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On Composite fields approach to Gribov copies elimination in Yang-Mills
theories: We suggest a method of introducing the Gribov--Zwanziger horizon functional,
$H$, for Yang--Mills theories by using the composite fields technique: $\sigma
(\phi )=H$. A different form of the same horizon functional in gauges $\chi $
and $\chi ^{\prime }$ is taken into account via (gauged) field-dependent BRST
transformations connecting quantum Yang--Mills actions in these gauges. We
introduce generating functionals of Green's functions with composite fields and
derive the corresponding Ward identities. A study of gauge dependence shows
that the effective action in Yang--Mills theories with the composite field $H$
does not depend on the gauge on the extremals determined by the Yang--Mills
fields $\phi $ alone. | Thermal one-point functions and single-valued polylogarithms: I point out that the thermal one-point functions of a pair of relevant
operators in massive free QFTs, in odd dimensions and in the presence of an
imaginary chemical potential for a U(1) global charge, are given by certain
classes of single-valued polylogarithms. This result is verified by a direct
calculation using the thermal OPE. The complex argument of the polylogarithms
parametrize a two-dimensional subspace of relevant deformations of generalised
free CFTs, while the rank of the polylogarithms is related to the dimension d.
This may be compared with the well-known representation of single-valued
polylogarithms as multiloop Feynman amplitudes. As an example, the thermal
one-point function of the U(1) charge in d-dimensions generalises the thermal
average of the twist operator in a pair of harmonic oscillators and is given by
the well-known conformal ladder graphs in four dimensions. |
T-duality of D-brane versus O-plane actions: It is known that, in the static gauge, the world-volume and the transverse
Kaluza-Klein (KK) reductions of the O-plane effective actions on a circle
satisfy the T-duality constraint for arbitrary base space background. In this
paper we show that due to the presence of the second fundamental form in the
D-brane couplings at order $\alpha'$ and higher, the T-duality is satisfied
only for a subclass of couplings for arbitrary base space background. They are
$m=0$ couplings where $m$ is the number of $\tilde{B}$-field (without
derivative on it). For $m>0$ couplings, the base space metric must be
block-diagonal and the momentum $U(1)$ vector field must be zero. However, the
derivatives of the metric and the vector field are arbitrary.
Using the assumption that the effective actions at the critical dimension are
background independent, we then show that the T-duality constraint for the
couplings at order $\alpha'$ and for $m=0$, fixes completely both bulk and
boundary actions. These couplings indicate that the propagators of the massless
open string fields receive $\alpha'$-correction.
We have also imposed the T-duality constraint on $m=1,2,3,4$ couplings.
Because of the above restriction on the base space background in these cases,
however, the T-duality can only partially fix the couplings for $m>0$. This
study shows that the Dirac-Born-Infeld (DBI) factor appears in both bulk and
boundary actions at order $\alpha'$. | Gravitons and Loops: The recently proposed loop representation, used previously to find exact
solutions to the quantum constraints of general relativity, is here used to
quantize linearized general relativity. The Fock space of graviton states and
its associated algebra of observables are represented in terms of functionals
of loops. The ``reality conditions'' are realized by an inner product that is
chiral asymmetric, resulting in a chiral asymmetric ordering for the
Hamiltonian and in an asymmetric description of the left and right handed
gravitons. This chirally asymmetric formulation depends on a splitting of the
linearized field into self-dual and anti-self dual parts rather than into
positive and negative frequency parts; as the former, but not the latter, is
meaningful away from flat backgrounds this is expected to be useful in
connecting the nonperturbative theory to the linearized theory. The formalism
depends on an arbitrary ``averaging'' function that controls certain
divergences, but does not appear in the final physical quantities. Inspite of
these somewhat unusual features, the loop quntization presented here is
completely equivalent to the standard quantization of linearized gravity. |
Exact solutions in quantum field theory under rotation: We discuss the construction and properties of rigidly-rotating states for
free scalar and fermion fields in quantum field theory. On unbounded Minkowski
space-time, we explain why such states do not exist for scalars. For the Dirac
field, we are able to construct rotating vacuum and thermal states, for which
expectation values can be computed exactly in the massless case. We compare
these quantum expectation values with the corresponding quantities derived in
relativistic kinetic theory. | Toroidal Black Holes and T-duality: We consider the toroidal black holes that arise as a generalization of the
AdS_5 times S^5 solution of type IIB supergravity. The symmetries of the
horizon space allow T-duality transformations that can be exploited to generate
new inequivalent black hole solutions of both type IIB and type IIA
supergravity, with non-trivial dilaton, B-field, and RR forms. We examine the
asymptotic structure and thermodynamical properties of these solutions. |
Testing the Uniqueness of the Open Bosonic String Field Theory Vacuum: The operators K_n are generators of reparameterization symmetries of Witten's
cubic open string field theory. One pertinent question is whether they can be
utilised to generate deformations of the tachyon vacuum and thereby violate its
uniqueness. We use level truncation to show that these transformations on the
vacuum are in fact pure gauge transformations to a very high accuracy, thus
giving new evidence for the uniqueness of the perturbatively stable vacuum.
Equivalently, this result implies the vanishing of some discrete cohomology
classes of the BRST operator in the stable vacuum. | Causality in String Field Theory: In this letter, we will investigate causality in string field theory using
pp-wave light-cone gauge string field theory. We will generalize the Ramsey
scheme to string field theory, and use it to analyze string field theoretical
processes. An explicit characteristic function for interactive string field
theory will be built using this string field theoretical Ramsey scheme. The
average of the difference between the initial and final values of any operator
described in string field theory will be obtained using this characteristic
function. We will use the quantum information theoretical technique based on
quantum fisher information to extract information about such string field
theoretical processes. |
Proof of the Impossibility of Non-Contextual Hidden Variables in All
Hilbert Space Dimensions: It is shown that the algebraic structure of finite Heisenberg groups
associated with the tensor product of two Hilbert spaces leads to a simple
demonstration valid in all Hilbert space dimensions of the impossibility of
non-contextual hidden variables. | Black Holes with Intrinsic Spin: We analyze the general black hole solutions to the four dimensional STU model
recently constructed by Chow and Compere. We define a dilute gas limit where
the black holes can be interpreted as excited states of an extremal ground
state. In this limit we express the black hole entropy and the excitation
energy in terms of physical quantities with no need for parametric charges. We
discuss a dual microscopic CFT description that incorporates all electric and
magnetic charges. This description is recovered geometrically by identification
of a near horizon BTZ region. We construct the subtracted geometry with no
restrictions on charges by analyzing the scalar wave equation in the full
geometry. We determine the matter sources that support the subtracted geometry
by studying a scaling limit and show that the general geometry permits a dilute
gas description with parameters that we specify. |
Can scalars have asymptotic symmetries?: Recently it has been understood that certain soft factorization theorems for
scattering amplitudes can be written as Ward identities of new asymptotic
symmetries. This relationship has been established for soft particles with
spins $s > 0$, most notably for soft gravitons and photons. Here we study the
remaining case of soft scalars. We show that a class of Yukawa-type theories,
where a massless scalar couples to massive particles, have an infinite number
of conserved charges. This raises the question as to whether one can associate
asymptotic symmetries to scalars. | String Theory Realizations of the Nilpotent Goldstino: We describe in detail how the spectrum of a single anti-D3-brane in
four-dimensional orientifolded IIB string models reproduces precisely the field
content of a nilpotent chiral superfield with the only physical component
corresponding to the fermionic goldstino. In particular we explicitly consider
a single anti-D3-brane on top of an O3-plane in warped throats, induced by
$(2,1)$ fluxes. More general systems including several anti-branes and other
orientifold planes are also discussed. This provides further evidence to the
claim that non-linearly realized supersymmetry due to the presence of
antibranes in string theory can be described by supersymmetric theories
including nilpotent superfields. Implications to the KKLT and related scenarios
of de Sitter moduli stabilization, to cosmology and to the structure of soft
SUSY-breaking terms are briefly discussed. |
Generalized Maxwell-Higgs vortices in models with enhanced symmetry: Topological vortices in relativistic gauge theories in flat three-dimensional
spacetime are investigated. We consider the symmetry $\rm{U(1)}\times...\times
\rm{U(1)}$, and for each $\rm{U(1)}$ subgroup, a complex scalar field
transforming under its action is introduced, as well as generalized
permeabilities through which the subsystems are coupled. We investigate in
detail the features of static, finite energy solutions within this class of
generalized Maxwell-Higgs models, and study the effect of the winding numbers
in the magnetic properties of each subsystem. A BPS bound and the related first
order equations are introduced for a large class of models. Finally, we present
some specific models and solve their equations of motion to find solutions
engendering many distinct features in relation to each other and to the
standard Nielsen-Olesen vortex. | Charged test-particle scattering and effective one-body metrics with
spin: Using recently developed techniques, we consider weak-field test-particle
scattering angle calculations in two distinct settings: Charged test-particles
in spacetimes of charged sources and Effective One-Body theory with spin. We
present scattering angle calculations up to $\mathcal O(G^4)$ of charged
particles in the Kerr-Newman metric, including electromagnetic interactions up
to second order in charge. Coulomb scattering is also discussed, and the
well-known Darwin scattering formula is rederived by resummation. An Effective
One-Body metric for a Kerr-Schwarzschild binary is constructed in a
post-Minkowskian framework up to $\mathcal O(G^2)$ and first order in spin.
Facilitated by explicit scattering calculations, our approach is equivalent
with existing literature through gauge-like transformations. Finally, we
investigate if the Newman Janis Algorithm applied to an Effective One-Body
metric of non-spinning binaries represents a binary system with spin. |
Patching DFT, T-duality and Gerbes: We clarify the role of the dual coordinates as described from the
perspectives of the Buscher T-duality rules and Double Field Theory. We show
that the T-duality angular dual coordinates cannot be identified with Double
Field Theory dual coordinates in any of the proposals that have been made in
the literature for patching the doubled spaces. In particular, we show with
explicit examples that the T-duality angular dual coordinates can have
non-trivial transition functions over a spacetime and that their identification
with the Double Field Theory dual coordinates is in conflict with proposals in
which the latter remain inert under the patching of the B-field. We then
demonstrate that the Double Field Theory coordinates can be identified with
some C-space coordinates and that the T-dual spaces of a spacetime are
subspaces of the gerbe in C-space. The construction provides a description of
both the local $O(d,d)$ symmetry and the T-dual spaces of spacetime. | Affine sl(2|1) and D(2|1;alpha) as Vertex Operator Extensions of Dual
Affine sl(2) Algebras: We discover a realisation of the affine Lie superalgebra sl(2|1) and of the
exceptional affine superalgebra D(2|1;alpha) as vertex operator extensions of
two affine sl(2) algebras with dual levels (and an auxiliary level 1 sl(2)
algebra). The duality relation between the levels is (k+1)(k'+1)=1. We
construct the representation of sl(2|1) at level k' on a sum of tensor products
of sl(2) at level k, sl(2) at level k' and sl(2) at level 1 modules and
decompose it into a direct sum over the sl(2|1) spectral flow orbit. This
decomposition gives rise to character identities, which we also derive. The
extension of the construction to the affine D(2|1;k') at level k is traced to
properties of sl(2)+sl(2)+sl(2) embeddings into D(2|1;alpha) and their relation
with the dual sl(2) pairs. Conversely, we show how the level k' sl(2)
representations are constructed from level k sl(2|1) representations. |
Quantum mechanical path integrals in curved spaces and the type-A trace
anomaly: Path integrals for particles in curved spaces can be used to compute trace
anomalies in quantum field theories, and more generally to study properties of
quantum fields coupled to gravity in first quantization. While their
construction in arbitrary coordinates is well understood, and known to require
the use of a regularization scheme, in this article we take up an old proposal
of constructing the path integral by using Riemann normal coordinates. The
method assumes that curvature effects are taken care of by a scalar effective
potential, so that the particle lagrangian is reduced to that of a linear sigma
model interacting with the effective potential. After fixing the correct
effective potential, we test the construction on spaces of maximal symmetry and
use it to compute heat kernel coefficients and type-A trace anomalies for a
scalar field in arbitrary dimensions up to d=12. The results agree with
expected ones, which are reproduced with great efficiency and extended to
higher orders. We prove explicitly the validity of the simplified path integral
on maximally symmetric spaces. This simplified path integral might be of
further use in worldline applications, though its application on spaces of
arbitrary geometry remains unclear. | Target space entanglement in Matrix Models: We study target space entanglement in gauged multi-matrix models as models of
entanglement between groups of D-branes separated by a planar entangling
surface, paying close attention to the implementation of gauge invariance. We
open with a review of target space entanglement between identical particles,
which shares some important features (specifically a gauged permutation
symmetry) with our main problem. For our matrix models, we implement a gauge
fixing well-adapted to the entangling surface. In this gauge, we map the matrix
model problem to that of entanglement of a $U(1)$ gauge theory on a complete or
all-to-all lattice. Matrix elements corresponding to open strings stretching
across the entangling surface in the target space lead to interesting
contributions to the entanglement entropy. |
World-Volume Description of M2-branes Ending on an M5-brane and
Holography: We consider world-volume description of M2-branes ending on an M5-brane. The
system can be described either as a solitonic solution of the M5-brane field
equations or in terms of an effective string propagating in 6-dimensions. We
show that the zeroth order scalar scattering amplitudes behave similarly in
both pictures. The soliton solution appears to have a horizon-like throat
region. Due to the underlying geometric structure of the M5-brane theory, modes
propagating near the horizon are subject to a large red-shift. This allows one
to define a decoupling limit and implies a holographic duality between two
theories which do not contain dynamical gravity. | Can the string scale be related to the cosmic baryon asymmetry?: In a previous work, a mechanism was presented by which baryon asymmetry can
be generated during inflation from elliptically polarized gravitons.
Nonetheless, the mechanism only generated a realistic baryon asymmetry under
special circumstances which requires an enhancement of the lepton number from
an unspecified GUT. In this note we provide a stringy embedding of this
mechanism through the Green-Schwarz mechanism, demonstrating that if the
model-independent axion is the source of the gravitational waves responsible
for the lepton asymmetry, one can observationally constrain the string scale
and coupling. |
Racah - Wigner quantum 6j Symbols, Ocneanu Cells for AN diagrams, and
quantum groupoids: We relate quantum 6J symbols of various types (quantum versions of Wigner and
Racah symbols) to Ocneanu cells associated with AN Dynkin diagrams. We check
explicitly the algebraic structure of the associated quantum groupoids and
analyze several examples (A3, A4). Some features relative to cells associated
with more general ADE diagrams are also discussed. | A novel approach to perturbative calculations for a large class of
interacting boson theories: We present a method of calculating the interacting S-matrix to an arbitrary
perturbative order for a large class of boson interaction Lagrangians. The
method takes advantage of a previously unexplored link between the $n$-point
Green's function and a certain system of linear Diophantine equations. By
finding all nonnegative solutions of the system, the task of perturbatively
expanding an interacting $S$-matrix becomes elementary for any number of
interacting fields, to an arbitrary perturbative order (irrespective of whether
it makes physical sense) and for a large class of scalar boson theories. The
method does not rely on the position-based Feynman diagrams and promises to be
extended to many perturbative models typically studied in quantum field theory.
Aside from interaction field calculations we showcase our approach by expanding
a pair of Unruh-DeWitt detectors coupled to Minkowski vacuum to an arbitrary
perturbative order in the coupling constant. We also link our result to Hafnian
as introduced by Caianiello and present a method to list all (2n-1)!! perfect
matchings of a complete graph on 2n vertices. |
Non-Invertible Symmetries from Discrete Gauging and Completeness of the
Spectrum: We study global 1- and $(d-2)$-form symmetries for gauge theories based on
disconnected gauge groups which include charge conjugation. For pure gauge
theories, the 1-form symmetries are shown to be non-invertible. In addition,
being the gauge groups disconnected, the theories automatically have a
$\mathbb{Z}_2$ global $(d-2)$-form symmetry. We propose String Theory
embeddings for gauge theories based on these groups. Remarkably, they all
automatically come with twist vortices which break the $(d-2)$-form global
symmetry. This is consistent with the conjectured absence of global symmetries
in Quantum Gravity. | Quantum Topology Change and Large N Gauge Theories: We study a model for dynamical localization of topology using ideas from
non-commutative geometry and topology in quantum mechanics. We consider a
collection $X$ of $N$ one-dimensional manifolds and the corresponding set of
boundary conditions (self-adjoint extensions) of the Dirac operator $D$. The
set of boundary conditions encodes the topology and is parameterized by unitary
matrices $g_N$. A particular geometry is described by a spectral triple
$x(g_N)=(A_X,{\cal H}_X, D(g_N))$. We define a partition function for the sum
over all $g_N$. In this model topology fluctuates but the dimension is kept
fixed. We use the spectral principle to obtain an action for the set of
boundary conditions. Together with invariance principles the procedure fixes
the partition function for fluctuating topologies. In the simplest case the
model has one free-parameter $\beta $ and it is equivalent to a one plaquette
gauge theory. We argue that topology becomes localized at $\beta=\infty$ for
any value of $N$. Moreover, the system undergoes a third-order phase transition
at $\beta=1$ for large $N$. We give a topological interpretation of the phase
transition by looking how it affects the topology. |
Ultra Unification: Strong, electromagnetic, and weak forces were unified in the Standard Model
(SM) with spontaneous gauge symmetry breaking. These forces were further
conjectured to be unified in a simple Lie group gauge interaction in the Grand
Unification (GUT). In this work, we propose a theory beyond the SM and GUT by
adding new gapped Topological Phase Sectors consistent with the nonperturbative
global anomaly cancellation and cobordism constraints (especially from the
baryon minus lepton number ${\bf B}-{\bf L}$, the electroweak hypercharge $Y$,
and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors
are constructed via symmetry extension, whose low energy contains unitary
Lorentz invariant topological quantum field theories (TQFTs): either 3+1d
non-invertible TQFT, or 4+1d invertible or non-invertible TQFT (short-range or
long-range entangled gapped phase). Alternatively, there could also be
right-handed "sterile" neutrinos, gapless unparticle physics, more general
interacting conformal field theories, or gravity with topological cobordism
constraints, or their combinations to altogether cancel the mixed
gauge-gravitational anomaly. We propose that a new high-energy physics frontier
beyond the conventional 0d particle physics relies on the new Topological Force
and Topological Matter including gapped extended objects (gapped 1d line and 2d
surface operators or defects, etc., whose open ends carry deconfined
fractionalized particle or anyonic string excitations) or gapless conformal
matter. Physical characterizations of these gapped extended objects require the
mathematical theories of cohomology, cobordism, or category. Although weaker
than the weak force, Topological Force is infinite-range or long-range which
does not decay in the distance, and mediates between the linked worldvolume
trajectories via fractional or categorical statistical interactions. | Asymptotic Form of Zero Energy Wave Functions in Supersymmetric Matrix
Models: We derive the power law decay, and asymptotic form, of SU(2) x Spin(d)
invariant wave-functions which are zero-modes of all s_d=2(d-1) supercharges of
reduced (d+1)-dimensional supersymmetric SU(2) Yang Mills theory, resp. of the
SU(2)-matrix model related to supermembranes in d+2 dimensions. |
Background field and time dependence effects in holographic models: This thesis deals with applications of holographic dualities to the study of
background field and time dependence effects in strongly coupled field
theories.
