminary
hints about the quantisation.
|
Constructing CFTs from AdS flows: We study the renormalization group flow equations for correlation functions
of weakly coupled quantum field theories in AdS. Taking the limit where the
external points approach the conformal boundary, we obtain a flow of
conformally invariant correlation functions. We solve the flow for one- and
two-point functions and show that the corrections to the conformal dimensions
can be obtained as an integral over the Mellin amplitude of the four-point
function. We also derive the flow of the Mellin amplitude for higher $n$-point
functions. We then consider the flows at tree level and one loop (in AdS), and
show that one obtains exactly the recursion relations for the corresponding
Mellin amplitudes derived earlier by Fitzpatrick et al. [arXiv:1107.1499] at
tree level and Yuan [arXiv:1710.01361,arXiv:1801.07283] at one loop. As an
application, we furthermore compute one-loop corrections to the conformal
dimensions for some operators in the CFT dual to an $\mathrm{O}(N)$ scalar
model in AdS.
|
Worldline Instantons II: The Fluctuation Prefactor: In a previous paper [1], it was shown that the worldline expression for the
nonperturbative imaginary part of the QED effective action can be approximated
by the contribution of a special closed classical path in Euclidean spacetime,
known as a worldline instanton. Here we extend this formalism to compute also
the prefactor arising from quantum fluctuations about this classical closed
path. We present a direct numerical approach for determining this prefactor,
and we find a simple explicit formula for the prefactor in the cases where the
inhomogeneous electric field is a function of just one spacetime coordinate. We
find excellent agreement between our semiclassical approximation, conventional
WKB, and recent numerical results using numerical worldline loops.
|
The finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model: Nonlinear integral equations are proposed for the description of the full
finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model in a
periodic box. Numerical results for the energy eigenvalues are compared to the
rotator spectrum and perturbation theory for small volumes and with the
recently proposed generalized Luscher formulas at large volumes.
|
Geometric Quantum Discord Signals Non-Factorization: We propose the information-theoretic quantity of geometric quantum discord
(GQD) as an indicator of the factorization properties of a given quantum
system. In particular, we show how non-vanishing discord implies that the
corresponding partition function does not factorize, both for generic pure
states and the thermofield double state as a state with a known geometric dual
in light of the AdS/CFT correspondence. Via this analysis, we give a novel
interpretation to the thermomixed double state as the best purely classical
approximation of the Einstein-Rosen bridge. We connect the non-vanishing of GQD
with the existence of wormhole microstates.
|
Master Equations for Master Amplitudes: The general lines of the derivation and the main properties of the master
equations for the master amplitudes associated to a given Feynman graph are
recalled. Some results for the 2-loop self-mass graph with 4 propagators are
then presented.
|
Open string with a background B-field as the first order mechanics,
noncommutativity and soldering formalism: To study noncommutativity properties of the open string with constant B-field
we construct a mechanical action which reproduces classical dynamics of the
string sector under consideration. It allows one to apply the Dirac
quantization procedure for constrained systems in a direct and unambiguous way.
The mechanical action turns out to be the first order system without taking the
strong field limit $B\longrightarrow\infty$. In particular, it is true for zero
mode of the string coordinate which means that the noncommutativity is
intrinsic property of this mechanical system. We describe the arbitrariness in
the relation existent between the mechanical and the string variables and show
that noncommutativity of the string variables on the boundary can be removed.
It is in correspondence with the result of Seiberg and Witten on relation among
noncommutative and ordinary Yang-Mills theories. The recently developed
soldering formalism helps us to establish a connection between the original
open string action and the Polyakov action.
|
Non-commutative Unification in Brane World: We point out that in (open) string compactifications with non-zero NS-NS
B-field we can have large Kaluza-Klein thresholds even in the small volume
limit. In this limit the corresponding gauge theory description is in terms of
a compactification on a non-commutative space (e.g., a torus or an orbifold
thereof). Based on this observation we discuss a brane world scenario of
non-commutative unification via Kaluza-Klein thresholds. In this scenario, the
unification scale can be lowered down to the TeV-range, yet the corresponding
compactification radii are smaller than the string length. We discuss a
potential application of this scenario in the context of obtaining mixing
between different chiral generations which is not exponentially suppressed - as
we point out, such mixing is expected to be exponentially suppressed in certain
setups with large volume compactifications. We also point out that T-duality is
broken by certain non-perturbative twisted open string sectors which are
supposed to give rise to chiral generations, so that in the case of a small
volume compactification with a rational B-field we cannot T-dualize to a large
volume description. In this sense, the corresponding field theoretic picture of
unification via Kaluza-Klein thresholds in this setup is best described in the
non-commutative language.
|
Comment on "Spontaneous Inflation and the Origin of the Arrow of Time": Recently, Carroll and Chen [hep-th/0410270] suggested a promising natural
explanation of the thermodynamic arrow of time. However, we criticize their
assertion that there exists a Cauchy hypersurface with a minimal entropy and
argue that such a Cauchy hypersurface is not needed for an explanation of the
arrow of time.
