anchor
stringlengths 50
3.92k
| positive
stringlengths 55
6.16k
|
|---|---|
Gaugino Condensates and D-terms from D7-branes: We investigate, at the microscopic level, the compatibility between D-term
potentials from world-volume fluxes on D7-branes and non-perturbative
superpotentials arising from gaugino condensation on a different stack of
D7-branes. This is motivated by attempts to construct metastable de Sitter
vacua in type IIB string theory via D-term uplifts. We find a condition under
which the Kaehler modulus, T, of a Calabi-Yau 4-cycle gets charged under the
anomalous U(1) on the branes with flux. If in addition this 4-cycle is wrapped
by a stack of D7-branes on which gaugino condensation takes place, the question
of U(1)-gauge invariance of the (T-dependent) non-perturbative superpotential
arises. In this case an index theorem guarantees that strings, stretching
between the two stacks, yield additional charged chiral fields which also
appear in the superpotential from gaugino condensation. We check that the
charges work out to make this superpotential gauge invariant, and we argue that
the mechanism survives the inclusion of higher curvature corrections to the
D7-brane action.
|
Universality From Very General Nonperturbative Flow Equations in QCD: In the context of very general exact renormalization groups, it will be shown
that, given a vertex expansion of the Wilsonian effective action, remarkable
progress can be made without making any approximations. Working in QCD we will
derive, in a manifestly gauge invariant way, an exact diagrammatic expression
for the expectation value of an arbitrary gauge invariant operator, in which
many of the non-universal details of the setup do not explicitly appear. This
provides a new starting point for attacking nonperturbative problems.
|
Geometry of AdS-Melvin Spacetimes: We study asymptotically AdS generalizations of Melvin spacetimes, describing
gravitationally bound tubes of magnetic flux. We find that narrow fluxtubes,
carrying strong magnetic fields but little total flux, are approximately
unchanged from the $\Lambda=0$ case at scales smaller than the AdS scale.
However, fluxtubes with weak fields, which for $\Lambda=0$ can grow arbitrarily
large in radius and carry unbounded magnetic flux, are limited in radius by the
AdS scale and like the narrow fluxtubes carry only small total flux. As a
consequence, there is a maximum magnetic flux $\Phi_{max} =
2\pi/\sqrt{-\Lambda}$ that can be carried by static fluxtubes in AdS. For flux
$\Phi_{tot}<\Phi_{max}$ there are two branches of solutions, with one branch
always narrower in radius than the other. We compute the ADM mass and tensions
for AdS-Melvin fluxtube, finding that the wider radius branch of solutions
always has lower mass. In the limit of vanishing flux, this branch reduces to
the AdS soliton.
|
Bootstrapping the half-BPS line defect CFT in $\mathcal{N}=4$ SYM at
strong coupling: We consider the 1d CFT defined by the half-BPS Wilson line in planar
$\mathcal{N}=4$ super Yang-Mills. Using analytic bootstrap methods we derive
the four-point function of the super-displacement operator at fourth order in a
strong coupling expansion. Via AdS/CFT, this corresponds to the first
three-loop correlator in AdS ever computed. To do so we address the operator
mixing problem by considering a family of auxiliary correlators. We further
extract the anomalous dimension of the lightest non-protected operator and find
agreement with the integrability-based numerical result of Grabner, Gromov and
Julius.
|
Supergravity on the noncommutative geometry: Two years ago, we found the supersymmetric counterpart of the spectral triple
which specified noncommutative geometry. Based on the triple, we derived gauge
vector supermultiplets, Higgs supermultiplets of the minimum supersymmetric
standard model and its action. However, unlike the famous theories of Connes
and his co-workers, the action does not couple to gravity. In this paper, we
obtain the supersymmetric Dirac operator $\mathcal{D}_M^{(SG)}$ on the
Riemann-Cartan curved space replacing derivatives which appear in that of the
triple with the covariant derivatives of general coordinate transformation. We
apply the supersymmetric version of the spectral action principle and
investigate the heat kernel expansion on the square of the Dirac operator. As a
result, we obtain a new supergravity action which does not include the Ricci
curvature tensor.
|
Bootstrability in Line-Defect CFT with Improved Truncation Methods: We study the conformal bootstrap of 1D CFTs on the straight Maldacena-Wilson
line in 4D ${\cal N}=4$ super-Yang-Mills theory. We introduce an improved
truncation scheme with an 'OPE tail' approximation and use it to reproduce the
'bootstrability' results of Cavagli\`a et al. for the OPE-coefficients squared
of the first three unprotected operators. For example, for the first
OPE-coefficient squared at 't Hooft coupling $(4\pi)^2$, linear-functional
methods with two sum rules from integrated correlators give the rigorous result
$0.294014873 \pm 4.88 \cdot 10^{-8}$, whereas our methods give with
machine-precision computations $0.294014228 \pm 6.77 \cdot 10^{-7}$. For our
numerical searches, we benchmark the Reinforcement Learning Soft Actor-Critic
algorithm against an Interior Point Method algorithm (IPOPT) and comment on the
merits of each algorithm.
|
Aspects of $σ$ Models: Some aspects and applications of $ \sigma$-models in particle and condensed
matter physics are briefly reviewed.
|
Renormalization of an Abelian Tensor Group Field Theory: Solution at
Leading Order: We study a just renormalizable tensorial group field theory of rank six with
quartic melonic interactions and Abelian group U(1). We introduce the formalism
of the intermediate field, which allows a precise characterization of the
leading order Feynman graphs. We define the renormalization of the model,
compute its (perturbative) renormalization group flow and write its expansion
in terms of effective couplings. We then establish closed equations for the two
point and four point functions at leading (melonic) order. Using the effective
expansion and its uniform exponential bounds we prove that these equations
admit a unique solution at small renormalized coupling.
|
Dilaton, Antisymmetric Tensor and Gauge Fields in String Effective
Theories at the One--loop Level: We investigate the dependence of the gauge couplings on the dilaton field in
string effective theories at the one--loop level. First we resolve the
discrepancies between statements based on symmetry considerations and explicit
calculations in string effective theories on this subject. A calculation of the
relevant one--loop scattering amplitudes in string theory gives us further
information and allows us to derive the exact form of the corresponding
effective Lagrangian. In particular there is no dilaton dependent one--loop
correction to the holomorphic $f$--function arising from massive string modes
in the loop. In addition we address the coupling of the antisymmetric tensor
field to the gauge bosons at one--loop. While the string S--matrix elements are
not reproduced using the usual supersymmetric Lagrangian with the chiral
superfield representation for the dilaton field, the analogue Lagrangian with
the dilaton in a linear multiplet naturally gives the correct answer.