The first chapters (2-5) aim to provide a self-contained review of the
Sakai-Sugimoto model (SSM) as a top-down approach to holographic QCD,
introducing first the necessary background on QCD, string theory and AdS/CFT.
Chapter 7 reviews finite temperature holography, to be used in the subsequent
chapters.
We use the non-Abelian ($N_f = 2$) SSM to study a possible magnetically
induced instability of the QCD vacuum towards a superconducting phase, as
previously discussed in phenomenological QCD models and there referred to as
"rho meson condensation". We find that this instability can indeed be
holographically described by the SSM, and obtain increasingly higher
predictions for the necessary critical magnetic field in increasingly
complicated (i.e. less simplified) set-ups. The obtained results are presented
in chapter 6 and are based on arXiv:1105.2217 and arXiv:1309.5042. In chapter 8
we discuss the splitting of chiral transition temperatures per flavour in the
finite temperature regime of the $N_f = 2$ SSM, indicating an intermediate
phase where chiral symmetry is only partially restored. This was previously
presented in arXiv:1303.5674.
In chapter 9, instead of a top-down approach, bottom-up models known as
"AdS-Vaidya" models are used in the context of condensed matter applications to
study far-from-equilibrium behaviour of strongly coupled electron systems. A
notion of a time-dependent spectral function is defined and calculated in
Reissner-Nordstr\"om-AdS$_4$-Vaidya as a very first step towards extracting in
principle measurable quantities in time-resolved ARPES experiments
[arXiv:1407.5975]. Focus is put on explaining the used numerical method
(pseudospectral method). | Exact superpotentials in N=1 theories with flavor and their matrix model
formulation: In this note we investigate the effective superpotential of an N=1 SU(N_c)
gauge theory with one adjoint chiral multiplet and N_f fundamental chiral
multiplets. We propose a matrix model prescription in which only matrix model
diagrams with less than two boundaries contribute to the gauge theory effective
superpotential. This prescription reproduces exactly the known gauge theory
physics for all N_f and $N_c$. For N_f < N_c this is given by the
Affleck-Dine-Seiberg superpotential. For N_f > N_c we present arguments leading
to the conclusion that the dynamics of these theories is also reproduced by the
matrix model. |
Supersymmetric Cubic Interactions For Lower Spins From "Higher Spin"
Approach: We demonstrate how to reconstruct standard cubic vertices for N=1
supersymmetric Yang-Mills and Supergravities using various techniques adopted
for the description of cubic interactions between higher spin fields. | Quantum field theories with boundaries and novel instabilities: Quantum physics on manifolds with boundary brings novel aspects due to
boundary conditions. One important feature is the appearance of localised
negative eigenmodes for the Laplacian on the boundary. These can potentially
lead to instabilities. We consider quantum field theories on such manifolds and
interpret these as leading to the onset of phase transitions. |
Modified N=2 supersymmetry and Fayet-Iliopoulos terms: We study peculiarities of realization of N=2 supersymmetry in N=2 abelian
gauge theory with two sorts of FI terms, electric and magnetic ones, within
manifestly supersymmetric formulations via the Mezincescu and harmonic-analytic
prepotentials. We obtain a `magnetic', duality- transformed superfield form of
the N=2 Maxwell effective holomorphic action with standard electric $FI$ term
and demonstrate that in such a system off-shell N=2 supersymmetry is inevitably
realized in an unusual Goldstone mode corresponding to the {\it partial}
spontaneous breaking down to N=1. On shell, the standard total breaking occurs.
In a system with the two sorts of FI terms, off-shell N=2 supersymmetry is
realized in the partial breaking mode both in the electric and magnetic
representations. This regime is retained on shell due to the Antoniadis-
Partouche-Taylor mechanism. We show that the off-shell algebra of N=2
supersymmetry in the partial breaking realization is modified on gauge-variant
objects like potentials and prepotentials. The closure of spinor charges
involves some special gauge transformations before any gauge-fixing. | Reducing heterotic M-theory to five dimensional supergravity on a
manifold with boundary: This paper constructs the reduction of heterotic $M$-theory in eleven
dimensions to a supergravity model on a manifold with boundary in five
dimensions using a Calabi-Yau three-fold. New results are presented for the
boundary terms in the action and for the boundary conditions on the bulk
fields. Some general features of dualisation on a manifold with boundary are
used to explain the origin of some topological terms in the action. The effect
of gaugino condensation on the fermion boundary conditions leads to a `twist'
in the chirality of the gravitino which can provide an uplifting mechanism in
the vacuum energy to cancel the cosmological constant after moduli
stabilisation. |
ABJM on ellipsoid and topological strings: It is known that the large N expansion of the partition function in ABJM
theory on a three-sphere is completely determined by the topological string on
local Hirzebruch surface F_0. In this note, we investigate the ABJM partition
function on an ellipsoid, which has a conventional deformation parameter b.
Using 3d mirror symmetry, we find a remarkable relation between the ellipsoid
partition function for b^2=3 (or b^2=1/3) in ABJM theory at k=1 and a matrix
model for the topological string on another Calabi-Yau threefold, known as
local P^2. As in the case of b=1, we can compute the full large N expansion of
the partition function in this case. This is the first example of the complete
large N solution in ABJM theory on the squashed sphere. Using the obtained
results, we also analyze the supersymmetric Renyi entropy. | Nonlinear differential equations for the correlation functions of the 2D
Ising model on the cylinder: We derive determinant representations and nonlinear differential equations
for the scaled 2-point functions of the 2D Ising model on the cylinder. These
equations generalize well-known results for the infinite lattice (Painlev\'e
III equation and the equation for the $\tau$-function of Painlev\'e V). |
Black rings with fourth dipole cause less hair loss: An example of entropy enigma with a controlled CFT dual was recently studied
in arXiv:1108.0411. The enigmatic bulk configurations, considered within the
STU model, can be mapped under spectral flow into black rings with three
monopole and dipole charges. Even though the bulk and CFT configurations
existed in the same region of parameter space, the Bekenstein-Hawking entropy
of the bulk configurations was found to be lower than the microscopic entropy
from the CFT. While it is possible that the difference in entropy is due to the
bulk and boundary configurations being at different points in the moduli space,
it is also possible that the bulk configurations embeddable within the STU
model are not the most entropic. New families of BPS black ring solutions with
four electric and four dipole magnetic charges have recently been explicitly
constructed in arXiv:1201.2585. These black rings are not embeddable within the
STU model. In this paper we investigate if these black rings can be
entropically dominant over the STU model black rings. We find that the new
black rings are always entropically subdominant to the STU-model black rings.
However, for small fourth dipole charge these black rings continue to be
dominant over the BMPV in a small region of parameters and are thus enigmatic. | BMS Modular Diaries: Torus one-point function: Two dimensional field theories invariant under the Bondi-Metzner-Sachs (BMS)
group are conjectured to be dual to asymptotically flat spacetimes in three
dimensions. In this paper, we continue our investigations of the modular
properties of these field theories. In particular, we focus on the BMS torus
one-point function. We use two different methods to arrive at expressions for
asymptotic structure constants for general states in the theory utilising
modular properties of the torus one-point function. We then concentrate on the
BMS highest weight representation, and derive a host of new results, the most
important of which is the BMS torus block. In a particular limit of large
weights, we derive the leading and sub-leading pieces of the BMS torus block,
which we then use to rederive an expression for the asymptotic structure
constants for BMS primaries. Finally, we perform a bulk computation of a probe
scalar in the background of a flatspace cosmological solution based on the
geodesic approximation to reproduce our field theoretic results. |
Wilson Loops in Open String Theory: Wilson loop elements on torus are introduced into the partition function of
open strings as Polyakov's path integral at one-loop level. Mass spectra from
compactification and expected symmetry breaking are illustrated by choosing the
correct weight for the contributions from annulus and M\"obius strip. We show
that Jacobi's imaginary transformation connects the mass spectra with the
Wilson loops. The application to thermopartition function and cosmological
implications are briefly discussed. | Almost-BPS solutions in multi-center Taub-NUT: Microstates of colinear black holes embedded in a multi-center Taub-NUT
spacetime are sought in 4 dimensions. A set of coupled ordinary partial
differential equations are obtained and solved for almost-BPS states, where
some supersymmetry is preserved in the context of N=2 supergravity in 4
dimensions. The regularity of solutions is being carefully considered and we
ensure that no CTC (closed time-like curves) are present. The larger framework
is that of 11-dimensional N=2 supergravity and the current theory is obtained
by compactifying down to 4 dimensions. |
Thermal one- and two-graviton Green's functions in the temporal gauge: The thermal one- and two-graviton Green's function are computed using a
temporal gauge. In order to handle the extra poles which are present in the
propagator, we employ an ambiguity-free technique in the imaginary-time
formalism. For temperatures T high compared with the external momentum, we
obtain the leading T^4 as well as the subleading T^2 and log(T) contributions
to the graviton self-energy. The gauge fixing independence of the leading T^4
terms as well as the Ward identity relating the self-energy with the one-point
function are explicitly verified. We also verify the 't Hooft identities for
the subleading T^2 terms and show that the logarithmic part has the same
structure as the residue of the ultraviolet pole of the zero temperature
graviton self-energy. We explicitly compute the extra terms generated by the
prescription poles and verify that they do not change the behavior of the
leading and sub-leading contributions from the hard thermal loop region. We
discuss the modification of the solutions of the dispersion relations in the
graviton plasma induced by the subleading T^2 contributions. | Duality invariant self-interactions of abelian p-forms in arbitrary
dimensions: We analyze non-linear interactions of 2N-form Maxwell fields in a space-time
of dimension D=4N. Based on the Pasti-Sorokin-Tonin (PST) method, we derive the
general consistency condition for the dynamics to respect both manifest
SO(2)-duality invariance and manifest Lorentz invariance. For a generic
dimension D=4N, we determine a canonical class of exact solutions of this
condition, which represent a generalization of the known non-linear duality
invariant Maxwell theories in D=4. The resulting theories are shown to be
equivalent to a corresponding class of canonical theories formulated a la
Gaillard-Zumino-Gibbons-Rasheed (GZGR), where duality is a symmetry only of the
equations of motion. In dimension D=8, via a complete solution of the PST
consistency condition, we derive new non-canonical manifestly duality invariant
quartic interactions. Correspondingly, we construct new non-trivial quartic
interactions also in the GZGR approach, and establish their equivalence with
the former. In the presence of charged dyonic p-brane sources, we reveal a
basic physical inequivalence of the two approaches. The power of our method
resides in its universal character, reducing the construction of non-linear
duality invariant Maxwell theories to a purely algebraic problem. |
Path-integral formula for local thermal equilibrium: We develop a complete path-integral formulation of relativistic quantum
fields in local thermal equilibrium, which brings about the emergence of
thermally induced curved spacetime. The resulting action is shown to have full
diffeomorphism invariance and gauge invariance in thermal spacetime with
imaginary-time independent backgrounds. This leads to the notable symmetry
properties of emergent thermal spacetime: Kaluza-Klein gauge symmetry, spatial
diffeomorphism symmetry, and gauge symmetry. A thermodynamic potential in local
thermal equilibrium, or the so-called Masseiu-Planck functional, is identified
as a generating functional for conserved currents such as the energy-momentum
tensor and the electric current. | Density response and collective modes of semi-holographic non-Fermi
liquids: Semi-holographic models of non-Fermi liquids have been shown to have
generically stable generalised quasi-particles on the Fermi surface. Although
these excitations are broad and exhibit particle-hole asymmetry, they were
argued to be stable from interactions at the Fermi surface. In this work, we
use this observation to compute the density response and collective behaviour
in these systems.
Compared to the Fermi liquid case, we find that the boundaries of the
particle-hole continuum are blurred by incoherent contributions. However, there
is a region inside this continuum, that we call inner core, within which
salient features of the Fermi liquid case are preserved. A particularly
striking prediction of our work is that these systems support a plasmonic
collective excitation which is well-defined at large momenta, has an
approximately linear dispersion relation and is located in the low-energy tail
of the particle-hole continuum.
Furthermore, the dynamic screening potential shows deep attractive regions as
a function of the distance at higher frequencies which might lead to long-lived
pair formation depending on the behaviour of the pair susceptibility. We also
find that Friedel oscillations are present in these systems but are highly
suppressed. |
One-loop tunnelling-induced energetics: Tunnelling between degenerate vacuua is allowed in finite-volume Quantum
Field Theory, and features remarkable energetic properties, which result from
the competition of different dominant configurations in the partition function.
We derive the one-loop effective potential based on two homogeneous vacuua of
the bare theory, and we discuss the resulting Null Energy Condition violation
in O(4)-symmetric Euclidean spacetime, as a result of a non-extensive effective
action. | The Yang Monopole in IIA Superstring: Multi-charge Disease and Enhancon
Cure: A brane picture in Type IIA superstring for the Yang Monopole is
reconsidered. It makes use of D2 and D4-branes wrapped on cycles in the K3
surface. When the model was first presented some problems concerning the
charges of the monopoles arised. In this paper, they are shown to be cured by
the model itself. Surprisingly, the incompatibility between the multi-charge
configuration and the spherical symmetry of the Yang Monopole is seen in the
brane description as the emergence of the enhancon shell and the fuzzy
geometry. This consistency is deep and surprising, and is the point that
triggered this work. It nontrivially relates a purely geometrical problem in
ordinary spacetime with the emergence of noncommutative geometries. Besides,
this paper includes an extended model for SO(4)-monopoles, a T-dual model in
Type IIB superstring and an analysis on the possible duality between our model
and another setup in M-Theory/Heterotics for the Yang monopole found before. |
Localization of Fields on a Brane in Six Dimensions: Universe is considered as a brane in infinite (2+4)-space.It is shown that
zero modes of all kinds of matter fields and 4-gravity are localized on the
brane by increasing transversal gravitational potential. | Faces of matrix models: Partition functions of eigenvalue matrix models possess a number of very
different descriptions: as matrix integrals, as solutions to linear and
non-linear equations, as tau-functions of integrable hierarchies and as
special-geometry prepotentials, as result of the action of W-operators and of
various recursions on elementary input data, as gluing of certain elementary
building blocks. All this explains the central role of such matrix models in
modern mathematical physics: they provide the basic "special functions" to
express the answers and relations between them, and they serve as a dream model
of what one should try to achieve in any other field. |
Generalized Hirota Equations in Models of 2D Quantum Gravity: We derive a set of bilinear functional equations of Hirota type for the
partition functions of the $sl(2)$ related integrable statistical models
defined on a random lattice. These equations are obtained as deformations of
the Hirota equations for the KP integrable hierarchy, which are satisfied by
the partition function of the ensemble of planar graphs. | Symmetries of the Self-Dual Sector of N=4 Super Yang-Mills on the Light
Cone: A recent paper proposes a way of constructing infinite dimensional symmetries
of the non-supersymmetric self-dual Yang-Mills action using isometries of the
space-time. We review the Lagrangian formulation of N = 4 super Yang-Mills MHV
rules and extend the approach taken for the non-supersymmetric case to
construct infinite dimensional symmetries of self-dual N = 4 super Yang-Mills. |
Holographic models with anisotropic scaling: We consider gravity duals to d+1 dimensional quantum critical points with
anisotropic scaling. The primary motivation comes from strongly correlated
electron systems in condensed matter theory but the main focus of the present
paper is on the gravity models in their own right. Physics at finite
temperature and fixed charge density is described in terms of charged black
branes. Some exact solutions are known and can be used to obtain a maximally
extended spacetime geometry, which has a null curvature singularity inside a
single non-degenerate horizon, but generic black brane solutions in the model
can only be obtained numerically. Charged matter gives rise to black branes
with hair that are dual to the superconducting phase of a holographic
superconductor. Our numerical results indicate that holographic superconductors
with anisotropic scaling have vanishing zero temperature entropy when the back
reaction of the hair on the brane geometry is taken into account. | (3+1) Massive Dirac Fermions with Ultracold Atoms in Optical Lattices: We propose the experimental realization of (3+1) relativistic Dirac fermions
using ultracold atoms in a rotating optical lattice or, alternatively, in a
synthetic magnetic field. This approach has the advantage to give mass to the
Dirac fermions by coupling the ultracold atoms to a Bragg pulse. A dimensional
crossover from (3+1) to (2+1) Dirac fermions can be obtained by varying the
anisotropy of the lattice. We also discuss under which conditions the
interatomic potentials give rise to relativistically invariant interactions
among the Dirac fermions. |
Five dimensional $O(N)$-symmetric CFTs from conformal bootstrap: We investigate the conformal bootstrap approach to $O(N)$ symmetric CFTs in
five dimension with particular emphasis on the lower bound on the current
central charge. The bound has a local minimum for all $N>1$, and in the large
$N$ limit we propose that the minimum is saturated by the critical $O(N)$
vector model at the UV fixed point, the existence of which has been recently
argued by Fei, Giombi, and Klebanov. The location of the minimum is generically
different from the minimum of the lower bound of the energy-momentum tensor
central charge when it exists for smaller $N$.