|
Democracy from topology: Chiral form fields in $d$ dimensions can be effectively described as edge
modes of topological Chern-Simons theories in $d+1$ dimensions. At the same
time, manifestly Lorentz-invariant Lagrangian description of such fields
directly in terms of a $d$-dimensional field theory is challenging and requires
introducing nontrivial auxiliary gauge fields eliminated on-shell with extra
gauge symmetries. A recent work by Arvanitakis et al.\ demonstrates
(emphasizing the case of 2d chiral bosons) that the two approaches are related,
and a peculiar reduction on the $(d+1)$-dimensional topological Lagrangian
automatically leads to $d$-dimensional Lagrangians with appropriate sets of
auxiliary fields. We develop this setup in three distinct directions. First, we
demonstrate how arbitrary Abelian self-interactions for chiral forms can be
included using nonlinear boundary terms in the Chern-Simons theory. Second, by
generalizing the Chern-Simons theory to the BF theory, we obtain an analogous
democratic description of non-chiral form fields, where electric and magnetic
potentials appear as explicit dynamical variables. Third, we discuss the
effects of introducing topological interactions in the higher-dimensional bulk,
which produce extra interaction terms in the boundary theory. When applied to a
topological 4-form field in 12 dimensions, this construction results in a
democratic description of the 3-form gauge field of the 11-dimensional
supergravity.
|
Intersecting Branes and Anti-de Sitter Spacetimes in $SU(2)\times SU(2)$
Gauged Supergravity: In this note we extend our work in a previous paper hep-th/9801038. We show
here that various intersecting brane-like configurations can be found in the
vacuum of $D=4, N=4$ supergravity with gauged R-symmetry group $SU(2)\times
SU(2)$. These include intersections of domain-walls, strings and point-like
objects. Some of these intersecting configurations preserve 1/2 and 1/4 of
supersymmetry. We observe that the previously obtained $AdS_3\times R^1$ pure
axionic vacuum or `axio-vac' is an intersection of domain-wall with extended
string with 1/2 supersymmetries. Also the solutions known as `electro-vac' with
geometry $AdS_2\times R^2$ can be simply interpreted as the intersection of
domain-wall with point-like object.
|
Quantum gravity and the measurement problem in quantum mechanics: The measurement problem in quantum mechanics is almost exclusively discussed
in situations where gravity is ignored. We discuss some recent developments in
our understanding of quantum gravity and argue that they significantly alter
the problem. Quantum gravity may even resolve one of the thorniest questions in
discussions of the measurement problem: who collapses the wavefunction of the
entire universe?
|
Tensor perturbations of $f(R)$-branes: We analyze the tensor perturbations of flat thick domain wall branes in
$f(R)$ gravity. Our results indicate that under the transverse and traceless
gauge, the metric perturbations decouple from the perturbation of the scalar
field. Besides, the perturbed equation reduces to the familiar Klein-Gordon
equation for massless spin-2 particles only when the bulk curvature is a
constant or when $f(R)=R$. As an application of our results, we consider the
possibility of localizing gravity on some flat thick branes. The stability of
these brane solutions is also shortly discussed.
|
Holographic Schwinger-Keldysh field theory of SU(2) diffusion: We construct effective field theory for SU(2) isospin charge diffusion, based
on holographic Schwinger-Keldysh contour arXiv:2008.01269. The holographic
model consists of a probe SU(2) gauge field in a doubled Schwarzschild-AdS$_5$
geometry. Accurate to first order in derivative expansion, we analytically
compute the effective action up to quartic order in hydrodynamical fields. The
effective theory contains both non-Gaussianity for noises and nonlinear
interactions between noises and dynamical variables. Moreover, the effective
theory captures both thermal and quantum fluctuations, which perfectly satisfy
dynamical Kubo-Martin-Schwinger (KMS) symmetry at quantum level. Interestingly,
the dynamical KMS symmetry, which is crucial in formulating non-equilibrium
effective field theory for a quantum many-body system, is found to have a nice
holographic interpretation.
|
Stringy Toda Cosmologies: We discuss a particular stringy modular cosmology with two axion fields in
seven space-time dimensions, decomposable as a time and two flat three-spaces.
The effective equations of motion for the problem are those of the $SU(3)$ Toda
molecule, and hence are integrable. We write down the solutions, and show that
all of them are singular. They can be thought of as a generalization of the
Pre-Big-Bang cosmology with excited internal degrees of freedom, and still
suffering from the graceful exit problem. Some of the solutions however show a
rather unexpected property: some of their spatial sections shrink to a point in
spite of winding modes wrapped around them. We also comment how more general,
anisotropic, solutions, with fewer Killing symmetries can be obtained with the
help of STU dualities.