|
Aharonov-Bohm defects: We discuss what happens when a field receiving an Aharonov-Bohm (AB) phase
develops a vacuum expectation value (VEV), with an example of an Alice string
in a $U(1) \times SU(2)$ gauge theory coupled with complex triplet scalar
fields. We introduce scalar fields belonging to the doublet representation of
$SU(2)$, charged or chargeless under the $U(1)$ gauge symmetry, that receives
an AB phase around the Alice string. When the doublet develops a VEV, the Alice
string turns to a global string in the absence of the interaction depending on
the relative phase between the doublet and triplet, while, in the presence of
such an interaction, the Alice string is confined by a soliton or domain wall
and therefore the spontaneous breaking of a spatial rotation around the string
is accompanied. We call such an object induced by an AB phase as an ``AB
defect'', and argue that such a phenomenon is ubiquitously appearing in various
systems.
|
Relativistic Beaming in AdS/CFT: We propose a mechanism of 'beaming' the backreaction of a relativistic source
in the bulk of AdS towards the boundary. Using this beaming mechanism to
estimate the energy distribution from radiation by a circling quark in strongly
coupled field theory, we find remarkable agreement with the previous results of
arXiv:1001.3880. Apart from explaining a puzzling feature of these results and
elucidating the scale/radius duality in AdS/CFT, our proposal provides a useful
computational technique.
|
Coleman-de Luccia instanton in dRGT massive gravity: We study the Coleman-de Luccia (CDL) instanton characterizing the tunneling
from a false vacuum to the true vacuum in a semi-classical way in dRGT
(deRham-Gabadadze-Tolley) massive gravity theory, and evaluate the dependence
of the tunneling rate on the model parameters. It is found that provided with
the same physical Hubble parameters for the true vacuum $H_{\rm T}$ and the
false vacuum $H_{\rm F}$ as in General Relativity (GR), the thin-wall
approximation method implies the same tunneling rate as GR. However, deviations
of tunneling rate from GR arise when one goes beyond the thin-wall
approximation and they change monotonically until the Hawking-Moss (HM) case.
Moreover, under the thin-wall approximation, the HM process may dominate over
the CDL one if the value for the graviton mass is larger than the inverse of
the radius of the bubble.
|
The Enhancon and N=2 Gauge Theory/Gravity RG Flows: We study the family of ten dimensional type IIB supergravity solutions
corresponding to renormalisation group flows from N=4 to N=2 supersymmetric
Yang-Mills theory. Part of the solution set corresponds to a submanifold of the
Coulomb branch of the gauge theory, and we use a D3-brane probe to uncover
details of this physics. At generic places where supergravity is singular, the
smooth physics of the probe yields the correct one-loop form of the effective
low energy gauge coupling. The probe becomes tensionless on a ring at finite
radius. Supergravity flows which end on this ``enhancon'' ring correspond to
the vacua where extra massless degrees of freedom appear in the gauge theory,
and the gauge coupling diverges there. We identify an SL(2,Z) duality action on
the enhancon ring which relates the special vacua, and comment on the massless
dyons within them. We propose that the supergravity solution inside the
enhancon ring should be excised, since the probe's tension is unphysical there.
|
Fuzzy Torus via q-Parafermion: We note that the recently introduced fuzzy torus can be regarded as a
q-deformed parafermion. Based on this picture, classification of the Hermitian
representations of the fuzzy torus is carried out. The result involves
Fock-type representations and new finite dimensional representations for q
being a root of unity as well as already known finite dimensional ones.
|
Numerical Analyses on Moduli Space of Vacua: We propose a new computational method to understand the vacuum moduli space
of (supersymmetric) field theories. By combining numerical algebraic geometry
(NAG) and elimination theory, we develop a powerful, efficient, and
parallelizable algorithm to extract important information such as the
dimension, branch structure, Hilbert series and subsequent operator counting,
as well as variation according to coupling constants and mass parameters. We
illustrate this method on a host of examples from gauge theory, string theory,
and algebraic geometry.
|
Black hole dynamics from thermodynamics in Anti-de Sitter space: We work on the relation between the local thermodynamic instability and the
dynamical instability of large black holes in four-dimensional anti-de Sitter
space proposed by Gubser and Mitra. We find that all perturbations suppressing
the metric fluctuations at linear order become dynamically unstable when black
holes lose the local thermodynamic stability. We discuss how dynamical
instabilities can be explained by the Second Law of Thermodynamics.
|
Strong Connections on Quantum Principal Bundles: A gauge invariant notion of a strong connection is presented and
characterized. It is then used to justify the way in which a global curvature
form is defined. Strong connections are interpreted as those that are induced
from the base space of a quantum bundle. Examples of both strong and non-strong
connections are provided. In particular, such connections are constructed on a
quantum deformation of the fibration $S^2 -> RP^2$. A certain class of strong
$U_q(2)$-connections on a trivial quantum principal bundle is shown to be
equivalent to the class of connections on a free module that are compatible
with the q-dependent hermitian metric. A particular form of the Yang-Mills
action on a trivial $U\sb q(2)$-bundle is investigated. It is proved to
coincide with the Yang-Mills action constructed by A.Connes and M.Rieffel.
Furthermore, it is shown that the moduli space of critical points of this
action functional is independent of q.
|
Graviton multi-point amplitudes for higher-derivative gravity in anti-de
Sitter space: We calculate graviton multi-point amplitudes in an anti-de Sitter black brane
background for higher-derivative gravity of arbitrary order in numbers of
derivatives. The calculations are performed using tensor graviton modes in a
particular regime of comparatively high energies and large scattering angles.
The regime simplifies the calculations but, at the same time, is well suited
for translating these results into the language of the dually related gauge
theory. After considering theories of up to eight derivatives, we generalize to
even higher-derivative theories by constructing a "basis" for the relevant
scattering amplitudes. This construction enables one to find the basic form of
the n-point amplitude for arbitrary n and any number of derivatives.