To better understand the situation, we examine the lower bounds of the
current central charge of $O(N)$ symmetric CFTs in three dimension to compare.
We find the similar agreement in the large $N$ limit but the discrepancy for
smaller $N$ with the other sectors of the conformal bootstrap. | Perturbations of spiky strings in flat spacetimes: Perturbations of a class of semiclassical strings known today as spiky
strings, are studied using the well-known Jacobi equations for small normal
deformations of an embedded timelike surface. It is shown that there exists
finite normal perturbations of the spiky string worldsheets embedded in a $2+1$
dimensional flat spacetime. Such perturbations lead to a rounding off of the
spikes, which, in a way, demonstrates the stable nature of the unperturbed
worldsheet. The same features appear for the dual spiky string solution and in
the spiky as well as their dual solutions in $3+1$ dimensional flat spacetime.
Our results are based on exact solutions of the corresponding Jacobi equations
which we obtain and use while constructing the profiles of the perturbed
configurations. |
Complexified boost invariance and holographic heavy ion collisions: At strong coupling holographic studies have shown that heavy ion collisions
do not obey normal boost invariance. Here we study a modified boost invariance
through a complex shift in time, and show that this leads to surprisingly good
agreement with numerical holographic computations. When including perturbations
the agreement becomes even better, both in the hydrodynamic and the
far-from-equilibrium regime. One of the main advantages is an analytic
formulation of the stress-energy tensor of the longitudinal dynamics of
holographic heavy ion collisions. | A rotating black ring in five dimensions: The vacuum Einstein equations in five dimensions are shown to admit a
solution describing an asymptotically flat spacetime regular on and outside an
event horizon of topology S^1 x S^2. It describes a rotating ``black ring''.
This is the first example of an asymptotically flat vacuum solution with an
event horizon of non-spherical topology. There is a range of values for the
mass and angular momentum for which there exist two black ring solutions as
well as a black hole solution. Therefore the uniqueness theorems valid in four
dimensions do not have simple higher dimensional generalizations. It is
suggested that increasing the spin of a five dimensional black hole beyond a
critical value results in a transition to a black ring, which can have an
arbitrarily large angular momentum for a given mass. |
On auxiliary fields and Lagrangians for relativistic wave equations: We address the problem of the existence of a Lagrangian for a given system of
linear PDEs with constant coefficients. As a subtask, this involves bringing
the system into a pre-Lagrangian form, wherein the number of equations matches
the number of unknowns. We introduce a class of overdetermined systems, called
co-flat, and show that they always admit a pre-Lagrangian form, which can be
explicitly constructed using auxiliary variables. Moreover, we argue that such
systems enjoy pre-Lagrangian formulations without auxiliary variables at all.
As an application of our method, we construct new pre-Lagrangian and Lagrangian
formulations for free massive fields of arbitrary integer spin. In contrast to
the well-known models of Singh and Hagen, our Lagrangians involve much fewer
auxiliary fields. | Universal flow equations and chaos bound saturation in 2d dilaton
gravity: We show that several features of the Jackiw-Teitelboim model are in fact
universal properties of two-dimensional Maxwell-dilaton gravity theories with a
broad class of asymptotics. These theories satisfy a flow equation with the
structure of a dimensionally reduced TTbar deformation, and exhibit chaotic
behavior signaled by a maximal Lyapunov exponent. One consequence of our
results is a no-go theorem for smooth flows from an asymptotically AdS2 region
to a de Sitter fixed point. |
Dear Qubitzers, GR=QM: These are some thoughts contained in a letter to colleagues, about the close
relation between gravity and quantum mechanics, and also about the possibility
of seeing quantum gravity in a lab equipped with quantum computers. I expect
this will become feasible sometime in the next decade or two. | Driven black holes: from Kolmogorov scaling to turbulent wakes: General relativity governs the nonlinear dynamics of spacetime, including
black holes and their event horizons. We demonstrate that forced black hole
horizons exhibit statistically steady turbulent spacetime dynamics consistent
with Kolmogorov's theory of 1941. As a proof of principle we focus on black
holes in asymptotically anti-de Sitter spacetimes in a large number of
dimensions, where greater analytic control is gained. We also demonstrate that
tidal deformations of the horizon induce turbulent dynamics. When set in motion
relative to the horizon a deformation develops a turbulent spacetime wake,
indicating that turbulent spacetime dynamics may play a role in binary mergers
and other strong-field phenomena. |
Bootstrapping Conformal Field Theories with the Extremal Functional
Method: The existence of a positive linear functional acting on the space of
(differences between) conformal blocks has been shown to rule out regions in
the parameter space of conformal field theories (CFTs). We argue that at the
boundary of the allowed region the extremal functional contains, in principle,
enough information to determine the dimensions and OPE coefficients of an
infinite number of operators appearing in the correlator under analysis. Based
on this idea we develop the Extremal Functional Method (EFM), a numerical
procedure for deriving the spectrum and OPE coefficients of CFTs lying on the
boundary (of solution space). We test the EFM by using it to rederive the low
lying spectrum and OPE coefficients of the 2d Ising model based solely on the
dimension of a single scalar quasi-primary -- no Virasoro algebra required. Our
work serves as a benchmark for applications to more interesting, less known
CFTs in the near future. | Strong coupling from the Hubbard model: It was recently observed that the one dimensional half-filled Hubbard model
reproduces the known part of the perturbative spectrum of planar N=4 super
Yang-Mills in the SU(2) sector. Assuming that this identification is valid
beyond perturbation theory, we investigate the behavior of this spectrum as the
't Hooft parameter \lambda becomes large. We show that the full dimension
\Delta of the Konishi superpartner is the solution of a sixth order polynomial
while \Delta for a bare dimension 5 operator is the solution of a cubic. In
both cases the equations can be solved easily as a series expansion for both
small and large \lambda and the equations can be inverted to express \lambda as
an explicit function of \Delta. We then consider more general operators and
show how \Delta depends on \lambda in the strong coupling limit. We are also
able to distinguish those states in the Hubbard model which correspond to the
gauge invariant operators for all values of \lambda. Finally, we compare our
results with known results for strings on AdS_5\times S^5, where we find
agreement for a range of R-charges. |
I. Calculation of the observed value of large mass hierarchy in modified
RS model: In generalized Randall-Sundrum (RS) model with dilaton where bulk potential
is generated by the antisymmetric tensor field the mass term of this field is
introduced into the brane's Action. This permits to stabilize brane's position
and hence to calculate the Planck/electroweek scales ratio which proves to
depend non-analytically on the dilaton-antisymmetric tensor field coupling
constant. The large observed number of mass hierarchy is achieved for the
moderate value of this coupling constant of order 0,3. In the subsequent Paper
II it is shown that the same approach in a higher dimensional theory without
dilaton permits to express mass hierarchy only through number of extra
dimensions. | Superstring Vacua of 4-dimensional PP-Waves with Enhanced Supersymmetry: We study the superstring vacua constructed from the conformal field theories
of the type H_4 x M, where H_4 denotes the super Nappi-Witten model (super WZW
model on the 4-dimensional Heisenberg group H_4) and M denotes an arbitrary N=2
rational superconformal field theory with c=9. We define (type II) superstring
vacua with 8 supercharges, which are twice as many as those on the backgrounds
of H_4 x CY_3. We explicitly construct as physical vertices the space-time SUSY
algebra that is a natural extension of H_4 Lie algebra. The spectrum of
physical states is classified into two sectors: (1) strings freely propagating
along the transverse plane of pp-wave geometry and possessing the integral
U(1)_R-charges in M sector, and (2) strings that do not freely propagate along
the transverse plane and possess the fractional U(1)_R-charges in M. The former
behaves like the string excitations in the usual Calabi-Yau compactification,
but the latter defines new sectors without changing the physics in ``bulk''
space. We also analyze the thermal partition functions of these systems,
emphasizing the similarity to the DLCQ string theory. As a byproduct we prove
the supersymmetric cancellation of conformal blocks in an arbitrary unitary N=2
SCFT of c=12 with the suitable GSO projection. |
On Newton-Cartan local renormalization group and anomalies: Weyl consistency conditions are a powerful tool to study the irreversibility
properties of the renormalization group. We apply this formalism to
non-relativistic theories in 2 spatial dimensions with boost invariance and
dynamical exponent z=2. Different possibilities are explored, depending on the
structure of the gravitational background used as a source for the
energy-momentum tensor. | Vacua scan of $5d$, $N=2$ consistent truncations: In this letter we present a scan for new vacua within consistent truncations
of eleven/ten-dimensional supergravity down to five dimensions that preserve $N
= 2$ supersymmetry, after their complete classification in arXiv:2112.03931. We
first make explicit the link between the equations of exceptional
Sasaki-Einstein backgrounds in arXiv:1602.02158 and the standard BPS equations
for $5d$ $N = 2$ of arXiv:1601.00482. This derivation allows us to expedite a
scan for vacua preserving $N = 2$ supersymmetry within the framework used for
the classification presented in arXiv:2112.03931. |
Generalized Second Law of Thermodynamics in Quintom Dominated Universe: In this paper we will investigate the validity of the Generalized Second Law
of thermodynamics for the Quintom model of dark energy. Reviewing briefly the
quintom scenario of dark energy, we will study the conditions of validity of
the generalized second law of thermodynamics in three cases: quintessence
dominated, phantom dominated and transition from quintessence to phantom will
be discussed. | Quantized Coulomb Branches, Monopole Bubbling and Wall-Crossing
Phenomena in 3d $\mathcal{N}=4$ Theories: To study the quantized Coulomb branch of 3d $\mathcal{N}=4$ unitary SQCD
theories, we propose a new method to compute correlators of monopole and
Casimir operators that are inserted in the
$\mathbb{R}\times\mathbb{R}^2_\epsilon$ Omega background. This method combines
results from supersymmetric localization with inputs from the brane realisation
of the correlators in type IIB string theory. The main challenge is the
computation of the partition functions of certain Super-Matrix-Models (SMMs),
which appear in the contribution of monopole bubbling sectors and are realised
as the theory living on the D1 strings in the brane construction. We find that
the non-commutativity arising in the monopole operator insertions is related to
a wall-crossing phenomenon in the FI parameter space of the SMM. We illustrate
our method in various examples and we provide explicit results for arbitrary
correlators of non-bubbling bare monopole operators. We also discuss the
realisation of the non-commutative product as a Moyal (star) product and use it
to successfully test our results. |
Lovelock black p-branes with fluxes: In this paper we construct compactifications of generic, higher curvature
Lovelock theories of gravity over direct product spaces of the type
$\mathcal{M}_D=\mathcal{M}_d \times \mathcal{S}^p $, with $D=d+p$ and $d\ge5$,
where $\mathcal{S}^p$ represents an internal, Euclidean manifold of positive
constant curvature. We show that this can be accomplished by including suitable
non-minimally coupled $p-1$-form fields with a field strength proportional to
the volume form of the internal space. We provide explicit details of this
constructions for the Einstein-Gauss-Bonnet theory in $d+2$ and $d+3$
dimensions by using one and two-form fundamental fields, and provide as well
the formulae that allows to construct the same family of compactification in
any Lovelock theory from dimension $d+p$ to dimension $d$. These fluxed
compactifications lead to an effective Lovelock theory on the compactfied
manifold, allowing therefore to find, in the Einstein-Gauss-Bonnet case, black
holes in the Boulware-Deser family. | On factorising twists in AdS_3 and AdS_2: In this paper we study factorising twists of the massless AdS_3 and AdS_2
integrable R-matrices, and explore the programme of analysis of form factors
which Maillet et al developed for ordinary spin-chains. We derive the
factorising twists from the universal R-matrix of the gl(1|1) Yangian double,
and discuss the RTT relations for the two- and three-site monodromy matrix. We
show how the twist can be used to compute a simple scalar product. We then
implement our construction in the language of free fermions. Finally, we show
how to obtain the massless AdS_2 quantum R-matrix from the Yangian universal
R-matrix, and compute a peculiar factorising twist for this case as well. |
Scale-invariant alternatives to general relativity: We study the general class of gravitational field theories constructed on the
basis of scale invariance (and therefore absence of any mass parameters) and
invariance under transverse diffeomorphisms (TDiff), which are the 4-volume
conserving coordinate transformations. We show that these theories are
equivalent to a specific type of scalar-tensor theories of gravity (invariant
under all diffeomorphisms) with a number of properties, making them
phenomenologically interesting. They contain, in addition to the dimensionless
coupling constants of the original theory, an arbitrary dimensionful parameter
$\Lambda_0$. This parameter is associated with an integration constant of the
equations of motion, similar to the arbitrary cosmological constant appearing
in unimodular gravity. We focus on the theories where Newton's constant and the
electroweak scale emerge from the spontaneous breaking of scale invariance and
are unrelated to $\Lambda_0$. The massless particle spectrum of these theories
contains the graviton and a new particle -- dilaton. For $\Lambda_0=0$, the
massless dilaton has only derivative couplings to matter fields and the bounds
on the existence of a 5th force are easily satisfied. As for the matter fields,
we determine the conditions leading to a renormalizable low-energy theory. If
$\Lambda_0\neq 0$, scale invariance is broken. The arbitrary constant
$\Lambda_0$ produces a "run-away" potential for the dilaton. As a consequence,
the dilaton can act as a dynamical dark energy component. We elucidate the
origin of the cosmological constant in the class of theories under
consideration and formulate the condition leading to its absence. If this
condition is satisfied, dark energy is purely dynamical and associated to the
dilaton. | OPE for all Helicity Amplitudes: We extend the Operator Product Expansion (OPE) for scattering amplitudes in
planar N=4 SYM to account for all possible helicities of the external states.
This is done by constructing a simple map between helicity configurations and
so-called charged pentagon transitions. These OPE building blocks are
generalizations of the bosonic pentagons entering MHV amplitudes and they can
be bootstrapped at finite coupling from the integrable dynamics of the color
flux tube. A byproduct of our map is a simple realization of parity in the
super Wilson loop picture. |
Quantum Matter near a Cosmological Singularity: General Relativity predicts that the spacetime near a cosmological
singularity undergoes an infinite number of chaotic oscillations between
different Kasner epochs with rapid transitions between them. This so-called BKL
behaviour persists in the presence of several types of classical matter. Little
is known in the presence of quantum effects. A major obstacle is the fact that
the fast metric oscillations inevitably drive the matter far from equilibrium.
We use holography to determine the evolution of the quantum stress tensor of a
non-conformal, strongly-coupled, four-dimensional gauge theory in a Kasner
spacetime. The stress tensor near the singularity is solely controlled by the
ultraviolet fixed point of the gauge theory, and it diverges in a universal way
common to all theories with a gravity dual. We then compute the backreaction of
the stress tensor on the Kasner metric to leading order in the gravitational
coupling. The modification of the Kasner exponents that we find suggests that
the BKL behaviour may be avoided in the presence of quantum matter. | 3D Flat Holography: Entropy and Logarithmic Corrections: We compute the leading corrections to the Bekenstein-Hawking entropy of the
Flat Space Cosmological (FSC) solutions in 3D flat spacetimes, which are the
flat analogues of the BTZ black holes in AdS3. The analysis is done by a
computation of density of states in the dual 2D Galilean Conformal Field Theory
and the answer obtained by this matches with the limiting value of the expected
result for the BTZ inner horizon entropy as well as what is expected for a
generic thermodynamic system. Along the way, we also develop other aspects of
holography of 3D flat spacetimes. |
Potentials for (p,0) and (1,1) supersymmetric sigma models with torsion: Using (1,0) superfield methods, we determine the general scalar potential
consistent with off-shell (p,0) supersymmetry and (1,1) supersymmetry in
two-dimensional non-linear sigma models with torsion. We also present an
extended superfield formulation of the (p,0) models and show how the (1,1)
models can be obtained from the (1,1)-superspace formulation of the gauged, but
massless, (1,1) sigma model. | BRST superspace and auxiliary fields for N=1 supersymmetric Yang-Mills
theory: We use a Becchi-Rouet-Stora-Tyutin (BRST) superspace approach to formulate
off-shell nilpotent BRST and anti-BRST transformations in four dimensional N=1
supersymmetric Yang-Mills theory. The method is based on the possibility of
introducing auxiliary fields through the supersymmetric transformations of the
superpartener of the gauge potential associated to a supersymmetric Yang-Mills
connection. These fields are required to achieve the off-shell nilpotency of
the BRST and anti-BRST operators. We also show how this off-shell structure is
used to build the BRST and anti-BRST invariant gauge-fixing quantum action. |
Non-Abelian Born-Infeld Action and Type I - Heterotic Duality (II):
Nonrenormalization Theorems: Type I - heterotic duality in D=10 predicts various relations and constraints
on higher order F^n couplings at different string loop levels on both sides. We
prove the vanishing of two-loop corrections to the heterotic F^4 terms, which
is one of the basic predictions from this duality. Furthermore, we show that
the heterotic F^5 and (CP even) F^6 couplings are not renormalized at one loop.