|
Poincare Series, 3D Gravity and CFT Spectroscopy: Modular invariance strongly constrains the spectrum of states of two
dimensional conformal field theories. By summing over the images of the modular
group, we construct candidate CFT partition functions that are modular
invariant and have positive spectrum. This allows us to efficiently extract the
constraints on the CFT spectrum imposed by modular invariance, giving
information on the spectrum that goes beyond the Cardy growth of the asymptotic
density of states. Some of the candidate modular invariant partition functions
we construct have gaps of size (c-1)/12, proving that gaps of this size and
smaller are consistent with modular invariance. We also revisit the partition
function of pure Einstein gravity in AdS3 obtained by summing over geometries,
which has a spectrum with two unphysical features: it is continuous, and the
density of states is not positive definite. We show that both of these can be
resolved by adding corrections to the spectrum which are subleading in the
semi-classical (large central charge) limit.
|
Noncommutative Superspace and Super Heisenberg Group: In this paper, we consider noncommutative superspace in relation with super
Heisenberg group. We construct a matrix representation of super Heisenberg
group and apply this to the two-dimensional deformed N=(2,2) superspace that
appeared in string theory. We also construct a toy model for non-centrally
extended `super Heisenberg group'.
|
Target space entanglement in quantum mechanics of fermions at finite
temperature: We consider the target space entanglement in quantum mechanics of
non-interacting fermions at finite temperature. Unlike pure states investigated
in arXiv:2105.13726, the (R\'enyi) entanglement entropy for thermal states does
not follow a simple bound because all states in the infinite-dimensional
Hilbert space are involved. We investigate a general formula of the target
space R\'enyi entropy for $N$ fermions at finite temperature, and present
numerical results of the entropy in a one-dimensional model. We also argue the
large $N$ behaviors with a comparison to the grand canonical ensemble.
|
Instability of hairy black holes in spontaneously-broken
Einstein-Yang-Mills-Higgs systems: The stability of a new class of hairy black hole solutions in the coupled
system of Einstein-Yang-Mills-Higgs is examined, generalising a method
suggested by Brodbeck and Straumann and collaborators, and Volkov and Gal'tsov.
The method maps the algebraic system of linearised radial perturbations of the
various field modes around the black hole solution into a coupled system of
radial equations of Schr\"odinger type. No detailed knowledge of the black hole
solution is required, except from the fact that the boundary conditions at the
physical space-time boundaries (horizons) must be such so as to guarantee the
{\it finiteness} of the various expressions involved. In this way, it is
demonstrated that the above Schr\"odinger equations have bound states, which
implies the instability of the associated black hole solution.
|
$η$-weak-pseudo-Hermiticity generators and radially symmetric
Hamiltonians: A class of spherically symmetric non-Hermitian Hamiltonians and their
\eta-weak-pseudo-Hermiticity generators are presented. An operators-based
procedure is introduced so that the results for the 1D Schrodinger Hamiltonian
may very well be reproduced. A generalization beyond the nodeless states is
proposed. Our illustrative examples include \eta-weak-pseudo-Hermiticity
generators for the non-Hermitian weakly perturbed 1D and radial oscillators,
the non-Hermitian perturbed radial Coulomb, and the non-Hermitian radial Morse
models.
|
A Generalization of Sachdev-Ye-Kitaev: The SYK model: fermions with a $q$-body, Gaussian-random, all-to-all
interaction, is the first of a fascinating new class of solvable large $N$
models. We generalize SYK to include $f$ flavors of fermions, each occupying
$N_a$ sites and appearing with a $q_a$ order in the interaction. Like SYK, this
entire class of models generically has an infrared fixed point. We compute the
infrared dimensions of the fermions, and the spectrum of singlet bilinear
operators. We show that there is always a dimension-two operator in the
spectrum, which implies that, like in SYK, there is breaking of conformal
invariance and maximal chaos in the infrared four-point function of the
generalized model. After a disorder average, the generalized model has a global
$O(N_1) \times O(N_2) \times \ldots\times O(N_f)$ symmetry: a subgroup of the
$O(N)$ symmetry of SYK; thereby giving a richer spectrum. We also elucidate
aspects of the large $q$ limit and the OPE, and solve $q=2$ SYK at finite $N$.
|
More on DBI action in 4D $\mathcal{N}=1$ supergravity: We construct a Dirac-Born-Infeld (DBI) action coupled to a two-form field in
four dimensional $\mathcal{N}=1$ supergravity. Our superconformal formulation
of the action shows a universal way to construct it in various Poincar\'e
supergravity formulations. We generalize the DBI action to that coupled to
matter sector. We also discuss duality transformations of the DBI action, which
are useful for phenomenological and cosmological applications.
|
D=10 supersymmetric chern-simons gauge theory: The Chern-Simons ten-dimensional manifestly supersymmetric non-Abelian gauge
theory is presented by performing the second quantization of the superparticle
theory. The equation of motion is $F = (d+A)^2 = 0$, where $d$ is the nilpotent
fermionic BRST operator of the first quantized theory and $A$ is the anti-
commuting connection for the gauge group. This equation can be derived as a
condition of the gauge independence of the first quantized theory in a
background field $A$, or from the string field theory Lagrangian of the Chern-
Simons type. The trivial solutions of the cohomology are the gauge symmetries,
the non-trivial solution is given by the D=10 superspace, describing the super
Yang-Mills theory on shell
|
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