Additionally, using the four-point amplitudes for six and eight-derivative
gravity, we re-express the scattering properties in terms of the Mandelstam
variables.
|
Semiclassical zero temperature black holes in spherically reduced
theories: We numerically integrate the semiclassical equations of motion for
spherically symmetric Einstein-Maxwell theory with a dilaton coupled scalar
field and look for zero temperature configurations. The solution we find is
studied in detail close to the horizon and comparison is made with the
corresponding one in the minimally coupled case.
|
Optimization of the derivative expansion in the nonperturbative
renormalization group: We study the optimization of nonperturbative renormalization group equations
truncated both in fields and derivatives. On the example of the Ising model in
three dimensions, we show that the Principle of Minimal Sensitivity can be
unambiguously implemented at order $\partial^2$ of the derivative expansion.
This approach allows us to select optimized cut-off functions and to improve
the accuracy of the critical exponents $\nu$ and $\eta$. The convergence of the
field expansion is also analyzed. We show in particular that its optimization
does not coincide with optimization of the accuracy of the critical exponents.
|
String Fluid in Local Equilibrium: We study the solutions of string fluid equations under assumption of a local
equilibrium which was previously obtained in the context of the kinetic theory.
We show that the fluid can be foliated into non-interacting submanifolds whose
equations of motion are exactly that of the wiggly strings considered
previously by Vilenkin and Carter. In a special case of negligible statistical
variance in either the left or the right-moving directions of microscopic
strings, the submanifolds are described by the action of chiral strings
proposed by Witten. When both variances vanish the submanifolds are described
by the Nambu-Goto action and the string fluid reduces to the string dust
introduced by Stachel.
|
The Backreacted Kähler Geometry of Wrapped Branes: For supersymmetric solutions of D3(M2) branes with AdS3(AdS2) factor, it is
known that the internal space is expressible as U(1) fibration over K\"ahler
space which satisfies a specific partial differential equation involving the
Ricci tensor. In this paper we study the wrapped brane solutions of D3 and
M2-branes which were originally constructed using gauged supergravity and
uplifted to D=10 and D=11. We rewrite the solutions in canonical form, identify
the backreacted K\"ahler geometry, and present a class of solutions which
satisfy the Killing spinor equation.
|
Vacuum Sampling in the Landscape during Inflation: We consider the phenomenological consequences of sampling multiple vacua
during inflation motivated by an enormous landscape. A generic consequence of
this sampling is the formation of domain walls, characterized by the scale
$\mu$ of the barriers that partition the accessed vacua. We find that the
success of Big Bang Nucleosynthesis (BBN) implies $\mu \gsim 10$ TeV, as long
as the sampled vacua have a non-degeneracy larger than $\cal{O}({{\rm
MeV}}^{\rm 4})$. Otherwise, the walls will dominate and eventually form black
holes that must reheat the universe sufficiently for BBN to take place; in this
case, we obtain $\mu \gsim 10^{-5}M_P$. These black holes are not allowed to
survive and contribute to cosmic dark matter density.
|
Duality considerations about the Maxwell-Podolsky theory through the
symplectic embedding formalism and spectrum analysis: We find the dual equivalent (gauge invariant) version of the Maxwell theory
in D=4 with a Proca-like mass term by using the symplectic embedding method.
The dual theory obtained (Maxwell-Podolsky) includes a higher-order derivative
term and preserve the gauge symmetry. We also furnish an investigation of the
pole structure of the vector propagator by the residue matrix which considers
the eventual existence of the negative-norm of the theory.
|
Black hole entropy function for toric theories via Bethe Ansatz: We evaluate the large-$N$ behavior of the superconformal indices of toric
quiver gauge theories, and use it to find the entropy functions of the dual
electrically charged rotating $\mathrm{AdS}_5$ black holes. To this end, we
employ the recently proposed Bethe Ansatz method, and find a certain set of
solutions to the Bethe Ansatz Equations of toric theories. This, in turn,
allows us to compute the large-$N$ behavior of the index for these theories,
including the infinite families $Y^{pq}$, $X^{pq}$ and $L^{pqr}$ of quiver
gauge theories. Our results are in perfect agreement with the predictions made
recently using the Cardy-like limit of the superconformal index. We also
explore the index structure in the space of chemical potentials and describe
the pattern of Stokes lines arising in the conifold theory case.
|
Symmetry enhancement in 4d Spin(n) gauge theories and compactification
from 6d: We consider a known sequence of dualities involving $4d$ ${\cal N}=1$
theories with $Spin(n)$ gauge groups and use it to construct a new sequence of
models exhibiting IR symmetry enhancement. Then, motivated by the observed
pattern of IR symmetries we conjecture six-dimensional theories the
compactification of which on a Riemann surface yields the $4d$ sequence of
models along with their symmetry enhancements, and put them to several
consistency checks.
|
Cosmic Rotation Axis, Birefrigence and Axions to detect Primordial
torsion fields: Nodland Ralston (PRL,1997) investigated the cosmological anisotropy of
electromagnetic fields.In this paper we show that it is possible obtain a
torsion correction to Nodland-Ralston action starting from the massive Proca
electrodynamics in Riemannian spacetime and performing the minimal coupling
with torsion.We end up with an action which contains the Nodland Ralston action
without breaking the gauge invariance.This mechanism however gives a photon a
mass generated by the nonlinear torsion terms.The torsion vector is along the
cosmic rotation axis and interacts with the massive photon.This method which
breaks conformal invariance allow us to determine a primordial torsion of the
order $10^{-29}eV$ from the well-known photon mass limits.
|
Phase transitions for deformations of JT supergravity and matrix models: We analyze deformations of $\mathcal{N}=1$ Jackiw-Teitelboim (JT)
supergravity by adding a gas of defects, equivalent to changing the dilaton
potential. We compute the Euclidean partition function in a topological
expansion and find that it matches the perturbative expansion of a random
matrix model to all orders. The matrix model implements an average over the
Hamiltonian of a dual holographic description and provides a stable
non-perturbative completion of these theories of $\mathcal{N}=1$
dilaton-supergravity. For some range of deformations, the supergravity spectral
density becomes negative, yielding an ill-defined topological expansion. To
solve this problem, we use the matrix model description and show the negative
spectrum is resolved via a phase transition analogous to the Gross-Witten-Wadia
transition. The matrix model contains a rich and novel phase structure that we
explore in detail, using both perturbative and non-perturbative techniques.
|
Lie Algebra Expansion and Integrability in Superstring Sigma-Models: Lie algebra expansion is a technique to generate new Lie algebras from a
given one. In this paper, we apply the method of Lie algebra expansion to
superstring $\sigma$-models with a $\mathbb{Z}_4$ coset target space. By
applying the Lie algebra expansion to the isometry algebra, we obtain different
$\sigma$-models, where the number of dynamical fields can change. We reproduce
and extend in a systematic way actions of some known string regimes (flat
space, BMN and non-relativistic in AdS$_5 \times$S$^5$). We define a criterion
for the algebra truncation such that the equations of motion of the expanded
action of the new $\sigma$-model are equivalent to the vanishing curvature
condition of the Lax connection obtained by expanding the Lax connection of the
initial model.
|
Convergence of hydrodynamic modes: insights from kinetic theory and
holography: We study the mechanisms setting the radius of convergence of hydrodynamic
dispersion relations in kinetic theory in the relaxation time approximation.