These results strengthen the conjecture that in D=10 any Tr F^(2n) coupling
appears only at the disc tree-level on type I side and at (n-1)-loop level on
the heterotic side. Our non-renormalization theorems are valid in any heterotic
string vacuum with sixteen supercharges. | A comment concerning cohomology and invariants of Lie algebras with
respect to contractions and deformations: Contrary to the expected behavior, we show the existence of non-invertible
deformations of Lie algebras which can generate invariants for the coadjoint
representation, as well as delete cohomology with values in the trivial or
adjoint module. A criterion to decide whether a given deformation is invertible
or not is given in dependence of the Poincar\'e polynomial. |
Conformal Transformation in Gravity: The conformal transformation in the Einstein - Hilbert action leads to a new
frame where an extra scalar degree of freedom is compensated by the local
conformal-like symmetry. We write down a most general action resulting from
such transformation and show that it covers both general relativity and
conformally coupled to gravity scalar field as the particular cases. On quantum
level the equivalence between the different frames is disturbed by the loop
corrections. New conformal-like symmetry in anomalous and, as a result, the
theory is not finite on shell at the one-loop order. | Dualities of 3D $\mathcal{N}=1$ SQCD from Branes and non-SUSY
deformations: We study the dynamics of an 'electric' $\mathcal{N}=1$ 3D
$U(N_c)_{k,k+\frac{N_c}{2}}$ SQCD theory. By embedding the theory in string
theory, we propose that the theory admits a 'magnetic' dual and analyse the low
energy dynamics of the theory using its dual. When $\frac{N_f}{2}
\ge\frac{N_c}{2}-k$ the IR dynamics is described by either a TQFT for large
quark masses, or a Grassmanian and a Wess-Zumino (WZ) term for small masses. We
also consider non-supersymmetric mass deformations and RG flows in the vicinity
of the SUSY point and find agreement between the IR of the electric and its
magnetic dual. When $\frac{N_f}{2} < \frac{N_c}{2}-k$ supersymmetry is broken
and the IR dynamics is a described by a TQFT accompanied by a Goldstino. We
also discuss SQCD theories based on $SO$/$USp$ gauge groups. |
Quantum field theory: Finiteness and Effectiveness: A new attempt is demonstrated that QFTs can be UV finite if they are viewed
as the low energy effective theories of a fundamental underlying theory (that
is complete and well-defined in all respects) according to the modern standard
point of view. This approach works for any interaction model and space-time
dimension. It is much simpler in principle and in technology comparing to any
known renormalization program.Unlike the known renormalization methods, the
importance of the procedure for defining the ambiguities (corresponding to the
choice of the renormalization conditions in the conventional program) is fully
appreciated in the new approach. It is shown that the high energy theory(s) or
the underlying theory(s) in fact 'stipulates (stipulate)' the low energy and
effective ones through these definitions within our approach while all the
conventional methods miss this important point. Some simple but important
nonperturbative examples are discussed to show the power and plausibility of
the new approach. Other related issues (especially the IR problem and the
implication of our new approach for the canonical quantization procedure) are
briefly touched. | Vortex solutions in the Abelian Higgs Model with a neutral scalar: We construct an extension of the Abelian Higgs model, which consists of a
complex scalar field by including an additional real, electromagnetically
neutral scalar field. We couple this real scalar field to the complex scalar
field via a quartic coupling and investigate $U(1)$ vortex solutions in this
"extended Abelian Higgs Model". Since this model has two additional homogeneous
ground states, the $U(1)$ vortices that can form in this model have a richer
structure than in the Abelian Higgs Model. We also find the "phase diagram" of
the model showing the parameter space in which the real scalar particle
condenses in the vortex state while having a zero vacuum expectation value in
the homogeneous ground state. |
Remarks on BMS${}_3$ invariant field theories: correlation functions and
nonunitary CFTs: We use the isomorphism between the BMS${}_3$ and the $W(2,2)$ algebras to
reconsider some generic aspects of CFTs with the BMS${}_3$ algebra defined as a
chiral symmetry. For unitarity theories, it is known that the extended symmetry
generator acts trivially, and the resulting theory is equivalent to a CFT with
a Virasoro symmetry only. For nonunitary CFTs, we define an operator depending
on a nilpotent variable, and we organize the Verma module through the action of
this new operator. Finally, we find the conditions imposed by the modified Ward
identity. | Asymptotic dynamics of three-dimensional gravity: These are the lectures notes of the course given at the Eleventh Modave
Summer School in Mathematical Physics, 2015, aimed at PhD candidates and junior
researchers in theoretical physics. We review in details the result of
Coussaert-Henneaux-van Driel showing that the asymptotic dynamics of $(2+1)$-
dimensional gravity with negative cosmological constant is described at the
classical level by Liouville theory. Boundary conditions implement the
asymptotic reduction in two steps: the first set reduces the $SL(2,\mathbb
R)\times SL(2,\mathbb R)$ Chern-Simons action, equivalent to the Einstein
action, to a non-chiral $SL(2,\mathbb R)$ Wess-Zumino-Witten model, while the
second set imposes constraints on the WZW currents that reduce further the
action to Liouville theory. We discuss the issues of considering the latter as
an effective description of the dual conformal field theory describing AdS$_3$
gravity beyond the semi-classical regime. |
Boundary contributions to three loop superstring amplitudes: In type II superstring theory, the vacuum amplitude at a given loop order $g$
can receive contributions from the boundary of the compactified, genus $g$
supermoduli space of curves $\overline{\mathfrak M}_g$. These contributions
capture the long distance or infrared behaviour of the amplitude. The boundary
parametrises degenerations of genus $g$ super Riemann surfaces. A holomorphic
projection of the supermoduli space onto its reduced space would then provide a
way to integrate the holomorphic, superstring measure and thereby give the
superstring vacuum amplitude at $g$-loop order. However, such a projection does
not generally exist over the bulk of the supermoduli spaces in higher genera.
Nevertheless, certain boundary divisors in $\partial\overline{\mathfrak M}_g$
may holomorphically map onto a bosonic space upon composition with universal
morphisms, thereby enabling an integration of the holomorphic, superstring
measure here. Making use of ansatz factorisations of the superstring measure
near the boundary, our analysis shows that the boundary contributions to the
three loop vacuum amplitude will vanish in closed oriented type II superstring
theory with unbroken spacetime supersymmetry. | Photon-Graviton Amplitudes from the Effective Action: We report on the status of an ongoing effort to calculate the complete
one-loop low-energy effective actions in Einstein-Maxwell theory with a massive
scalar or spinor loop, and to use them for obtaining the explicit form of the
corresponding M-graviton/N-photon amplitudes. We present explicit results for
the effective actions at the one-graviton four-photon level, and for the
amplitudes at the one-graviton two-photon level. As expected on general
grounds, these amplitudes relate in a simple way to the corresponding
four-photon amplitudes. We also derive the gravitational Ward identity for the
1PI one-graviton -- N photon amplitude. |
Black hole formation, holographic thermalization and the AdS/CFT
correspondence: The AdS/CFT correspondence is one of the most important discoveries in
theoretical physics in recent years. It states that certain quantum mechanical
theories can actually be described by classical gravity in one higher
dimension, in a spacetime called anti-de Sitter (AdS) space. What makes this
duality so useful is that it relates theories with weak coupling to theories
with strong coupling and thus provides a new tool for tackling strongly coupled
quantum field theories, which are notoriously difficult to handle using
conventional methods. During the course of my PhD I have mostly studied time
dependent processes, in particular thermalization processes, in quantum field
theories using the AdS/CFT correspondence. On the gravity side, this is dual to
dynamical formation of black holes from the collapse of matter fields. By
studying the gravitational collapse process in detail, we can then draw
conclusions about the dynamical formation of a thermal state in the dual
quantum field theory. Using mostly numerical methods, I have studied how
confinement affects thermalization in quantum field theories, where the system
may never thermalize and field theory observables undergo interesting
quasiperiodic behaviour. I have also studied formation of black holes in three
dimensions which due to the simplified nature of three-dimensional gravity can
be done using analytical methods. This has led to the discovery of new
solutions of three-dimensional gravity corresponding to the formation of black
holes without spherical symmetry, which can provide a deeper understanding of
thermalization in two-dimensional quantum field theories. In a third line of
research, I have studied higher spin gravity in three dimensions, an exotic
extension of three-dimensional gravity which includes fields with spin higher
than two, and we outline a new method to construct black hole solutions
carrying higher spin charge. | A holographic model for black hole complementarity: We explore a version of black hole complementarity, where an approximate
semiclassical effective field theory for interior infalling degrees of freedom
emerges holographically from an exact evolution of exterior degrees of freedom.
The infalling degrees of freedom have a complementary description in terms of
outgoing Hawking radiation and must eventually decohere with respect to the
exterior Hamiltonian, leading to a breakdown of the semiclassical description
for an infaller. Trace distance is used to quantify the difference between the
complementary time evolutions, and to define a decoherence time. We propose a
dictionary where the evolution with respect to the bulk effective Hamiltonian
corresponds to mean field evolution in the holographic theory. In a particular
model for the holographic theory, which exhibits fast scrambling, the
decoherence time coincides with the scrambling time. The results support the
hypothesis that decoherence of the infalling holographic state and disruptive
bulk effects near the curvature singularity are complementary descriptions of
the same physics, which is an important step toward resolving the black hole
information paradox. |
Large-N limit of the generalized 2D Yang-Mills theory on cylinder: Using the collective field theory approach of large-N generalized
two-dimensional Yang-Mills theory on cylinder, it is shown that the classical
equation of motion of collective field is a generalized Hopf equation. Then,
using the Itzykson-Zuber integral at the large-N limit, it is found that the
classical Young tableau density, which satisfies the saddle-point equation and
determines the large-N limit of free energy, is the inverse of the solution of
this generalized Hopf equation, at a certain point. | Distinguishing Elliptic Fibrations with AI: We use the latest techniques in machine-learning to study whether from the
landscape of Calabi-Yau manifolds one can distinguish elliptically fibred ones.
Using the dataset of complete intersections in products of projective spaces
(CICY3 and CICY4, totalling about a million manifolds) as a concrete
playground, we find that a relatively simple neural network with
forward-feeding multi-layers can very efficiently distinguish the elliptic
fibrations, much more so than using the traditional methods of manipulating the
defining equations. We cross-check with control cases to ensure that the AI is
not randomly guessing and is indeed identifying an inherent structure. Our
result should prove useful in F-theory and string model building as well as in
pure algebraic geometry. |
Spectral Dimension of kappa-deformed space-time: We investigate the spectral dimension of $\kappa$-space-time using the
$\kappa$-deformed diffusion equation. The deformed equation is constructed for
two different choices of Laplacians in $n$-dimensional, $\kappa$-deformed
Euclidean space-time. We use an approach where the deformed Laplacians are
expressed in the commutative space-time itself. Using the perturbative
solutions to diffusion equations, we calculate the spectral dimension of
$\kappa$-deformed space-time and show that it decreases as the probe length
decreases. By introducing a bound on the deformation parameter, spectral
dimension is guaranteed to be positive definite. We find that, for one of the
choices of the Laplacian, the non-commutative correction to the spectral
dimension depends on the topological dimension of the space-time whereas for
the other, it is independent of the topological dimension. We have also
analysed the dimensional flow for the case where the probe particle has a
finite extension, unlike a point particle. | Zilch Vortical Effect for Fermions: We consider the notion of zilch current that was recently discussed in the
literature as an alternative helicity measure for photons. Developing this
idea, we suggest the generalization of the zilch for the systems of fermions.
We start with the definition of the photonic zilch current in chiral kinetic
theory framework and work out field-theoretical definition of the fermionic
zilch using the Wigner function formalism. This object has similar properties
to the photonic zilch and is conserved in the non-interacting theory. We also
show that, in full analogy with a case of photons, the fermionic zilch acquires
a non-trivial contribution due to the medium rotation - zilch vortical effect
(ZVE) for fermions. Combined with a previously studied ZVE for photons, these
results form a wider set of chiral effects parameterized by the spin of the
particles and the spin of the current. We briefly discuss the origin of the
ZVE, its possible relation to the anomalies in the underlying microscopic
theory and possible application for studying the spin polarization in chiral
media. |
Exploring the Tensor Networks/AdS Correspondence: In this paper we study the recently proposed tensor networks/AdS
correspondence. We found that the Coxeter group is a useful tool to describe
tensor networks in a negatively curved space. Studying generic tensor network
populated by perfect tensors, we find that the physical wave function
generically do not admit any connected correlation functions of local
operators. To remedy the problem, we assume that wavefunctions admitting such
semi-classical gravitational interpretation are composed of tensors close to,
but not exactly perfect tensors. Computing corrections to the connected two
point correlation functions, we find that the leading contribution is given by
structures related to geodesics connecting the operators inserted at the
boundary physical dofs. Such considerations admit generalizations at least to
three point functions. This is highly suggestive of the emergence of the
analogues of Witten diagrams in the tensor network. The perturbations alone
however do not give the right entanglement spectrum. Using the Coxeter
construction, we also constructed the tensor network counterpart of the BTZ
black hole, by orbifolding the discrete lattice on which the network resides.
We found that the construction naturally reproduces some of the salient
features of the BTZ black hole, such as the appearance of RT surfaces that
could wrap the horizon, depending on the size of the entanglement region A. | Higher-Spin Self-Dual Yang-Mills and Gravity from the twistor space: We lift the recently proposed theories of higher-spin self-dual Yang-Mills
(SDYM) and gravity (SDGR) to the twistor space. We find that the most natural
room for the twistor formulation of these theories is not in the projective,
but in the full twistor space, which is the total space of the spinor bundle
over the 4-dimensional manifold. In the case of higher-spin extension of the
SDYM we prove an analogue of the Ward theorem, and show that there is a
one-to-one correspondence between the solutions of the field equations and
holomorphic vector bundles over the twistor space. In the case of the
higher-spin extension of SDGR we show show that there is a one-to-one
correspondence between solutions of the field equations and Ehresmann
connections on the twistor space whose horizontal distributions are Poisson,
and whose curvature is decomposable. These data then define an almost complex
structure on the twistor space that is integrable. |
Renormalization Group Circuits for Weakly Interacting Continuum Field
Theories: We develop techniques to systematically construct local unitaries which map
scale-invariant, product state wavefunctionals to the ground states of weakly
interacting, continuum quantum field theories. More broadly, we devise a
"quantum circuit perturbation theory" to construct local unitaries which map
between any pair of wavefunctionals which are each Gaussian with arbitrary
perturbative corrections. Further, we generalize cMERA to interacting continuum
field theories, which requires reworking the existing formalism which is
tailored to non-interacting examples. Our methods enable the systematic
perturbative calculation of cMERA circuits for weakly interacting theories, and
as a demonstration we compute the 1-loop cMERA circuit for scalar $\varphi^4$
theory and analyze its properties. In this case, we show that Wilsonian
renormalization of the spatial momentum modes is equivalent to a local position
space cMERA circuit. This example provides new insights into the connection
between position space and momentum space renormalization group methods in
quantum field theory. The form of cMERA circuits derived from perturbation
theory suggests useful ansatzes for numerical variational calculations. | The AdS^2_θ/CFT_1 Correspondence and Noncommutative Geometry II:
Noncommutative Quantum Black Holes: In this article we present the construction of noncommutative AdS^2_{\theta}
black hole and its four-dimensional Yang-Mills IKKT-type matrix model which
includes two competing Myers term one responsible for the condensation of pure
AdS^2_{\theta} and the other one responsible for the condensation of the
dilaton field. It is argued that the phase diagram of this matrix model
features three phases: 1) A gravitational phase (AdS^2_{\theta} black hole), 2)
A geometric phase (AdS^2_{\theta} background) and 3) A Yang-Mills phase. The
Hawking process is therefore seen as an exotic line of discontinuous
transitions between the gravitational and geometrical phases. Alternatively, a
noncommutative non-linear sigma model describing the transition of the dilaton
field between the gravitational and geometrical phases is also constructed. |
On The Entanglement Entropy For Gauge Theories: We propose a definition for the entanglement entropy of a gauge theory on a
spatial lattice. Our definition applies to any subset of links in the lattice,
and is valid for both Abelian and Non-Abelian gauge theories. For
$\mathbb{Z}_N$ and $U(1)$ theories, without matter, our definition agrees with
a particular case of the definition given by Casini, Huerta and Rosabal. We
also argue that in general, both for Abelian and Non-Abelian theories, our
definition agrees with the entanglement entropy calculated using a definition
of the replica trick. Our definition, however, does not agree with some
standard ways to measure entanglement, like the number of Bell pairs which can
be produced by entanglement distillation. | Effective Field Theory of Black Hole Perturbations in Vector-Tensor
Gravity: We formulate the effective field theory (EFT) of vector-tensor gravity for
perturbations around an arbitrary background with a ${\it timelike}$ vector
profile, which can be applied to study black hole perturbations. The vector
profile spontaneously breaks both the time diffeomorphism and the $U(1)$
symmetry, leaving their combination and the spatial diffeomorphism as the
residual symmetries in the unitary gauge. We derive two sets of consistency
relations which guarantee the residual symmetries of the EFT. Also, we provide
the dictionary between our EFT coefficients and those of generalized Proca (GP)
theories, which enables us to identify a simple subclass of the EFT that
includes the GP theories as a special case. For this subclass, we consider the
stealth Schwarzschild(-de Sitter) background solution with a constant temporal
component of the vector field and study the decoupling limit of the
longitudinal mode of the vector field, explicitly showing that the strong
coupling problem arises due to vanishing sound speeds. This is in sharp
contrast to the case of gauged ghost condensate, in which perturbations are
weakly coupled thanks to certain higher-derivative terms, i.e., the scordatura
terms. This implies that, in order to consistently describe this type of
stealth solutions within the EFT, the scordatura terms must necessarily be
taken into account in addition to those already included in the simple
subclass. |
BRST Lagrangian construction for spin-2 field in Einstein space: We explore a new possibility of BRST construction in higher spin field theory
to obtain a consistent Lagrangian for massive spin-2 field in Einstein space.
Such approach automatically leads to gauge invariant Lagrangian with suitable
auxiliary and Stuckelberg fields. It is proved that in this case a propagation
of spin-2 field is hyperbolic and causal. Also we extend notion of partial
masslessness for spin-2 field in the background under consideration. | Higher Spins in D=2+1: We give a brief overview of some three-dimensional toy models for higher-spin
interactions. We first review the construction of pure higher-spin gauge
theories in terms of Chern-Simons theories. We then discuss how this setup
could be modified along the lines of the known topologically massive theories. |
Umbral Moonshine and String Duality: By studying 2d string compactifications with half-maximal supersymmetry in a
variety of duality frames, we find a natural physical setting for understanding
Umbral moonshine. Near points in moduli space with enhanced gauge symmetry, we
find that the Umbral symmetry groups arise as symmetries of the theory. In one
duality frame -- a flux compactification on $T^4/Z_2\times T^4$ -- the
24-dimensional permutation representations of the Umbral groups act on
D1-branes strung between a set of NS5-branes. The presence of these NS5-branes
is used to explain the Umbral moonshine decompositions of the K3 twining
genera, and in particular of the K3 elliptic genus. The fundamental string in
this frame is dual to the type IIA string on K3$\times T^4$ and to a
compactified heterotic little string theory. The latter provides an interesting
example of a little string theory, as the string-scale geometry transverse to
the 5-brane plays an important role in its construction. | Superfield Formulation of Nonlinear N=4 Supermultiplets: We propose a unified superfield formulation of N=4 off-shell supermultiplets
in one spacetime dimension using the standard N=4 superspace. The main idea of
our approach is a "gluing" together of two linear supermultiplets along their
fermions. The functions defining such a gluing obey a system of equations. Each
solution of this system provides a new supermultiplet, linear or nonlinear,
modulo equivalence transformations. In such a way we reproduce all known linear
and nonlinear N=4, d=1 supermultiplets and propose some new ones. Particularly
interesting is an explicit construction of nonlinear N=4 hypermultiplets. |
Dense and Hot Holographic QCD: Finite Baryonic E Field: We investigate the response of dense and hot holographic QCD (hQCD) to a
static and baryonic electric field E using the chiral model of Sakai and
Sugimoto. Strong fields with E>(\sqrt\lambda M_{KK})^2 free quark pairs,
causing the confined vacuum and matter state to decay. We generalize
Schwinger's QED persistence function to dense hQCD. At high temperature and
density, Ohm's law is derived generalizing a recent result by Karch and
O'Bannon to the chiral case. | F-term Moduli Stabilization and Uplifting: We study K\"ahler moduli stabilization in IIB superstring theory. We propose
a new moduli stabilization mechanism by the supersymmetry-braking chiral
superfield which is coupled to K\"ahler moduli in K\"ahler potential. We also
study uplifting of the Large Volume Scenario (LVS) by it. In both cases, the
form of superpotential is crucial for moduli stabilization. We confirm that our
uplifting mechanism does not destabilize the vacuum of the LVS drastically. |
Modular invariance and uniqueness of $T\bar{T}$ deformed CFT: Any two dimensional quantum field theory that can be consistently defined on
a torus is invariant under modular transformations. In this paper we study
families of quantum field theories labeled by a dimensionful parameter $t$,
that have the additional property that the energy of a state at finite $t$ is a
function only of $t$ and of the energy and momentum of the corresponding state
at $t=0$, where the theory becomes conformal. We show that under this
requirement, the partition sum of the theory at $t=0$ uniquely determines the
partition sum (and thus the spectrum) of the perturbed theory, to all orders in
$t$, to be that of a $T\bar T$ deformed CFT. Non-perturbatively, we find that
for one sign of $t$ (for which the energies are real) the partition sum is
uniquely determined, while for the other sign we find non-perturbative
ambiguities. We characterize these ambiguities and comment on their possible
relations to holography. | Exact holography and black hole entropy in N=8 and N=4 string theory: We compute the exact entropy of one-eighth and one-quarter BPS black holes in
N=8 and N=4 string theory respectively. This includes all the N=4 CHL models in
both K3 and T^4 compactifications. The main result is a measure for the finite
dimensional integral that one obtains after localization of supergravity on
AdS_2xS^2. This measure is determined entirely by an anomaly in supersymmetric
Chern-Simons theory on local AdS_3 and takes into account the contribution from
all the supergravity multiplets. In Chern-Simons theory on compact manifolds
this is the anomaly that computes a certain one-loop dependence on the volume
of the manifold. For one-eighth BPS black holes our results are a first
principles derivation of a measure proposed in arXiv:1111.1161, while in the
case of one-quarter BPS black holes our result computes exactly all the
perturbative or area corrections. Moreover, we argue that instantonic
contributions can be incorporated and give evidence by computing the measure
which matches precisely the microscopics. Along with this, we find an unitary
condition that truncates the answer to a finite sum of instantons in perfect
agreement with a microscopic formula. Our results solve a number of puzzles
related to localization in supergravity and constitute a larger number of
examples where holography can be shown to hold exactly. |
A Novel Application of Quantum Speed Limit to String Theory: In this work, we investigate the implications of the concept of quantum speed
limit in string field theory. We adopt a novel approach to the problem of time
on world-sheet based on Fisher information, and arrive at a minimum time for a
particle state to evolve into another particle state. This is done using both
the Mandelstam-Tamm bound and the Margolus-Levitin bound. This implies that any
interaction has to be smeared over such an interval, and any interaction in the
effective quantum field theory has to be non-local. As non-local quantum field
theories are known to be finite, it is expected that divergences should be
removed from effective quantum field theories due to the quantum speed limit of
string theory. | Orthosymplectic Implosions: We propose quivers for Coulomb branch constructions of universal implosions
for orthogonal and symplectic groups, extending the work on special unitary
groups in arXiv:2004.09620. The quivers are unitary-orthosymplectic as opposed
to the purely unitary quivers in the A-type case. Where possible we check our
proposals using Hilbert series techniques. |
Witten Index and Superconducting Strings: The Yukawa interaction sector of superstring inspired models that give
superconducting strings, can be described in terms of a supersymmetric quantum
mechanics algebra. We relate the Witten index of susy quantum mechanics with an
index characteristic to superconducting string models. | Remarks on the Atick-Witten behavior and strings near black hole
horizons: We present arguments pointing to a behavior of the string free energy in the
presence of a black hole horizon similar to the Atick-Witten dependence on
temperature beyond the Hagedorn transition. We give some evidence based on
orbifold techniques applied to Rindler space and further support is found
within a Hamiltonian approach. However, we argue that the interpretation in
terms of a reduction of degrees of freedom is confronted by serious problems.
Finally, we point out the problems concerning heuristic red-shift arguments and
the local interpretation of thermodynamical quantities. |
Renormalizable quantum field theory as a limit of a quantum field model
on the loop space: A nonlocal generalization of quantum field theory in which momentum space is
the space of continuous maps of a circle into $\mathbf{R}^4$ is proposed.
Functional integrals in this theory are proved to exist. Renormalized quantum
field model is obtained as a local limit of the proposed theory. | The Shear Viscosity in Anisotropic Phases: We construct anisotropic black brane solutions and analyse the behaviour of
some of their metric perturbations. These solutions correspond to field theory
duals in which rotational symmetry is broken due an externally applied,
spatially constant, force. We find, in several examples, that when the
anisotropy is sufficiently big compared to the temperature, some components of
the viscosity tensor can become very small in units of the entropy density,
parametrically violating the KSS bound. We obtain an expression relating these
components of the viscosity, in units of the entropy density, to a ratio of
metric components at the horizon of the black brane. This relation is generally
valid, as long as the forcing function is translationally invariant, and it
directly connects the parametric violation of the bound to the anisotropy in
the metric at the horizon. Our results suggest the possibility that such small
components of the viscosity tensor might also arise in anisotropic strongly
coupled fluids found in nature. |
String cosmology coupled to Weyl-integrable geometry: The requirement that the laws of physics must be invariant under
point-dependent transformations of the units of length, time, and mass is used
as a selection principle while studying different generic effective theories of
gravity. Thereof theories with non-minimal coupling of the dilaton both to the
curvature and to the Lagrangian of the matter fields seem to represent the most
viable low-energy [and low-curvature] description of gravity. Consequently, the
cosmological singularity problem is treated within the context of string
cosmology with non-minimal coupling of the dilaton to a barotropic gas of
solitonic p-brane. The results obtained are to be interpreted on the grounds of
Weyl-integrable geometry. The implications of these results for the Mach's
principle are briefly discussed. | Self-dual gravity and self-dual Yang-Mills in the context of
Macdowell-Mansouri formalism: In this work we propose an action which unifies self-dual gravity and
self-dual Yang-Mills in the context of the Macdowell-Mansouri formalism. We
claim that such an action may be used to find the S-dual action for both
self-dual gravity and self-dual Yang-Mills. |
Multibrane solutions in cubic superstring field theory: Using the elements of the so-called $KBc\gamma$ subalgebra, we study a class
of analytic solutions depending on a single function $F(K)$ in the modified
cubic superstring field theory. We compute the energy associated to these
solutions and show that the result can be expressed in terms of a contour
integral. For a particular choice of the function $F(K)$, we show that the
energy is given by integer multiples of a single D-brane tension. | Comment on: "The Casimir force on a piston in the spacetime with extra
compactified dimensions" [Phys. Lett. B 668 (2008) 72]: We offer a clarification of the significance of the indicated paper of H.
Cheng. Cheng's conclusions about the attractive nature of Casimir forces
between parallel plates are valid beyond the particular model in which he
derived them; they are likely to be relevant to other recent literature on the
effects of hidden dimensions on Casimir forces. |
A Covariant Action for the Eleven Dimensional Superstring: We suggest a super Poincar\'e invariant action for closed eleven dimensional
superstring. The sector of physical variables $x^i$, $\theta_a$,
$\bar\theta_{\dot a}$, with $a,\dot a=1...8$ and $x^i$ the transverse part of
the D=11 $x^\mu$ coordinate is shown to possess free dynamics. | Ising Field Theory on a Pseudosphere: We show how the symmetries of the Ising field theory on a pseudosphere can be
exploited to derive the form factors of the spin fields as well as the
non-linear differential equations satisfied by the corresponding two-point
correlation functions. The latter are studied in detail and, in particular, we
present a solution to the so-called connection problem relating two of the
singular points of the associated Painleve VI equation. A brief discussion of
the thermodynamic properties is also presented. |
Twisted Elliptic Genera of N=2 SCFTs in Two Dimensions: The elliptic genera of two-dimensional N=2 superconformal field theories can
be twisted by the action of the integral Heisenberg group if their U(1) charges
are fractional. The basic properties of the resulting twisted elliptic genera
and the associated twisted Witten indices are investigated with due attention
to their behaviors in orbifoldization. Our findings are illustrated by and
applied to several concrete examples. We give a better understanding of the
duality phenomenon observed long before for certain Landau-Ginzburg models. We
revisit and prove an old conjecture of Witten which states that every ADE
Landau-Ginzburg model and the corresponding minimal model share the same
elliptic genus. Mathematically, we establish ADE generalizations of the
quintuple product identity. | AdS$_2$ geometries and non-Abelian T-duality in non-compact spaces: We obtain an AdS$_{2}$ solution to Type IIA supergravity with 4 Poincare
supersymmetries, via non-Abelian T-duality with respect to a freely acting
SL(2,$\mathbf{R}$) isometry group, operating on the
AdS$_3\times$S$^3\times$CY$_2$ solution to Type IIB. That is, non-Abelian
T-duality on AdS$_3$. The dual background obtained fits in the class of
AdS$_2\times$S$^3\times$CY$_2$ solutions to massive Type IIA constructed in
[1]. We propose and study a quiver quantum mechanics dual to this solution that
we interpret as describing the backreaction of the baryon vertex of a D4-D8
brane intersection. |
Poisson-Lie plurals of Bianchi cosmologies and Generalized Supergravity
Equations: Poisson-Lie T-duality and plurality are important solution generating
techniques in string theory and (generalized) supergravity. Since
duality/plurality does not preserve conformal invariance, the usual beta
function equations are replaced by Generalized Supergravity Equations
containing vector $\mathcal{J}$. In this paper we apply Poisson-Lie T-plurality
on Bianchi cosmologies. We present a formula for the vector $\mathcal{J}$ as
well as transformation rule for dilaton, and show that plural backgrounds
together with this dilaton and $\mathcal{J}$ satisfy the Generalized
Supergravity Equations. The procedure is valid also for non-local dilaton and
non-constant $\mathcal{J}$. We also show that $Div\,\Theta$ of the
non-commutative structure $\Theta$ used for non-Abelian T-duality or integrable
deformations does not give correct $\mathcal{J}$ for Poisson-Lie T-plurality. | An introduction to non-commutative differential geometry on quantum
groups: We give a pedagogical introduction to the differential calculus on quantum
groups by stressing at all stages the connection with the classical case ($q
\rightarrow 1$ limit). The Lie derivative and the contraction operator on forms
and tensor fields are found. A new, explicit form of the Cartan--Maurer
equations is presented. The example of a bicovariant differential calculus on
the quantum group $GL_q(2)$ is given in detail. The softening of a quantum
group is considered, and we introduce $q$-curvatures satisfying q-Bianchi
identities, a basic ingredient for the construction of $q$-gravity and
$q$-gauge theories. |
Free energy of topologically massive gravity and flat space holography: We calculate the free energy from the on-shell action for topologically
massive gravity with negative and vanishing cosmological constant, thereby
providing a first principles derivation of the free energy of
Banados-Teitelboim-Zanelli (BTZ) black holes and flat space cosmologies. We
summarize related recent checks of flat space holography. | Phenomenology of the CAH+ measure: The CAH+ measure regulates the infinite spacetime volume of the multiverse by
constructing a surface of constant comoving apparent horizon (CAH) and then
removing the future lightcones of all points on that surface (the latter
prescription is referred to by the "+" in the name of the measure). This
measure was motivated by the conjectured duality between the bulk of the
multiverse and its future infinity and by the causality condition, requiring
that the cutoff surfaces of the measure should be spacelike or null. Here we
investigate the phenomenology of the CAH+ measure and find that it does not
suffer from any known pathologies. The distribution for the cosmological
constant Lambda derived from this measure is in a good agreement with the
observed value, and the distribution for the number of inflationary e-foldings
satisfies the observational constraint. The CAH+ measure does not exhibit any
"runaway" behaviors at zero or negative values of Lambda, which have been
recently shown to afflict a number of other measures. |
Chiral Four-Dimensional Heterotic Covariant Lattices: In the covariant lattice formalism, chiral four-dimensional heterotic string
vacua are obtained from certain even self-dual lattices which completely
decompose into a left-mover and a right-mover lattice. The main purpose of this
work is to classify all right-mover lattices that can appear in such a chiral
model, and to study the corresponding left-mover lattices using the theory of
lattice genera. In particular, the Smith-Minkowski-Siegel mass formula is
employed to calculate a lower bound on the number of left-mover lattices. Also,
the known relationship between asymmetric orbifolds and covariant lattices is
considered in the context of our classification. | The Lax pair for the fermionic Bazhanov-Stroganov $R$-operator: We derive the Lax connection of the free fermion model on a lattice starting
from the fermionic formulation of Bazhanov-Stroganov's three-parameter elliptic
parametrization for the R-operator. It results in the Yang-Baxter and decorated
Yang-Baxter equations of difference type in one of the spectral parameters,
which is the most suitable form to obtain any relativistic model of free
fermions in the continuous limit. |
Analytic Treatment of Positronium Spin Splittings in Light-Front QED: We study the QED bound-state problem in a light-front hamiltonian approach.
Starting with a bare cutoff QED Hamiltonian, $H_{_{B}}$, with matrix elements
between free states of drastically different energies removed, we perform a
similarity transformation that removes the matrix elements between free states
with energy differences between the bare cutoff, $\Lambda$, and effective
cutoff, $\lam$ ($\lam < \Lam$). This generates effective interactions in the
renormalized Hamiltonian, $H_{_{R}}$. These effective interactions are derived
to order $\alpha$ in this work, with $\alpha \ll 1$. $H_{_{R}}$ is renormalized
by requiring it to satisfy coupling coherence. A nonrelativistic limit of the
theory is taken, and the resulting Hamiltonian is studied using bound-state
perturbation theory (BSPT). The effective cutoff, $\lam^2$, is fixed, and the
limit, $0 \longleftarrow m^2 \alpha^2\ll \lam^2 \ll m^2 \alpha \longrightarrow
\infty$, is taken. This upper bound on $\lam^2$ places the effects of
low-energy (energy transfer below $\lam$) emission in the effective
interactions in the $| e {\overline e} > $ sector. This lower bound on $\lam^2$
insures that the nonperturbative scale of interest is not removed by the
similarity transformation. As an explicit example of the general formalism
introduced, we show that the Hamiltonian renormalized to $O(\alpha)$ reproduces
the exact spectrum of spin splittings, with degeneracies dictated by rotational
symmetry, for the ground state through $O(\alpha^4)$. The entire calculation is
performed analytically, and gives the well known singlet-triplet ground state
spin splitting of positronium, $7/6 \alpha^2 Ryd$. We discuss remaining
corrections other than the spin splittings and how they can be treated in
calculating the spectrum with higher precision. | Extremal surfaces as bulk probes in AdS/CFT: Motivated by the need for further insight into the emergence of AdS bulk
spacetime from CFT degrees of freedom, we explore the behaviour of probes
represented by specific geometric quantities in the bulk. We focus on geodesics
and n-dimensional extremal surfaces in a general static asymptotically AdS
spacetime with spherical and planar symmetry, respectively. While our arguments
do not rely on the details of the metric, we illustrate some of our findings
explicitly in spacetimes of particular interest (specifically AdS,
Schwarzschild-AdS and extreme Reissner-Nordstrom-AdS). In case of geodesics, we
find that for a fixed spatial distance between the geodesic endpoints,
spacelike geodesics at constant time can reach deepest into the bulk. We also
present a simple argument for why, in the presence of a black hole, geodesics
cannot probe past the horizon whilst anchored on the AdS boundary at both ends.