This introduces a qualitatively new feature with respect to holography: a
nonhydrodynamic sector represented by a branch cut in the retarded Green's
function. In contrast with existing holographic examples, we find that the
radius of convergence in the shear channel is set by a collision of the
hydrodynamic pole with a branch point. In the sound channel it is set by a
pole-pole collision on a non-principal sheet of the Green's function. More
generally, we examine the consequences of the Implicit Function Theorem in
hydrodynamics and give a prescription to determine a set of points that
necessarily includes all complex singularities of the dispersion relation. This
may be used as a practical tool to assist in determining the radius of
convergence of hydrodynamic dispersion relations.
|
Kramers-Moyall cumulant expansion for the probability distribution of
parallel transporters in quantum gauge fields: A general equation for the probability distribution of parallel transporters
on the gauge group manifold is derived using the cumulant expansion theorem.
This equation is shown to have a general form known as the Kramers-Moyall
cumulant expansion in the theory of random walks, the coefficients of the
expansion being directly related to nonperturbative cumulants of the shifted
curvature tensor. In the limit of a gaussian-dominated QCD vacuum the obtained
equation reduces to the well-known heat kernel equation on the group manifold.
|
6D SCFTs and Phases of 5D Theories: Starting from 6D superconformal field theories (SCFTs) realized via F-theory,
we show how reduction on a circle leads to a uniform perspective on the phase
structure of the resulting 5D theories, and their possible conformal fixed
points. Using the correspondence between F-theory reduced on a circle and
M-theory on the corresponding elliptically fibered Calabi--Yau threefold, we
show that each 6D SCFT with minimal supersymmetry directly reduces to a
collection of between one and four 5D SCFTs. Additionally, we find that in most
cases, reduction of the tensor branch of a 6D SCFT yields a 5D generalization
of a quiver gauge theory. These two reductions of the theory often correspond
to different phases in the 5D theory which are in general connected by a
sequence of flop transitions in the extended Kahler cone of the Calabi--Yau
threefold. We also elaborate on the structure of the resulting conformal fixed
points, and emergent flavor symmetries, as realized by M-theory on a canonical
singularity.
|
Mutual Interactions of Phonons, Rotons, and Gravity: We introduce an effective point-particle action for generic particles living
in a zero-temperature superfluid. This action describes the motion of the
particles in the medium at equilibrium as well as their couplings to sound
waves and generic fluid flows. While we place the emphasis on elementary
excitations such as phonons and rotons, our formalism applies also to
macroscopic objects such as vortex rings and rigid bodies interacting with
long-wavelength fluid modes. Within our approach, we reproduce phonon decay and
phonon-phonon scattering as predicted using a purely field-theoretic
description of phonons. We also correct classic results by Landau and
Khalatnikov on roton-phonon scattering. Finally, we discuss how phonons and
rotons couple to gravity, and show that the former tend to float while the
latter tend to sink but with rather peculiar trajectories. Our formalism can be
easily extended to include (general) relativistic effects and couplings to
additional matter fields. As such, it can be relevant in contexts as diverse as
neutron star physics and light dark matter detection.
|
Strongly Coupled String-inspired Infinite Derivative Non-local
Yang-Mills: Diluted Mass Gap: We investigate the non-perturbative regimes in the class of non-Abelian
theories that have been proposed as an ultraviolet completion 4-D Quantum Field
Theory (QFT) generalizing the kinetic energy operators to an infinite series of
higher-order derivatives inspired by string field theory. We prove that, at the
non-perturbative level, the physical spectrum of the theory is actually
corrected by the 'infinite number of derivatives' present in the action. We
derive a set of Dyson-Schwinger equations in differential form, for correlation
functions till two-points, the solution for which are known in the local
theory. We obtain that just like in the local theory, the non-local counterpart
displays a mass gap, depending also on the mass scale of non-locality, and show
that it is damped in the deep UV reaching asymptotically the conformal limit.
We point out some possible implications of our result in particle physics and
cosmology and discuss aspects of non-local QCD-like scenarios. We end with some
comments on the infinite-derivative non-local gravity which is quantum gravity
approach to ghost-free, re-normalizable theories of gravity valid upto infinte
ebergy scales in the UV.
|
Some Relations for Quark Confinement and Chiral Symmetry Breaking in QCD: We analytically study the relation between quark confinement and spontaneous
chiral-symmetry breaking in QCD. In terms of the Dirac eigenmodes, we derive
some formulae for the Polyakov loop, its fluctuations, and the string tension
from the Wilson loop. We also investigate the Polyakov loop in terms of the
eigenmodes of the Wilson, the clover and the domain wall fermion kernels,
respectively. For the confinement quantities, the low-lying Dirac/fermion
eigenmodes are found to give negligible contribution, while they are essential
for chiral symmetry breaking. These relations indicate no direct one-to-one
correspondence between confinement and chiral symmetry breaking in QCD, which
seems to be natural because confinement is realized independently of the quark
mass.
|
The large N limit of M2-branes on Lens spaces: We study the matrix model for N M2-branes wrapping a Lens space L(p,1) =
S^3/Z_p. This arises from localization of the partition function of the ABJM
theory, and has some novel features compared with the case of a three-sphere,
including a sum over flat connections and a potential that depends
non-trivially on p. We study the matrix model both numerically and analytically
in the large N limit, finding that a certain family of p flat connections give
an equal dominant contribution. At large N we find the same eigenvalue
distribution for all p, and show that the free energy is simply 1/p times the
free energy on a three-sphere, in agreement with gravity dual expectations.
|
T-Duality Transformation and Universal Structure of Non-Critical String
Field Theory: We discuss a T-duality transformation for the c=1/2 matrix model for the
purpose of studying duality transformations in a possible toy example of
nonperturbative frameworks of string theory. Our approach is to first
investigate the scaling limit of the Schwinger-Dyson equations and the
stochastic Hamiltonian in terms of the dual variables and then compare the
results with those using the original spin variables. It is shown that the
c=1/2 model in the scaling limit is T-duality symmetric in the sphere
approximation. The duality symmetry is however violated when the higher-genus
effects are taken into account, owing to the existence of global Z_2 vector
fields corresponding to nontrivial homology cycles. Some universal properties
of the stochastic Hamiltonians which play an important role in discussing the
scaling limit and have been discussed in a previous work by the last two
authors are refined in both the original and dual formulations. We also report
a number of new explicit results for various amplitudes containing macroscopic
loop operators.
|
Holographic Schwinger Effect and the Geometry of Entanglement: In this note we point out that the recently proposed bulk dual of an
entangled pair of a quark and an anti-quark corresponds to the Lorentzian
continuation of the tunneling instanton describing Schwinger pair creation in
the dual field theory. This observation supports and further explains the claim
by Jensen & Karch that the bulk dual of an EPR pair is a string with a wormhole
on its world sheet. We suggest that this constitutes an AdS/CFT realization of
the creation of a Wheeler wormhole.
|
Self-dual Perturbiner in Yang-Mills theory: The perturbiner approach to the multi-gluonic amplitudes in Yang-Mills theory
is reviewed.
|
Classical Double Copy of Worldline Quantum Field Theory: The recently developed worldline quantum field theory (WQFT) formalism for
the classical gravitational scattering of massive bodies is extended to
massive, charged point particles coupling to bi-adjoint scalar field theory,
Yang-Mills theory, and dilaton-gravity. We establish a classical double copy
relation in these WQFTs for classical observables (deflection, radiation). The
bi-adjoint scalar field theory fixes the locality structure of the double copy
from Yang-Mills to dilaton-gravity. Using this the eikonal scattering phase (or
free energy of the WQFT) is computed to next-to-leading order (NLO) in coupling
constants using the double copy as well as directly finding full agreement. We
clarify the relation of our approach to previous studies in the effective field
theory formalism. Finally, the equivalence of the WQFT double copy to the
double copy relation of the classical limit of quantum scattering amplitudes is
shown explicitly up to NLO.
|
Anomaly Cancellation in Noncritical String Theory: We construct new two dimensional unoriented superstring theories in two
dimensions with a chiral closed string spectrum and show that anomalies cancel
upon supplying the appropriate chiral open string degrees of freedom imposed by
tadpole cancellation.
|
Thermalization and confinement in strongly coupled gauge theories: Quantum field theories of strongly interacting matter sometimes have a useful
holographic description in terms of the variables of a gravitational theory in
higher dimensions. This duality maps time dependent physics in the gauge theory
to time dependent solutions of the Einstein equations in the gravity theory. In
order to better understand the process by which "real world" theories such as
QCD behave out of thermodynamic equilibrium, we study time dependent
perturbations to states in a model of a confining, strongly coupled gauge
theory via holography. Operationally, this involves solving a set of non-linear
Einstein equations supplemented with specific time dependent boundary
conditions. The resulting solutions allow one to comment on the timescale by
which the perturbed states thermalize, as well as to quantify the properties of
the final state as a function of the perturbation parameters. We comment on the
influence of the dual gauge theory's confinement scale on these results, as
well as the appearance of a previously anticipated universal scaling regime in
the "abrupt quench" limit.
|
Topological Lattice Models in Four Dimensions: We define a lattice statistical model on a triangulated manifold in four
dimensions associated to a group $G$. When $G=SU(2)$, the statistical weight is
constructed from the $15j$-symbol as well as the $6j$-symbol for recombination
of angular momenta, and the model may be regarded as the four-dimensional
version of the Ponzano-Regge model. We show that the partition function of the
model is invariant under the Alexander moves of the simplicial complex, thus it
depends only on the piecewise linear topology of the manifold. For an
orientable manifold, the model is related to the so-called $BF$ model. The
$q$-analogue of the model is also constructed, and it is argued that its
partition function is invariant under the Alexander moves. It is discussed how
to realize the 't Hooft operator in these models associated to a closed surface
in four dimensions as well as the Wilson operator associated to a closed loop.
Correlation functions of these operators in the $q$-deformed version of the
model would define a new type of invariants of knots and links in four
dimensions.
|
Landau-Khalatnikov-Fradkin transformation and the mystery of even
$ζ$-values in Euclidean massless correlators: The Landau-Khalatnikov-Fradkin (LKF) transformation is a powerful and elegant
transformation allowing to study the gauge dependence of the propagator of
charged particles interacting with gauge fields. With the help of this
transformation, we derive a non-perturbative identity between massless
propagators in two different gauges. From this identity, we find that the
corresponding perturbative series can be exactly expressed in terms of a hatted
transcendental basis that eliminates all even Euler $\zeta$-functions. This
explains the mystery of even $\zeta$-values observed in multi-loop calculations
of Euclidean massless correlators for almost three decades now. Our
construction further allows us to derive an exact formula relating hatted and
standard $\zeta$-functions to all orders of perturbation theory.
|
Tachyon Condensation and Black Hole Entropy: String propagation on a cone with deficit angle $2\pi(1-{1\over N})$ is
considered for the purpose of computing the entropy of a large mass black hole.
The entropy computed using the recent results on condensation of twisted-sector
tachyons in this theory is found to be in precise agreement with the
Bekenstein-Hawking entropy.
|
Space-time dimensionality from brane collisions: Collisions and subsequent decays of higher dimensional branes leave behind
three-dimensional branes and anti-branes, one of which could play the role of
our universe. This process also leads to the production of one-dimensional
branes and anti-branes, however their number is expected to be suppressed.
Brane collisions may also lead to the formation of bound states of branes.