The reach of an extremal n-dimensional surface anchored on a given region
depends on its dimensionality, the shape and size of the bounding region, as
well as the bulk metric. We argue that for a fixed extent or volume of the
boundary region, spherical regions give rise to the deepest reach of the
corresponding extremal surface. Moreover, for physically sensible spacetimes,
at fixed extent of the boundary region, higher-dimensional surfaces reach
deeper into the bulk. Finally, we show that in a static black hole spacetime,
no extremal surface (of any dimensionality, anchored on any region in the
boundary) can ever penetrate the horizon. |
Cosmological Entropy Bounds: I review some basic facts about entropy bounds in general and about
cosmological entropy bounds. Then I review the Causal Entropy Bound, the
conditions for its validity and its application to the study of cosmological
singularities. This article is based on joint work with Gabriele Veneziano and
subsequent related research. | Direct photons emission rate and electric conductivity in twice
anisotropic QGP holographic model with first-order phase transition: The electric conductivity and direct photons emission rate are considered in
the holographic theory with two types of anisotropy. The electric conductivity
is derived in two different ways, and their equivalence for the twice
anisotropic theory is shown. Numerical calculations of the electric
conductivity were done for Einstein-dilaton-three-Maxwell holographic model
[29]. The dependence of the conductivity on the temperature, the chemical
potential, the external magnetic field, and the spatial anisotropy of the
heavy-ions collision (HIC) is studied. The electric conductivity jumps near the
first-order phase transition are observed. This effect is similar to the jumps
of holographic entanglement that were studied previously. |
Knot theory and a physical state of quantum gravity: We discuss the theory of knots, and describe how knot invariants arise
naturally in gravitational physics. The focus of this review is to delineate
the relationship between knot theory and the loop representation of
non-perturbative canonical quantum general relativity (loop quantum gravity).
This leads naturally to a discussion of the Kodama wavefunction, a state which
is conjectured to be the ground state of the gravitational field with positive
cosmological constant. This review can serve as a self-contained introduction
to loop quantum gravity and related areas. Our intent is to make the paper
accessible to a wider audience that may include topologists, knot-theorists,
and other persons innocent of the physical background to this approach to
quantum gravity. | On integrability of massless AdS_4 x CP^3 superparticle equations: Lax representation is elaborated for the equations of motion of massless
superparticle on the AdS_4 x CP^3 superbackground that proves their classical
integrability. |
D6-brane Splitting on Type IIA Orientifolds: We study the open-string moduli of supersymmetric D6-branes, addressing both
the string and field theory aspects of D6-brane splitting on Type IIA
orientifolds induced by open-string moduli Higgsing (i.e., their obtaining
VEVs). Specifically, we focus on the Z_2 x Z_2 orientifolds and address the
symmetry breaking pattern for D6-branes parallel with the orientifold 6-planes
as well as those positioned at angles. We demonstrate that the string theory
results, i.e., D6-brane splitting and relocating in internal space, are in one
to one correspondence with the field theory results associated with the
Higgsing of moduli in the antisymmetric representation of Sp(2N) gauge symmetry
(for branes parallel with orientifold planes) or adjoint representation of U(N)
(for branes at general angles). In particular, the moduli Higgsing in the
open-string sector results in the change of the gauge structure of D6-branes
and thus changes the chiral spectrum and family number as well. As a
by-product, we provide the new examples of the supersymmetric Standard-like
models with the electroweak sector arising from Sp(2N)_L x Sp(2N)_R gauge
symmetry; and one four-family example is free of chiral Standard Model exotics. | Theoretical and Phenomenological Aspects of Superstring Theories: We discuss aspects of the heterotic string effective field theories in
orbifold constructions of the heterotic string. We calculate the moduli
dependence of threshold corrections to gauge couplings in (2,2) symmetric
orbifold compactifications. We perform the calculation of the threshold
corrections for a particular class of abelian (2,2) symmetric non-decomposable
orbifold models... internal twist is realized as generalized Coxeter
automorphism. We define the limits for the existence of states causing
singularities in the moduli space in the perturbative regime for a generic
vacuum of the heterotic string. The 'proof' provides evidence for the
explanation of the stringy 'Higgs effect'. Furthermore, we calculate the moduli
dependence of threshold corrections as target space invariant free energies for
non-decomposable orbifolds, identifying the Hauptmodul' functions for the
relevant congruence subgroups. The required solutions provide for the \mu mass
term generation in the effective low energy theory and affect the induced
sypersymmetry breaking by gaugino condensation. In addition, we discuss the one
loop gauge and gravitational couplings in (0,2) non-decomposable orbifold
compactifications. In the second part of the Thesis the one loop correction to
the Kahler metric for a generic N=2 orbifold compactification of the heterotic
string is calculated... In this way, with the use of the one loop string
amplitudes, the prepotential of the vector multiplets of the N=2 effective
low-energy heterotic string is calculated in decomposable toroidal
compactifications of the heterotic string ... This method provides the solution
for the one loop correction to the prepotential of the vector multiplets of the
heterotic string compactified on the K_3 \times T^2... |
Solitonic photons and intermediate vector bosons: A four-dimensional topological field theory is introduced which generalises
$B\wedge F$ theory to give a Bogomol'nyi structure. A class of non-singular,
finite-Action, stable solutions to the variational field equations is
identified. The solitonic solutions are analogous to the instanton in
Yang-Mills theory. The solutions to the Bogomol'nyi equations in the
topologically least complicated $U(1)$ theory have a well-behaved (covariant)
phase space of dimension four---the same as that for photons. The dimensional
reduction of the four-dimensional Lagrangian is also examined. Bogomol'nyi
$U(2)$ solitons resembling the intermediate vector bosons $Z_o$, $W^\pm$ are
identified. | Constant Curvature and Non-Perturbative W3 Gravity: We show that the new classical action for two dimensional gravity (the
Jackiw-Teitelboim model) possesses a $W_3$ algebra. We quantise the resulting
$W_3$ gravity in the presence of matter fields with arbitrary central charges
and obtain the critical exponents. The auxiliary field of the model, expressing
the constancy of the scalar curvature, can be interpreted as one of the
physical degrees of freedom of the $W_3$ gravity. Our expressions are
corrections to some previously published results for this model where the $W_3$
symmetry was not accounted for. |
Rotating black holes with equal-magnitude angular momenta in d=5
Einstein-Gauss-Bonnet theory: We construct rotating black hole solutions in Einstein-Gauss-Bonnet theory in
five spacetime dimensions. These black holes are asymptotically flat, and
possess a regular horizon of spherical topology and two equal-magnitude angular
momenta associated with two distinct planes of rotation. The action and global
charges of the solutions are obtained by using the quasilocal formalism with
boundary counterterms generalized for the case of Einstein-Gauss-Bonnet theory.
We discuss the general properties of these black holes and study their
dependence on the Gauss-Bonnet coupling constant $\alpha$. We argue that most
of the properties of the configurations are not affected by the higher
derivative terms. For fixed $\alpha$ the set of black hole solutions terminates
at an extremal black hole with a regular horizon, where the Hawking temperature
vanishes and the angular momenta attain their extremal values. The domain of
existence of regular black hole solutions is studied. The near horizon geometry
of the extremal solutions is determined by employing the entropy function
formalism. | Holographic DC Conductivity for Backreacted NLED in Massive Gravity: In this work a holographic model with the charge current dual to a general
nonlinear electrodynamics (NLED) is discussed in the framework of massive
gravity. Massive graviton can breaks the diffeomorphism invariance in the bulk
and generates momentum dissipation in the dual boundary theory. The expression
of DC conductivities in a finite magnetic field are obtained, with the
backreaction of NLED field on the background geometry. General transport
properties in various limits are presented, and then we turn to the three of
specific NLED models: the conventional Maxwell electrodynamics, the
Maxwell-Chern-Simons electrodynamics, and the Born-Infeld electrodynamics, to
study the parameter-dependence of in-plane resistivity. Two mechanisms leading
to the Mott-insulating behaviors and negative magneto-resistivity are revealed
at zero temperature, and the role played by the massive gravity coupling
parameters are discussed. |
Cosmological perturbations in the 5D Big Bang: Bucher [Bucher2001] has recently proposed an interesting brane-world
cosmological scenario where the ``Big Bang'' hypersurface is the locus of
collision of two vacuum bubbles which nucleate in a five dimensional flat
space. This gives rise to an open universe, where the curvature can be very
small provided that $d/R_0$ is sufficiently large. Here, d is the distance
between bubbles and $R_0$ is their size at the time of nucleation. Quantum
fluctuations develop on the bubbles as they expand towards each other, and
these in turn imprint cosmological perturbations on the initial hypersurface.
We present a simple formalism for calculating the spectrum of such
perturbations and their subsequent evolution. We conclude that, unfortunately,
the spectrum is very tilted, with spectral index $n_s=3$. The amplitude of
fluctuations at horizon crossing is given by $<(\delta \rho/\rho)^2> \sim
(R_0/d)^2 S_E^{-1} k^2$, where $S_E\gg 1$ is the Euclidean action of the
instanton describing the nucleation of a bubble and k is the wavenumber in
units of the curvature scale. The spectrum peaks on the smallest possible
relevant scale, whose wave-number is given by $k\sim d/R_0$. We comment on the
possible extension of our formalism to more general situations where a Big Bang
is ignited through the collision of 4D extended objects. | Supersymmetry Restoration in Superstring Perturbation Theory: Superstring perturbation theory based on the 1PI effective theory approach
has been useful for addressing the problem of mass renormalization and vacuum
shift. We derive Ward identities associated with space-time supersymmetry
transformation in this approach. This leads to a proof of the equality of
renormalized masses of bosons and fermions and identities relating fermionic
amplitudes to bosonic amplitudes after taking into account the effect of mass
renormalization. This also relates unbroken supersymmetry to a given order in
perturbation theory to absence of tadpoles of massless scalars to higher order.
The results are valid at the perturbative vacuum as well as in the shifted
vacuum when the latter describes the correct ground state of the theory. We
apply this to SO(32) heterotic string theory on Calabi-Yau 3-folds where a one
loop Fayet-Iliopoulos term apparently breaks supersymmetry at one loop, but
analysis of the low energy effective field theory indicates that there is a
nearby vacuum where supersymmetry is restored. We explicitly prove that the
perturbative amplitudes of this theory around the shifted vacuum indeed satisfy
the Ward identities associated with unbroken supersymmetry. We also test the
general arguments by explicitly verifying the equality of bosonic and fermionic
masses at one loop order in the shifted vacuum, and the appearance of two loop
dilaton tadpole in the perturbative vacuum where supersymmetry is expected to
be broken. |
The universal thermodynamic properties of Extremely Compact Objects: An extremely compact object (ECO) is defined as a quantum object without
horizon, whose radius is just a small distance $s$ outside its Schwarzschild
radius. We show that any ECO of mass $M$ in $d+1$ dimensions with $s\ll
(M/m_p)^{2/(d-2)(d+1)}l_p$ must have (at leading order) the same thermodynamic
properties -- temperature, entropy and radiation rates -- as the corresponding
semiclassical black hole of mass $M$. An essential aspect of the argument
involves showing that the Tolman-Oppenheimer-Volkoff equation has no consistent
solution in the region just outside the ECO surface, unless this region is
filled with radiation at the (appropriately blueshifted) Hawking temperature.
In string theory it has been found that black hole microstates are fuzzballs --
objects with no horizon -- which are expected to have a radius that is only a
little larger than the horizon radius. Thus the arguments of this paper provide
a nice closure to the fuzzball paradigm: the absence of a horizon removes the
information paradox, and the thermodynamic properties of the semiclassical hole
are nonetheless recovered to an excellent approximation. | Quarks in an External Electric Field in Finite Temperature Large N Gauge
Theory: We use a ten dimensional dual string background to aspects of the physics
large N four dimensional SU(N) gauge theory, where its fundamental quarks are
charged under a background electric field. The theory is N=2 supersymmetric for
vanishing temperature and electric field. At zero temperature, we observe that
the electric field induces a phase transition associated with the dissociation
of the mesons into their constituent quarks. This is an analogue of an
insulator-metal transition, since the system goes from being an insulator with
zero current (in the applied field) to a conductor with free charge carriers
(the quarks). At finite temperature this phenomenon persists, with the
dissociation transition become subsumed into the more familiar meson melting
transition. Here, the dissociation phenomenon reduces the critical melting
temperature. |
Pole inflation in Jordan frame supergravity: We investigate inflation models in Jordan frame supergravity, in which an
inflaton non-minimally couples to the scalar curvature. By imposing the
condition that an inflaton would have the canonical kinetic term in the Jordan
frame, we construct inflation models with asymptotically flat potential through
pole inflation technique and discuss their relation to the models based on
Einstein frame supergravity. We also show that the model proposed by Ferrara et
al. has special position and the relation between the K\"ahler potential and
the frame function is uniquely determined by requiring that scalars take the
canonical kinetic terms in the Jordan frame and that a frame function consists
only of a holomorphic term (and its anti-holomorphic counterpart) for symmetry
breaking terms. Our case corresponds to relaxing the latter condition. | On Two-Current Realization of KP Hierarchy: A simple description of the KP hierarchy and its multi-hamiltonian structure
is given in terms of two Bose currents. A deformation scheme connecting various
W-infinity algebras and relation between two fundamental nonlinear structures
are discussed. Properties of Fa\'a di Bruno polynomials are extensively
explored in this construction. Applications of our method are given for the
Conformal Affine Toda model, WZNW models and discrete KP approach to Toda
lattice chain. |
Massive Gravity: Exorcising the Ghost: We consider Higgs massive gravity [1,2] and investigate whether a nonlinear
ghost in this theory can be avoided. We show that although the theory
considered in [10,11] is ghost free in the decoupling limit, the ghost
nevertheless reappears in the fourth order away from the decoupling limit. We
also demonstrate that there is no direct relation between the value of the
Vainshtein scale and the existence of nonlinear ghost. We discuss how massive
gravity should be modified to avoid the appearance of the ghost. | On correlation functions in $J\bar T$-deformed CFTs: The $J\bar T$ deformation, built from the components of the stress tensor and
of a $U(1)$ current, is a universal irrelevant deformation of two-dimensional
CFTs that preserves the left-moving conformal symmetry, while breaking locality
on the right-moving side. Operators in the $J\bar T$-deformed CFT are naturally
labeled by the left-moving position and right-moving momentum and transform in
representations of the one-dimensional extended conformal group. We derive an
all-orders formula for the spectrum of conformal dimensions and charges of the
deformed CFT, which we cross-check at leading order using conformal
perturbation theory. We also compute the linear corrections to the
one-dimensional OPE coefficients and comment on the extent to which the
correlation functions in $J\bar T$-deformed CFTs can be obtained from
field-dependent coordinate transformations. |
Large Dimensions and Small Curvatures from Supersymmetric Brane
Back-reaction: We compute the back-reaction of pairs of codimension-two branes within an
explicit flux-stabilized compactification, to trace how its properties depend
on the parameters that define the brane-bulk couplings. Both brane tension and
magnetic couplings to the stabilizing flux play an important role in the
resulting dynamics, with the magnetic coupling allowing some of the flux to be
localized on the branes (thus changing the flux-quantization conditions). We
find that back-reaction lifts the classical flat directions of the bulk
supergravity, and we calculate both the scalar potential and changes to the
extra-dimensional and on-brane geometries that result, as functions of the
assumed brane couplings. When linearized about simple rugby-ball geometries the
resulting solutions allow a systematic exploration of the system's response.
Several of the systems we explore have remarkable properties. Among these are a
propensity for the extra dimensions to stabilize at exponentially large sizes,
providing a mechanism for generating extremely large volumes. In some
circumstances the brane-dilaton coupling allows the bulk dilaton to adjust to
suppress the on-brane curvature parametrically below the change in brane
tension, potentially providing a mechanism for reducing the vacuum energy. We
explore the stability of this suppression to quantum effects in the case where
their strength is controlled by the value of the field along the classical flat
direction, and find it can (but need not) be stable. | Gauge theories and non-commutative geometry: It is shown that a $d$-dimensional classical SU(N) Yang-Mills theory can be
formulated in a $d+2$-dimensional space, with the extra two dimensions forming
a surface with non-commutative geometry. In this paper we present an explicit
proof for the case of the torus and the sphere. |
Large N Gauge Theory -- Expansions and Transitions: We use solvable two-dimensional gauge theories to illustrate the issues in
relating large N gauge theory to string theory. We also give an introduction to
recent mathematical work which allows constructing master fields for higher
dimensional large N theories. We illustrate this with a new derivation of the
Hopf equation governing the evolution of the spectral density in matrix quantum
mechanics. Based on lectures given at the 1994 Trieste Spring School on String
Theory, Gauge Theory and Quantum Gravity. | Translation-Invariant Renormalizable Noncommutative Chern-Simons Theory: In this paper we show the renormalizability of the translation invariant
noncommutative Chern-Simons theory, motivated by the work done on
noncommutative scalar field theory [06]. We add a new term to the bilinear part
of the action. In addition, we prove, the finiteness of the theory at one- and
two-loop level despite this modification. Finally we perform the one-loop two
point functions of the gluon contribution. |
Dark Energy: the equation of state description versus scalar-tensor or
modified gravity: Dark energy dynamics of the universe can be achieved by equivalent
mathematical descriptions taking into account generalized fluid equations of
state in General Relativity, scalar-tensor theories or modified F(R) gravity in
Einstein or Jordan frames. The corresponding technique transforming equation of
state description to scalar-tensor or modified gravity is explicitly presented.
We show that such equivalent pictures can be discriminated by matching
solutions with data capable of selecting the true physical frame. | On differential operators and unifying relations for $1$-loop Feynman
integrands: We generalize the unifying relations for tree amplitudes to the $1$-loop
Feynman integrands. By employing the $1$-loop CHY formula, we construct
differential operators which transmute the $1$-loop gravitational Feynman
integrand to Feynman integrands for a wide range of theories, include
Einstein-Yang-Mills theory, Einstein-Maxwell theory, pure Yang-Mills theory,
Yang-Mills-scalar theory, Born-Infeld theory, Dirac-Born-Infeld theory,
bi-adjoint scalar theory, non-linear sigma model, as well as special Galileon
theory. The unified web at $1$-loop level is established. Under the well known
unitarity cut, the $1$-loop level operators will factorize into two tree level
operators. Such factorization is also discussed. |
Generalized Calogero model in arbitrary dimensions: We define a new multispecies model of Calogero type in D dimensions with
harmonic, two-body and three-body interactions. Using the underlying conformal
SU(1,1) algebra, we indicate how to find the complete set of the states in
Bargmann-Fock space. There are towers of states, with equidistant energy
spectra in each tower. We explicitely construct all polynomial eigenstates,
namely the center-of-mass states and global dilatation modes, and find their
corresponding eigenenergies. We also construct ladder operators for these
global collective states. Analysing corresponding Fock space, we detect the
universal critical point at which the model exhibits singular behavior. The
above results are universal for all systems with underlying conformal SU(1,1)
symmetry. | Minimal Unitary Models and The Closed SU(2)-q Invariant Spin Chain: We consider the Hamiltonian of the closed $SU(2)_{q}$ invariant chain. We
project a particular class of statistical models belonging to the unitary
minimal series. A particular model corresponds to a particular value of the
coupling constant. The operator content is derived. This class of models has
charge-dependent boundary conditions. In simple cases (Ising, 3-state Potts)
corresponding Hamiltonians are constructed. These are non-local as the original
spin chain. |
A lattice approach to the conformal $\OSp(2S+2|2S)$ supercoset sigma
model. Part II: The boundary spectrum: We consider the partition function of the boundary $OSp(2S+2|2S)$ coset sigma
model on an annulus, based on the lattice regularization introduced in the
companion paper. Using results for the action of $OSp(2S+2|2S)$ and $B_L(2)$ on
the corresponding spin chain, as well as mini-superspace and small $g_\sigma^2$
calculations, we conjecture the full spectrum and set of degeneracies on the
entire critical line. Potential relationship with the $OSp(2S+2|2S)$
Gross-Neveu model is also discussed. | New Constraints on Chiral Gauge Theories: Recently, a new constraint on the structure of a wide class of strongly
coupled field theories has been proposed. It takes the form of an inequality
limiting the number of degrees of freedom in the infrared description of a
theory to be no larger than the number of underlying, ultraviolet degrees of
freedom. Here we apply this inequality to chiral gauge theories. For some
models we find that it is always satisfied, while for others we find that the
assumption of the validity of the inequality implies a strong additional
restriction on the spectrum of massless composite particles. |
The AdS(4) x CP(3) string and its Bethe equations in the near plane wave
limit: We perform a detailed study of bosonic type IIA string theory in a large
light-cone momentum / near plane wave limit of $AdS_4 \times CP_3$. In order to
attain this we derive the Hamiltonian up to cubic and quartic order in number
of fields and calculate the energies for string excitations in a $R\times S^2
\times S^2$ subspace. The computation for the string energies is performed for
arbitrary length excitations utilizing an unitary transformation which allows
us to remove the cubic terms in the Hamiltonian. We then rewrite a recent set
of proposed all loop Bethe equations in a light-cone language and compare their
predictions with the obtained string energies. We find perfect agreement. | A scattering theory of ultrarelativistic solitons: We construct a perturbative framework for understanding the collision of
solitons (more precisely, solitary waves) in relativistic scalar field
theories. Our perturbative framework is based on the suppression of the
space-time interaction area proportional to $1/(\gamma v)$, where $v$ is the
relative velocity of an incoming solitary wave and $\gamma = 1/\sqrt{1-v^2} \gg
1$. We calculate the leading order results for collisions of (1+1) dimensional
kinks in periodic potentials, and provide explicit, closed form expressions for
the phase shift and the velocity change after the collisions. We find excellent
agreement between our results and detailed numerical simulations. Crucially,
our perturbation series is controlled by a kinematic parameter, and hence not
restricted to small deviations around integrable cases such as the Sine-Gordon
model. |
Wilson Loops in Noncommutative Yang Mills: We study the correlation functions of the Wilson loops in noncommutative
Yang-Mills theory based upon its equivalence to twisted reduced models. We
point out that there is a crossover at the noncommutativity scale. At large
momentum scale, the Wilson loops in noncommmutative Yang-Mills represent
extended objects. They coincide with those in ordinary Yang-Mills theory in low
energy limit. The correlation functions on D-branes in IIB matrix model exhibit
the identical crossover behavior. It is observed to be consistent with the
supergravity description with running string coupling. We also explain that the
results of Seiberg and Witten can be simply understood in our formalism. | Steady-state Physics, Effective Temperature Dynamics in Holography: Using the gauge-gravity duality, we argue that for a certain class of
out-of-equilibrium steady-state systems in contact with a thermal background at
a given temperature, the macroscopic physics can be captured by an effective
thermodynamic description. The steady-state is obtained by applying a constant
electric field that results in a stationary current flow. Within holography, we
consider generic probe systems where an open string equivalence principle and
an open string metric govern the effective thermodynamics. This description
comes equipped with an effective temperature, which is larger than the
background temperature, and a corresponding effective entropy. For conformal or
scale-invariant theories, certain scaling behaviours follow immediately. In
general, in the large electric field limit, this effective temperature is also
observed to obey generic relations with various physical parameters in the
system. |
N=1 Non-Abelian Tensor Multiplet in Four Dimensions: We carry out the N=1 supersymmetrization of a physical non-Abelian tensor
with non-trivial consistent couplings in four dimensions. Our system has three
multiplets: (i) The usual non-Abelian vector multiplet (VM) (A_\mu{}^I,
\lambda^I), (ii) A non-Abelian tensor multiplet (TM) (B_{\mu\nu}{}^I, \chi^I,
\varphi^I), and (iii) A compensator vector multiplet (CVM) (C_\mu{}^I, \rho^I).
All of these multiplets are in the adjoint representation of a non-Abelian
group G. Unlike topological theory, all of our fields are propagating with
kinetic terms. The C_\mu{}^I-field plays the role of a Stueckelberg compensator
absorbed into the longitudinal component of B_{\mu\nu}{}^I. We give not only
the component lagrangian, but also a corresponding superspace reformulation,
reconfirming the total consistency of the system. The adjoint representation of
the TM and CVM is further generalized to an arbitrary real representation of
general SO(N) gauge group. We also couple the globally N=1 supersymmetric
system to supergravity, as an additional non-trivial confirmation. | Trapped States and bound states of a soliton in a well: The nature of the interaction of a soliton with an attractive well is
elucidated using a model of two interacting point particles. The model explains
the existence of trapped states at positive kinetic energy, as well as
reflection by an attractive impurity. The transition from a trapped soliton
state to a bound state is studied. Bound states of the soliton in a well are
also found. |
On the semiclassical 3-point function in AdS_3: We reconsider the problem of determining the semiclassical 3-point function
in the Euclidean AdS_3 model. Exploiting the affine symmetry of the model we
use solutions of the classical Knizhnik-Zamolodchikov (KZ) equation to compute
the saddle point of the action in the presence of three vertex operators. This
alternative derivation reproduces the "heavy charge" classical limit of the
quantum 3-point correlator. It is different from the recently proposed
expression obtained by generalised Pohlmeyer reduction in AdS_2 | Matrix Theory, U-Duality and Toroidal Compactifications of M-Theory: Using U-duality, the properties of the matrix theories corresponding to the
compactification of M-theory on $T^d$ are investigated. The couplings of the
$d+1$ dimensional effective Super-Yang-Mills theory to all the M-theory moduli
is deduced and the spectrum of BPS branes in the SYM gives the corresponding
spectrum of the matrix theory.Known results are recovered for $d\le 5$ and
predictions for $d>5$ are proposed. For $d>3$, the spectrum includes $d-4$
branes arising from YM instantons, and U-duality interchanges momentum modes
with brane wrapping modes.For $d=6$, there is a generalised $\th $-angle which
couples to instantonic 3-branes and which combines with the SYM coupling
constant to take values in $SL(2,\R)/U(1)$, acted on by an $SL(2,\Z)$ subgroup
of the U-duality group $E_6(\Z)$. For $d=4,7,8$, there is an $SL(d+1)$
symmetry, suggesting that the matrix theory could be a scale-invariant $d+2$
dimensional theory on $T^{d+1} \times \R$ in these cases, as is already known
to be the case for $d=4$; evidence is found suggesting this happens for $d=8$
but not $d=7$. |
Dynamics of warped flux compactifications with backreacting anti-branes: We revisit the effective low-energy dynamics of the volume modulus in warped
flux compactifications with anti-D3-branes in order to analyze the prospects
for meta-stable de Sitter vacua and brane inflation along the lines of
KKLT/KKLMMT. At the level of the 10d supergravity solution, anti-branes in flux
backgrounds with opposite charge are known to source singular terms in the
energy densities of the bulk fluxes, which led to a debate on the consistency
of such constructions in string theory. A straightforward yet non-trivial check
of the singular solution is to verify that its dimensional reduction in the
large-volume limit reproduces the 4d low-energy dynamics expected from known
results where the anti-branes are treated as a probe. Taking into account the
anti-brane backreaction in the effective scalar potential, we find that both
the volume scaling and the coefficient of the anti-brane uplift term are in
exact agreement with the probe potential if the singular fluxes satisfy a
certain near-brane boundary condition. This condition can be tested explicitly
and may thus help to decide whether flux singularities should be interpreted as
pathological or benign features of flux compactifications with anti-branes.
Throughout the paper, we also comment on a number of subtleties related to the
proper definition of warped effective field theory with anti-branes. | Fermion Conformal Bootstrap in 4d: We apply numerical conformal bootstrap techniques to the four-point function
of a Weyl spinor in 4d non-supersymmetric CFTs. We find universal bounds on
operator dimensions and OPE coefficients, including bounds on operators in
mixed symmetry representations of the Lorentz group, which were inaccessible in
previous bootstrap studies. We find discontinuities in some of the bounds on
operator dimensions, and we show that they arise due to a generic yet
previously unobserved fake primary effect, which is related to the existence of
poles in conformal blocks. We show that this effect is also responsible for
similar discontinuities found in four-fermion bootstrap in 3d, as well as in
the mixed-correlator analysis of the 3d Ising CFT. As an important byproduct of
our work, we develop a practical technology for numerical approximation of
general 4d conformal blocks. |
Corners in M-theory: M-theory can be defined on closed manifolds as well as on manifolds with
boundary. As an extension, we show that manifolds with corners appear naturally
in M-theory. We illustrate this with four situations: The lift to bounding
twelve dimensions of M-theory on Anti de Sitter spaces, ten-dimensional
heterotic string theory in relation to twelve dimensions, and the two M-branes
within M-theory in the presence of a boundary. The M2-brane is taken with (or
as) a boundary and the worldvolume of the M5-brane is viewed as a tubular
neighborhood. We then concentrate on (variant) of the heterotic theory as a
corner and explore analytical and geometric consequences. In particular, we
formulate and study the phase of the partition function in this setting and
identify the corrections due to the corner(s). The analysis involves
considering M-theory on disconnected manifolds, and makes use of the extension
of the Atiyah-Patodi-Singer index theorem to manifolds with corners and the
b-calculus of Melrose. | Sugawara-type constraints in hyperbolic coset models: In the conjectured correspondence between supergravity and geodesic models on
infinite-dimensional hyperbolic coset spaces, and E10/K(E10) in particular, the
constraints play a central role. We present a Sugawara-type construction in
terms of the E10 Noether charges that extends these constraints infinitely into
the hyperbolic algebra, in contrast to the truncated expressions obtained in
arXiv:0709.2691 that involved only finitely many generators. Our extended
constraints are associated to an infinite set of roots which are all imaginary,
and in fact fill the closed past light-cone of the Lorentzian root lattice. The
construction makes crucial use of the E10 Weyl group and of the fact that the
E10 model contains both D=11 supergravity and D=10 IIB supergravity. Our
extended constraints appear to unite in a remarkable manner the different
canonical constraints of these two theories. This construction may also shed
new light on the issue of `open constraint algebras' in traditional canonical
approaches to gravity. |
Multi-Trace Operators and the Generalized AdS/CFT Prescription: We show that multi-trace interactions can be consistently incorporated into
an extended AdS/CFT prescription involving the inclusion of generalized
boundary conditions and a modified Legendre transform prescription. We find new
and consistent results by considering a self-contained formulation which
relates the quantization of the bulk theory to the AdS/CFT correspondence and
the perturbation at the boundary by double-trace interactions. We show that
there exist particular double-trace perturbations for which irregular modes are
allowed to propagate as well as the regular ones. We perform a detailed
analysis of many different possible situations, for both minimally and
non-minimally coupled cases. In all situations, we make use of a new constraint
which is found by requiring consistence. In the particular non-minimally
coupled case, the natural extension of the Gibbons-Hawking surface term is
generated. | Exact renormalization of a noncommutative φ^3 model in 6 dimensions: The noncommutative selfdual \phi^3 model in 6 dimensions is quantized and
essentially solved, by mapping it to the Kontsevich model. The model is shown
to be renormalizable and asymptotically free, and solvable genus by genus. It
requires both wavefunction and coupling constant renormalization. The exact
(all-order) renormalization of the bare parameters is determined explicitly,
which turns out to depend on the genus 0 sector only. The running coupling
constant is also computed exactly, which decreases more rapidly than predicted
by the one-loop beta function. A phase transition to an unstable phase is
found. |
Mother Moose: Generating Extra Dimensions from Simple Groups at Large N: We show that there exists a correspondence between four dimensional gauge
theories with simple groups and higher dimensional gauge theories at large N.
As an example, we show that a four dimensional {N}=2 supersymmetric SU(N) gauge
theory, on the Higgs branch, has the same correlators as a five dimensional
SU(N) gauge theory in the limit of large N provided the couplings are
appropriately rescaled. We show that our results can be applied to the AdS/CFT
correspondence to derive correlators of five or more dimensional gauge theories
from solutions of five dimensional supergravity in the large t'Hooft coupling
limit. | Chiral strings, the sectorized description and their integrated vertex
operators: A chiral string can be seen as an ordinary string in a singular gauge for the
worldsheet metric and has the ambitwistor string as its tensionless limit. As
proposed by Siegel, there is a one-parameter ($\beta$) gauge family
interpolating between the chiral limit and the usual conformal gauge in string
theory. This idea was used to compute scattering amplitudes of tensile chiral
strings, which are given by standard string amplitudes with modified
($\beta$-dependent) antiholomorphic propagators.
Due to the absence of a sensible definition of the integrated vertex
operator, there is still no ordinary prescription for higher than $3$-point
amplitude computations directly from the chiral model. The exception is the
tensionless limit.
In this work this gap will be filled. Starting with a chiral string action,
the integrated vertex operator is defined, relying on the so-called sectorized
interpretation. As it turns out, this construction effectively emulates a
left/right factorization of the scattering amplitude and introduces a relative
sign flip in the propagator for the sector-split target space coordinates.
$N$-point tree-level amplitudes can be easily shown to coincide with the
results of Siegel et al. |
Virtues of a symmetric-structure double copy: We demonstrate a physical motivation for extending color-dual or BCJ
double-copy construction to include theories with kinematic numerators that
obey the same algebraic relations as symmetric structure constants,
$d^{abc}=\text{Tr}[\{T^{a},T^{b}\}T^c]$. We verify that $U(N_c)$ nonlinear
sigma model (NLSM) pions, long known to be color-dual in terms of antisymmetric
adjoint factors, $f^{abc}$, are also color-dual in the sense of symmetric color
structures, $d^{abc}$, explicitly through six-point scattering. This reframing
of NLSM pion amplitudes complements our compositional construction of $d^{abc}$
color-dual higher derivative gauge operators. With adjoint and symmetric
color-dual kinematics, we can span all four-point effective photon operators
via a double-copy construction using amplitudes from physical theories. We
further comment on a tension between locality and adjoint effective numerators,
and the implications for spanning gravitational effective operators with
non-adjoint kinematics. | Bianchi-type string cosmology: Bianchi-type string cosmology involves generalizations of the FRW backgrounds
with three transitive spacelike Killing symmetries, but without any a priori
assumption of isotropy in the 3D sections of homogeneity. With emphasis on
those cases with diagonal metrics and vanishing cosmological constant which
which have not been previously examined in the literature, the present findings
allow an overview and the classification of all Bianchi-type backgrounds. These
string solutions (at least to lowest order in alpha prime) offer prototypes for
the study of spatial anisotropy and its impact on the dynamics of the early
universe. |
Brane Webs and Random Processes: We study $(p,q)$ 5-brane webs dual to certain $N$ M5-brane configurations and
show that the partition function of these brane webs gives rise to cylindric
Schur process with period $N$. This generalizes the previously studied case of
period $1$. We also show that open string amplitudes corresponding to these
brane webs are captured by the generating function of cylindric plane
partitions with profile determined by the boundary conditions imposed on the
open string amplitudes. | Anomaly cancellation with an extra gauge boson: Many extensions of the Standard Model include an extra gauge boson, whose
couplings to fermions are constrained by the requirement that anomalies cancel.