Their existence does not alter this result, it just allows for the existence of
one-dimensional branes captured within the three-dimensional ones.
|
Problems With Complex Actions: We consider Euclidean functional integrals involving actions which are not
exclusively real. This situation arises, for example, when there are $t$-odd
terms in the the Minkowski action. Writing the action in terms of only real
fields (which is always possible), such terms appear as explicitly imaginary
terms in the Euclidean action. The usual quanization procedure which involves
finding the critical points of the action and then quantizing the spectrum of
fluctuations about these critical points fails. In the case of complex actions,
there do not exist, in general, any critical points of the action on the space
of real fields, the critical points are in general complex. The proper
definition of the function integral then requires the analytic continuation of
the functional integration into the space of complex fields so as to pass
through the complex critical points according to the method of steepest
descent. We show a simple example where this procedure can be carried out
explicitly. The procedure of finding the critical points of the real part of
the action and quantizing the corresponding fluctuations, treating the
(exponential of the) complex part of the action as a bounded integrable
function is shown to fail in our explicit example, at least perturbatively.
|
General considerations of the cosmological constant and the
stabilization of moduli in the brane-world picture: We argue that the brane-world picture with matter-fields confined to 4-d
domain walls and with gravitational interactions across the bulk disallows
adding an arbitrary constant to the low-energy, 4-d effective theory -- which
finesses the usual cosmological constant problem. The analysis also points to
difficulties in stabilizing moduli fields; as an alternative, we suggest
scenarios in which the moduli motion is heavily damped by various cosmological
mechanisms and varying ultra-slowly with time.
|
Real-time finite-temperature correlators from AdS/CFT: In this paper we use AdS/CFT ideas in conjunction with insights from finite
temperature real-time field theory formalism to compute 3-point correlators of
${\cal N}{=}4$ super Yang-Mills operators, in real time and at finite
temperature. To this end, we propose that the gravity field action is
integrated only over the right and left quadrants of the Penrose diagram of the
Anti de Sitter-Schwarzschild background, with a relative sign between the two
terms. For concreteness we consider the case of a scalar field in the black
hole background. Using the scalar field Schwinger-Keldysh bulk-to-boundary
propagators, we give the general expression of a 3-point real-time Green's
correlator. We then note that this particular prescription amounts to adapting
the finite-temperature analog of Veltman's circling rules to tree-level Witten
diagrams, and comment on the retarded and Feynman scalar bulk-to-boundary
propagators. We subject our prescription to several checks: KMS identities, the
largest time equation and the zero-temperature limit. When specializing to a
particular retarded (causal) 3-point function, we find a very simple answer:
the momentum-space correlator is given by three causal (two retarded and one
advanced) bulk-to-boundary propagators, meeting at a vertex point which is
integrated from spatial infinity to the horizon only. This result is expected
based on analyticity, since the retarded n-point functions are obtained by
analytic continuation from the imaginary time Green's function, and based on
causality considerations.
|
$q$-nonabelianization for line defects: We consider the $q$-nonabelianization map, which maps links $L$ in a
3-manifold $M$ to links $\widetilde{L}$ in a branched $N$-fold cover
$\widetilde{M}$. In quantum field theory terms, $q$-nonabelianization is the
UV-IR map relating two different sorts of defect: in the UV we have the
six-dimensional $(2,0)$ superconformal field theory of type $\mathfrak{gl}(N)$
on $M \times \mathbb{R}^{2,1}$, and we consider surface defects placed on $L
\times \{x^4 = x^5 = 0\}$; in the IR we have the $(2,0)$ theory of type
$\mathfrak{gl}(1)$ on $\widetilde{M} \times \mathbb{R}^{2,1}$, and put the
defects on $\widetilde{L} \times \{x^4 = x^5 = 0\}$. In the case $M =
\mathbb{R}^3$, $q$-nonabelianization computes the Jones polynomial of a link,
or its analogue associated to the group $U(N)$. In the case $M = C \times
\mathbb{R}$, when the projection of $L$ to $C$ is a simple non-contractible
loop, $q$-nonabelianization computes the protected spin character for framed
BPS states in 4d $\mathcal{N}=2$ theories of class $S$. In the case $N=2$ and
$M = C \times \mathbb{R}$, we give a concrete construction of the
$q$-nonabelianization map. The construction uses the data of the WKB foliations
associated to a holomorphic covering $\widetilde{C} \to C$.
|
On the Renormalization of Hamiltonians: We introduce a novel method for the renormalization of the Hamiltonian
operator in Quantum Field Theory in the spirit of the Wilson renormalization
group. By a series of unitary transformations that successively decouples the
high-frequency degrees of freedom and partially diagonalizes the high-energy
part, we obtain the effective Hamiltonian for the low energy degrees of
freedom. We successfully apply this technique to compute the 2-loop
renormalized Hamiltonian in scalar $\lambda \phi^4$ theory.
|
Quantum Horizons of the Standard Model Landscape: The long-distance effective field theory of our Universe--the Standard Model
coupled to gravity--has a unique 4D vacuum, but we show that it also has a
landscape of lower-dimensional vacua, with the potential for moduli arising
from vacuum and Casimir energies. For minimal Majorana neutrino masses, we find
a near-continuous infinity of AdS3xS1 vacua, with circumference ~20 microns and
AdS3 length 4x10^25 m. By AdS/CFT, there is a CFT2 of central charge c~10^90
which contains the Standard Model (and beyond) coupled to quantum gravity in
this vacuum. Physics in these vacua is the same as in ours for energies between
10^-1 eV and 10^48 GeV, so this CFT2 also describes all the physics of our
vacuum in this energy range. We show that it is possible to realize
quantum-stabilized AdS vacua as near-horizon regions of new kinds of quantum
extremal black objects in the higher-dimensional space--near critical black
strings in 4D, near-critical black holes in 3D. The violation of the
null-energy condition by the Casimir energy is crucial for these horizons to
exist, as has already been realized for analogous non-extremal 3D black holes
by Emparan, Fabbri and Kaloper. The new extremal 3D black holes are
particularly interesting--they are (meta)stable with an entropy independent of
hbar and G_N, so a microscopic counting of the entropy may be possible in the
G_N->0 limit. Our results suggest that it should be possible to realize the
larger landscape of AdS vacua in string theory as near-horizon geometries of
new extremal black brane solutions.
|
New vacua for Yang-Mills theory on a 3-torus: In this thesis we discuss recent new insights in the structure of the moduli
space of flat connections of Yang-Mills theory on a 3-torus. Chapter 2
discusses the computation of Witten's index for 4-dimensional gauge theories,
and the paradox that arises in comparing various computations. This was
resolved by the discovery that for orthogonal and exceptional gauge groups,
periodic flat connections exist that are contained in seperate, disconnected
components of the moduli space. Chapter 3 and 4 discuss some aspects of the
construction of holonomies parametrising vacua on such disconnected components.