We find a general solution to the resulting diophantine equations in the
plausible case where the chiral fermion content is that of the Standard Model
plus 3 right-handed neutrinos. |
No-force condition and BPS combinations of p-branes in 11 and 10
dimensions: The condition of vanishing of static force on a q-brane probe in the
gravitational background produced by another p-brane is used to give a simple
derivation of the pair-wise intersection rules which govern the construction of
BPS combinations of branes. These rules, while implied also by supersymmetry
considerations, thus have purely bosonic origin. Imposing the no-force
requirement makes possible to add branes `one by one' to construct composite
BPS configurations (with zero binding energy) of 2-branes and 5-branes in D=11
and of various p-branes in D=10. The advantage of this elementary approach is
its universality, i.e. the cases of different dimensions and different types of
branes (e.g., NS-NS, R-R and `mixed' combinations of NS-NS and R-R branes in
D=10) are all treated in the same way. | Open Branes and Little Strings: This is a short review of the newly discovered ODp-theories that are
non-gravitational six-dimensional theories defined as the decoupling limit of
NS5-branes in the presence of a near-critical (p+1)-form RR fields. We discuss
the motivation for these new theories, their definitions and properties, and
their relation to NCOS theory, OM theory and Little String Theory, focusing on
the cases p=1,2. |
On Decay of K-theory: Closed string tachyon condensation resolves the singularities of
nonsupersymmetric orbifolds, however the resolved space typically has fewer
D-brane charges than that of the orbifold. The description of the tachyon
condensation process via a gauged linear sigma model enables one to track the
topology as one passes from the sigma model's ``orbifold phase'' to its
resolved, ``geometric phase,'' and thus to follow how the D-brane charges
disappear from the effective spacetime dynamics. As a mathematical consequence,
our results point the way to a formulation of a ``quantum McKay
correspondence'' for the resolution of toric orbifold singularities. | Classification of the N=1 Seiberg-Witten Theories: We present a systematic study of N=1 supersymmetric gauge theories which are
in the Coulomb phase. We show how to find all such theories based on a simple
gauge group and no tree-level superpotential. We find the low-energy solution
for the new theories in terms of a hyperelliptic Seiberg-Witten curve. This
work completes the study of all N=1 supersymmetric gauge theories where the
Dynkin index of the matter fields equals the index of the adjoint (mu=G), and
consequently all theories for which mu<G. |
Faddeev-Popov ghosts in quantum gravity beyond perturbation theory: We study the Faddeev-Popov ghost sector of asymptotically safe quantum
gravity, which becomes non-perturbative in the ultraviolet. We point out that
nonzero matter-ghost couplings and higher-order ghost self-interactions exist
at a non-Gaussian fixed point for the gravitational couplings, i.e., in the
ultraviolet. Thus the ghost sector in this non-perturbative ultraviolet
completion does not keep the structure of a simple Faddeev-Popov determinant.
We discuss implications of the new ghost couplings for the Renormalization
Group flow in gravity, the form of the ultraviolet completion, and the relevant
couplings, i.e., free parameters, of the theory. | Fluxes and Branes in Type II Vacua and M-theory Geometry with G(2) and
Spin(7) Holonomy: We discuss fluxes of RR and NSNS background fields in type II string
compactifications on non-compact Calabi-Yau threefolds together with their dual
brane description which involves bound states of branes. Simultaneously turning
on RR and NSNS 2-form fluxes in an 1/2 supersymmetric way can be geometrically
described in M-theory by a SL(2,Z) family of metrics of G(2) holonomy. On the
other hand, if the flux configuration only preserves 1/4 of supersymmetries, we
postulate the existence of a new eight-dimensional manifold with spin(7)
holonomy, which does not seem to fit into the classes of known examples. The
latter situation is dual to a 1/4 supersymmetric web of branes on the deformed
conifold. In addition to the 2-form fluxes, we also present some considerations
on type IIA NSNS 4-form and 6-form fluxes. |
Constraints and Period Relations in Bosonic Strings at Genus-g: We examine some of the implications of implementing the usual boundary
conditions on the closed bosonic string in the hamiltonian framework. Using the
KN formalism, it is shown that at the quantum level, the resulting constraints
lead to relations among the periods of the basis 1-forms. These are compared
with those of Riemanns' which arise from a different consideration. | Domain walls and flow equations in supergravity: Domain wall solutions have attracted much attention due to their relevance
for brane world scenarios and the holographic RG flow. In this talk I discuss
the following aspects for these applications: (i) derivation of the first order
flow equations as Bogomol'nyi bound; (ii) different types of critical points of
the superpotential; (iii) the superpotential needed to localize gravity; (iv)
the constraints imposed by supersymmetry including an example for an $N$=1 flow
and finally (v) sources and exponential trapping of gravity. |
Zero modes, gauge fixing, monodromies, $ζ$-functions and all that: We discuss various issues associated with the calculation of the reduced
functional determinant of a special second order differential operator
$\boldmath${F}$ =-d^2/d\tau^2+\ddot g/g$, $\ddot g\equiv d^2g/d\tau^2$, with a
generic function $g(\tau)$, subject to periodic and Dirichlet boundary
conditions. These issues include the gauge-fixed path integral representation
of this determinant, the monodromy method of its calculation and the
combination of the heat kernel and zeta-function technique for the derivation
of its period dependence. Motivations for this particular problem, coming from
applications in quantum cosmology, are also briefly discussed. They include the
problem of microcanonical initial conditions in cosmology driven by a conformal
field theory, cosmological constant and cosmic microwave background problems. | A note on Gribov copies in 3D Chern-Simons theory: Using powerful tools of harmonic maps and integrable systems, all the Gribov
copies in the Coulomb gauge in 3D Chern-Simons theory are constructed. Some
issues about the Gribov and the modular re- gions are shortly discussed. The
Gribov copies of the vacuum in 3D QCD in the Coulomb gauge are described. An
interesting implication of the presence of Gribov copies is briefy pointed out. |
Neutrino-Antineutrino Asymmetry From The Space-time Noncommutativity: A new mechanism having as an origin the space-time noncommutativity has been
shown to generate anisotropy and axial-like interaction giving rise to a
leptonic asymmetry for fermionic particles propagating in a curved
noncommutative $FRW$ universe. As a by-product, for ultra-relativistic
particles like neutrinos, an analytical expression of this asymmetry is derived
explicitly. Constraints and bounds from the cosmological parameters are also
discussed. | Mirror effect induced by the dilaton field on the Hawking radiation: We discuss the string creation in the near-extremal NS1 black string
solution. The string creation is described by an effective field equation
derived from a fundamental string action coupled to the dilaton field in a
conformally invariant manner. In the non-critical string model the dilaton
field causes a timelike mirror surface outside the horizon when the size of the
black string is comparable to the Planck scale. Since the fundamental strings
are reflected by the mirror surface, the negative energy flux does not
propagate across the surface. This means that the evaporation stops just before
the naked singularity of the extremal black string appears even though the
surface gravity is non-zero in the extremal limit. |
Bosonisation Excercise in Three Dimensions: Gauged Massive Thirring
Model: Bosonisation of the massive Thirring model, with a non-minimal and
non-abelian gauging is studied in 2+1-dimensions. The static abelian model is
solved completely in the large fermion mass limit and the spectrum is obtained.
The non-abelian model is solved for a restricted class of gauge fields. In both
cases explicit expressions for bosonic currents corresponding to the fermion
currents are given. | $I$ in generalized supergravity: We showed in previous work that for homogeneous Yang-Baxter (YB) deformations
of AdS$_5\times$S$^5$, the open string metric and coupling, and as a result the
closed string density $e^{-2 \Phi} \sqrt{g}$, remain undeformed. In this work,
in addition to extending these results to the deformation associated with the
modified CYBE, or $\eta$-deformation, we identify the Page forms as the open
string counterpart for RR fields and demonstrate case by case that the non-zero
Page forms remain invariant under YB deformations. We give a physical meaning
to the Killing vector $I$ of generalized supergravity and show for all YB
deformations: 1) $I$ appears as a current for center of mass motion on the
worldvolume of a D-branes probing the background, 2) $I$ is equal to the
divergence of the noncommutativity parameter, 3) $I$ exhibits "holographic"
behavior, where the radial component of $I$ vanishes at the AdS boundary, and
4) in pure spinor formalism $I$ is related to a certain state in the BRST
cohomology. |
Asymptotically Safe $f(R)$-Gravity Coupled to Matter II: Global
Solutions: Ultraviolet fixed point functions of the functional renormalisation group
equation for $f(R)$-gravity coupled to matter fields are discussed. The metric
is split via the exponential parameterisation into a background and a
fluctuating metric, the former is chosen to be the one of a four-sphere. Also
when scalar, fermion and vector fields are included global quadratic solutions
exist as in the pure gravity case for discrete sets of values for some
endomorphism parameters defining the coarse-graining scheme. The asymptotic,
large-curvature behaviour of the fixed point functions is analysed for generic
values of these parameters. Examples for global numerical solutions are
provided. A special focus is given to the question whether matter fields might
destabilise the ultraviolet fixed point function. Similar to a previous
analysis of a polynomial, small-curvature approximation to the fixed point
functions different classes for such functions are found. | CFT Correlators and CP-Violating Trace Anomalies: We analyze the parity-odd correlators $\langle JJO\rangle_{odd}$, $\langle
JJT\rangle_{odd}$, $\langle TTO\rangle_{odd}$ and $\langle TTT\rangle_{odd}$ in
momentum space, constrained by conformal Ward identities, extending our former
investigation of the parity-odd chiral anomaly vertex. We investigate how the
presence of parity-odd trace anomalies affect such correlators. Motivations for
this study come from holography, early universe cosmology and from a recent
debate on the chiral trace anomaly of a Weyl fermion. In the current CFT
analysis, $O$ can be either a scalar or a pseudoscalar operator and it can be
identified with the trace of the stress energy tensor. We find that the
$\langle JJO\rangle_{odd}$ and $\langle TTO\rangle_{odd}$ can be different from
zero in a CFT. This occurs when the conformal dimension of the scalar operator
is $\Delta_3=4$, as in the case of $O=T^\mu_\mu$. Moreover, if we assume the
existence of parity-odd trace anomalies, the conformal $\langle
JJT\rangle_{odd}$ and $\langle TTT\rangle_{odd}$ are nonzero. In particular, in
the case of $\langle JJT\rangle_{odd}$ the transverse-traceless component is
constrained to vanish, and the correlator is determined only by the trace part
with the anomaly pole. |
Free Field Representation For Massive Integrable Models: A new approach to massive integrable models is considered. It allows one to
find symmetry algebras which define spaces of local operators and to get
general integral representations for form-factors in the\ $ SU(2)$\ Thirring
and Sine-Gordon models. | All-loop Mondrian Reduction of 4-particle Amplituhedron at Positive
Infinity: This article introduces a systematic framework to understand (not to derive
yet) the all-loop 4-particle amplituhedron in planar N=4 SYM, utilizing both
positivity and the Mondrian diagrammatics. Its key idea is the simplest one so
far: we can decouple one or more sets of loop variables (x,y,z,w) from the rest
by just setting these variables to either zero or infinity so that their
relevant positivity conditions are trivialized, then the all-loop consistency
requires that we get lower loop amplituhedra as "residues". These decoupling
relations connect higher loop DCI integrals with the lower ones, enabling us to
identify their coefficients starting from the 3-loop case. And surprisingly,
the delicate mechanism of this process is the simple Mondrian rule D=X+Y, which
forces those visually non-Mondrian DCI integrals to have the correct
coefficients such that the amplituhedron can exactly reduce to the lower loop
one. Examples cover all DCI integrals at L=3,4,5,6, especially, the subtle
6-loop coefficients +2 and 0 are neatly explained in this way. |
Finitized Conformal Spectra of the Ising Model on the Klein Bottle and
Moebius Strip: We study the conformal spectra of the critical square lattice Ising model on
the Klein bottle and M\"obius strip using Yang-Baxter techniques and the
solution of functional equations. In particular, we obtain expressions for the
finitized conformal partition functions in terms of finitized Virasoro
characters. This demonstrates that Yang-Baxter techniques and functional
equations can be used to study the conformal spectra of more general exactly
solvable lattice models in these topologies. The results rely on certain
properties of the eigenvalues which are confirmed numerically. | Trace Anomaly and Quantization of Maxwell's Theory on Non-Commutative
Spaces: The canonical and symmetrical energy-momentum tensors and their non-zero
traces in Maxwell's theory on non-commutative spaces have been found. Dirac's
quantization of the theory under consideration has been performed. I have found
the extended Hamiltonian and equations of motion in the general gauge covariant
form. |
N = (2, 2) Non-Linear sigma-Models: A Synopsis: We review N=(2,2) supersymmetric non-linear sigma-models in two dimensions
and their relation to generalized Kahler and Calabi-Yau geometry. We illustrate
this with an explicit non-trivial example. | Semiclassical strings and AdS/CFT: We discuss AdS/CFT duality in the sector of ``semiclassical'' string states
with large quantum numbers. We review the coherent-state effective action
approach, in which similar 2d sigma model actions appear from the AdS_5 x S^5
string action and from the integrable spin chain Hamiltonian representing the
N=4 super Yang-Mills dilatation operator. We consider mostly the leading-order
terms in the energies/anomalous dimensions which match but comment also on
higher-order corrections. |
Chiral Decomposition For Non-Abelian Bosons: We study the non-abelian extension for the splitting of a scalar field into
chiral components. Using this procedure we find a non ambiguous way of coupling
a non abelian chiral scalar field to gravity. We start with a (non-chiral) WZW
model covariantly coupled to a background metric and, after the splitting,
arrive at two chiral Wess-Zumino-Witten (WZW) models coupled to gravity. | Strings in Time-Dependent Orbifolds: We continue and extend our earlier investigation ``Strings in a
Time-Dependent Orbifold'' (hep-th/0204168). We formulate conditions for an
orbifold to be amenable to perturbative string analysis and classify the low
dimensional orbifolds satisfying these conditions. We analyze the tree and
torus amplitudes of some of these orbifolds. The tree amplitudes exhibit a new
kind of infrared divergences which are a result of some ultraviolet effects.
These UV enhanced IR divergences can be interpreted as due to back reaction of
the geometry. We argue that for this reason the three dimensional parabolic
orbifold is not amenable to perturbation theory. Similarly, the smooth four
dimensional null-brane tensored with sufficiently few noncompact dimensions
also appears problematic. However, when the number of noncompact dimensions is
sufficiently large perturbation theory in these time dependent backgrounds
seems consistent. |
Wall crossing in local Calabi Yau manifolds: We study the BPS states of a D6-brane wrapping the conifold and bound to
collections of D2 and D0 branes. We find that in addition to the complexified
Kahler parameter of the rigid sphere it is necessary to introduce an extra real
parameter to describe BPS partition functions and marginal stability walls. The
supergravity approach to BPS state-counting gives a simple derivation of
results of Szendroi concerning Donaldson-Thomas theory on the noncommutative
conifold. This example also illustrates some interesting limitations on the
supergravity approach to BPS state-counting and wall-crossing. | Quantum Vacua of 2d Maximally Supersymmetric Yang-Mills Theory: We analyze the classical and quantum vacua of 2d $\mathcal{N}=(8,8)$
supersymmetric Yang-Mills theory with $SU(N)$ and $U(N)$ gauge group,
describing the worldvolume interactions of $N$ parallel D1-branes with flat
transverse directions $\mathbb{R}^8$. We claim that the IR limit of the $SU(N)$
theory in the superselection sector labeled $M \pmod{N}$ --- identified with
the internal dynamics of $(M,N)$-string bound states of Type IIB string theory
--- is described by the symmetric orbifold $\mathcal{N}=(8,8)$ sigma model into
$(\mathbb{R}^8)^{D-1}/\mathbb{S}_D$ when $D=\gcd(M,N)>1$, and by a single
massive vacuum when $D=1$, generalizing the conjectures of E. Witten and
others. The full worldvolume theory of the D1-branes is the $U(N)$ theory with
an additional $U(1)$ 2-form gauge field $B$ coming from the string theory
Kalb-Ramond field. This $U(N)+B$ theory has generalized field configurations,
labeled by the $\mathbb{Z}$-valued generalized electric flux and an independent
$\mathbb{Z}_N$-valued 't Hooft flux. We argue that in the quantum mechanical
theory, the $(M,N)$-string sector with $M$ units of electric flux has a
$\mathbb{Z}_N$-valued discrete $\theta$ angle specified by $M \pmod{N}$ dual to
the 't Hooft flux. Adding the brane center-of-mass degrees of freedom to the
$SU(N)$ theory, we claim that the IR limit of the $U(N) + B$ theory in the
sector with $M$ bound F-strings is described by the $\mathcal{N}=(8,8)$ sigma
model into ${\rm Sym}^{D} ( \mathbb{R}^8)$. We provide strong evidence for
these claims by computing an $\mathcal{N}=(8,8)$ analog of the elliptic genus
of the UV gauge theories and of their conjectured IR limit sigma models, and
showing they agree. Agreement is established by noting that the elliptic genera
are modular-invariant Abelian (multi-periodic and meromorphic) functions, which
turns out to be very restrictive. |
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