Chapter 5 demonstrates a construction of vacua and holonomies for gauge
theories with classical groups, with non-periodic (twisted) boundary
conditions, using an orientifold description. The new solutions with
exceptional and orthogonal gauge groups also occur in string theory. Chapter 6,
containing previously unpublished material, shows that they can be realised
within heterotic string theories as asymmetric orbifolds. The presence of
string winding states modifies the analysis for the gauge theory in a crucial
way, eliminating many possibilities. The remaining ones are related by string
dualities to known and new theories.
|
No entropy enigmas for N=4 dyons: We explain why multi-centered black hole configurations where at least one of
the centers is a large black hole do not contribute to the indexed degeneracies
in theories with N=4 supersymmetry. This is a consequence of the fact that such
configurations, although supersymmetric, belong to long supermultiplets. As a
result, there is no entropy enigma in N=4 theories, unlike in N=2 theories.
|
Towards Field Theory in Spaces with Multivolume Junctions: We consider a spacetime formed by several pieces having common timelike
boundary which plays the role of a junction between them. We establish junction
conditions for fields of various spin and derive the resulting laws of wave
propagation through the junction, which turn out to be quite similar for fields
of all spins. As an application, we consider the case of multivolume junctions
in four-dimensional spacetime that may arise in the context of the theory of
quantum creation of a closed universe on the background of a big mother
universe. The theory developed can also be applied to braneworld models and to
the superstring theory.
|
A Point's Point of View of Stringy Geometry: The notion of a "point" is essential to describe the topology of spacetime.
Despite this, a point probably does not play a particularly distinguished role
in any intrinsic formulation of string theory. We discuss one way to try to
determine the notion of a point from a worldsheet point of view. The derived
category description of D-branes is the key tool. The case of a flop is
analyzed and Pi-stability in this context is tied in to some ideas of
Bridgeland. Monodromy associated to the flop is also computed via Pi-stability
and shown to be consistent with previous conjectures.
|
IR Inflation from Multiple Branes: In this paper we examine the IR inflation scenario using the DBI action,
where we have $N$ multiple branes located near the tip of a warped geometry. At
large $N$ the solutions are similar in form to the more traditional single
brane models, however we find that it is difficult to simultaneously satisfy
the WMAP bounds on the scalar amplitude and the scalar spectral index. We go on
to examine two new solutions where N=2 and N=3 respectively, which both have
highly non-linear actions. The sound speed in both cases is dramatically
different from previous works, and for the N=3 case it can actually be zero. We
show that inflation is possible in both frameworks, and find that the scalar
spectral index is bounded from above by unity. The level of non-gaussian
fluctuations are smaller in the N=2 case compared to the single brane models,
whilst those in the N=3 case are much larger.
|
Time-loops in Dirac materials, torsion and unconventional Supersymmetry: We propose a scenario where the effects of dislocations, in bidimensional
Dirac materials at low energies, can be described within a Dirac field theory
by a vertex proportional to the totally antisymmetric component of the torsion
generated by such dislocations. The well-known geometrical obstruction to have
a nonzero torsion term of that kind in this two-dimensional settings is
overcome through exotic time-loops, obtained from ingeniously manipulated
particle-hole dynamics. If such torsion/dislocation is indeed present, a net
flow of particles-antiparticles (holes) can be inferred and possibly measured.
Finally, we comment on how these discoveries pave the way to a laboratory
realization on Dirac materials of Unconventional Supersymmetry, as a top-down
description of the $\pi$-electrons in backgrounds with a nonzero torsion.
|
Inflation as a Probe of Short Distance Physics: We show that a string-inspired Planck scale modification of general
relativity can have observable cosmological effects. Specifically, we present a
complete analysis of the inflationary perturbation spectrum produced by a
phenomenological Lagrangian that has a standard form on large scales but
incorporates a string-inspired short distance cutoff, and find a deviation from
the standard result. We use the de Sitter calculation as the basis of a
qualitative analysis of other inflationary backgrounds, arguing that in these
cases the cutoff could have a more pronounced effect, changing the shape of the
spectrum. Moreover, the computational approach developed here can be used to
provide unambiguous calculations of the perturbation spectrum in other
heuristic models that modify trans-Planckian physics and thereby determine
their impact on the inflationary perturbation spectrum. Finally, we argue that
this model may provide an exception to constraints, recently proposed by Tanaka
and Starobinsky, on the ability of Planck-scale physics to modify the
cosmological spectrum.
|
Black hole bulk-cone singularities: Lorentzian correlators of local operators exhibit surprising singularities in
theories with gravity duals. These are associated with null geodesics in an
emergent bulk geometry. We analyze singularities of the thermal response
function dual to propagation of waves on the AdS Schwarzschild black hole
background. We derive the analytic form of the leading singularity dual to a
bulk geodesic that winds around the black hole. Remarkably, it exhibits a
boundary group velocity larger than the speed of light, whose dual is the
angular velocity of null geodesics at the photon sphere. The strength of this
singularity is controlled by the classical Lyapunov exponent associated with
the instability of nearly bound photon orbits. In this sense, the bulk-cone
singularity can be identified as the universal feature that encodes the
ubiquitous black hole photon sphere in a dual holographic CFT. To perform the
computation analytically, we express the two-point correlator as an infinite
sum over Regge poles, and then evaluate this sum using WKB methods. We also
compute the smeared correlator numerically, which in particular allows us to
check and support our analytic predictions. We comment on the resolution of
black hole bulk-cone singularities by stringy and gravitational effects into
black hole bulk-cone "bumps". We conclude that these bumps are robust, and
could serve as a target for simulations of black hole-like geometries in
table-top experiments.
|
Dynamics of Domain Wall Networks: Networks or webs of domain walls are admitted in Abelian or non-Abelian gauge
theory coupled to fundamental Higgs fields with complex masses. We examine the
dynamics of the domain wall loops by using the moduli approximation and find a
phase rotation induces a repulsive force which can be understood as a Noether
charge of Q-solitons. Non-Abelian gauge theory allows different types of loops
which can be deformed to each other by changing a modulus. This admits the
moduli geometry like a sandglass made by gluing the tips of the two
cigar-(cone-)like metrics of a single triangle loop. We conclude that the sizes
of all loops tend to grow for a late time in general models with complex Higgs
masses, while the sizes are stabilized at some values once triplet masses are
introduced for the Higgs fields. We also show that the stationary motion on the
moduli space of the domain wall webs represents 1/4 BPS Q-webs of walls.
|
Reconstructing the Vacuum Functional of Yang-Mills from its Large
Distance Behaviour: For fields that vary slowly on the scale of the lightest mass the logarithm
of the vacuum functional can be expanded as a sum of local functionals. For
Yang-Mills theory the leading term in the expansion dominates large distance
effects and leads to an area law for the Wilson loop. However, this expansion
cannot be expected to converge for fields that vary more rapidly. By studying
the analyticity of the vacuum functional under scale transformations we show
how to re-sum this series so as to reconstruct the vacuum functional for
arbitrary fields.
|
Structural phase transition and its critical dynamics from holography: We introduce a gravitational lattice theory defined in an AdS$_3$ black hole
background that provides a holographic dual description of the linear-to-zigzag
structural phase transition, characterized by the spontaneous breaking of
parity symmetry observed in, e.g., confined Coulomb crystals. The transition
from the high-symmetry linear phase to the broken-symmetry doubly-degenerate
zigzag phase can be driven by quenching the coupling between adjacent sites
through the critical point. An analysis of the equilibrium correlation length
and relaxation time reveals mean-field critical exponents. We explore the
nonequilibrium phase transition dynamics leading to kink formation. The kink
density obeys universal scaling laws in the limit of slow quenches, described
by the Kibble-Zurek mechanism (KZM), and at fast quenches, characterized by a
universal breakdown of the KZM.
|
Quantum Field Theory in a Multi-Metric Background: By means of simple models in a flat spacetime manifold we examine some of the
issues that arise when quantizing interacting quantum fields in multi-metric
backgrounds. In particular we investigate the maintenance of a causal structure
in the models. In this context we introduce and explain the relevance of an
interpolating metric that is a superposition of the individual metrics in the
models. We study the renormalisation of a model with quartic interactions and
elucidate the structure of the renormalisation group and its implications for
Lorentz symmetry breakdown.
|
On 3d extensions of AGT relation: An extension of the AGT relation from two to three dimensions begins from
connecting the theory on domain wall between some two S-dual SYM models with
the 3d Chern-Simons theory. The simplest kind of such a relation would
presumably connect traces of the modular kernels in 2d conformal theory with
knot invariants. Indeed, the both quantities are very similar, especially if
represented as integrals of the products of quantum dilogarithm functions.
However, there are also various differences, especially in the "conservation
laws" for integration variables, which hold for the monodromy traces, but not
for the knot invariants. We also discuss another possibility: interpretation of
knot invariants as solutions to the Baxter equations for the relativistic Toda
system. This implies another AGT like relation: between 3d Chern-Simons theory
and the Nekrasov-Shatashvili limit of the 5d SYM.
|
Renormalization and asymptotic safety in truncated quantum Einstein
gravity: A perturbative quantum theory of the 2-Killing vector reduction of general
relativity is constructed. Although non-renormalizable in the standard sense,
we show that to all orders of the loop expansion strict cut-off independence
can be achieved in a space of Lagrangians differing only by a field dependent
conformal factor. In particular the Noether currents and the quantum
constraints can be defined as finite composite operators. The form of the field
dependence in the conformal factor changes with the renormalization scale and a
closed formula is obtained for the beta functional governing its flow. The flow
possesses a unique fixed point at which the trace anomaly is shown to vanish.
The approach to the fixed point adheres to Weinberg's ``asymptotic safety''
scenario, both in the gravitational wave/cosmological sector and in the
stationary sector.
|
Observables of Non-Commutative Gauge Theories: We construct gauge invariant operators in non-commutative gauge theories
which in the IR reduce to the usual operators of ordinary field theories (e.g.
F^2). We show that in the deep UV the two-point functions of these operators
admit a universal exponential behavior which fits neatly with the dual
supergravity results. We also consider the ratio between n-point functions and
two-point functions to find exponential suppression in the UV which we compare
to the high energy fixed angle scattering of string theory.
|
Canonical Quantization, Space-Time Noncommutativity and Deformed
Symmetries in Field Theory: Within the spirit of Dirac's canonical quantization, noncommutative spacetime
field theories are introduced by making use of the reparametrization invariance
of the action and of an arbitrary non-canonical symplectic structure. This
construction implies that the constraints need to be deformed, resulting in an
automatic Drinfeld twisting of the generators of the symmetries associated with
the reparametrized theory. We illustrate our procedure for the case of a scalar
field in 1+1- spacetime dimensions, but it can be readily generalized to
arbitrary dimensions and arbitrary types of fields.
|
A boundary stress tensor for higher-derivative gravity in AdS and
Lifshitz backgrounds: We investigate the Brown-York stress tensor for curvature-squared theories.
This requires a generalized Gibbons-Hawking term in order to establish a
well-posed variational principle, which is achieved in a universal way by
reducing the number of derivatives through the introduction of an auxiliary
tensor field. We examine the boundary stress tensor thus defined for the
special case of `massive gravity' in three dimensions, which augments the
Einstein-Hilbert term by a particular curvature-squared term. It is shown that
one obtains finite results for physical parameters on AdS upon adding a
`boundary cosmological constant' as a counterterm, which vanishes at the
so-called chiral point. We derive known and new results, like the value of the
central charges or the mass of black hole solutions, thereby confirming our
prescription for the computation of the stress tensor. Finally, we inspect
recently constructed Lifshitz vacua and a new black hole solution that is
asymptotically Lifshitz, and we propose a novel and covariant counterterm for
this case.
|
Logarithmic Conformal Field Theory - or - How to Compute a Torus
Amplitude on the Sphere: We review some aspects of logarithmic conformal field theories which might
shed some light on the geometrical meaning of logarithmic operators. We
consider an approach, put forward by V. Knizhnik, where computation of
correlation functions on higher genus Riemann surfaces can be replaced by
computations on the sphere under certain circumstances. We show that this
proposal naturally leads to logarithmic conformal field theories, when the
additional vertex operator insertions, which simulate the branch points of a
ramified covering of the sphere, are viewed as dynamical objects in the theory.
We study the Seiberg-Witten solution of supersymmetric low energy effective
field theory as an example where physically interesting quantities, the periods
of a meromorphic one-form, can effectively be computed within this conformal
field theory setting. We comment on the relation between correlation functions
computed on the plane, but with insertions of twist fields, and torus vacuum
amplitudes.
|
Supersymmetric Brane-Worlds: We present warped metrics which solve Einstein equations with arbitrary
cosmological constants in both in upper and lower dimensions. When the
lower-dimensional metric is the maximally symmetric one compatible with the
chosen value of the cosmological constant, the upper-dimensional metric is also
the maximally symmetric one and there is maximal unbroken supersymmetry as
well. We then introduce brane sources and find solutions with analogous
properties, except for supersymmetry, which is generically broken in the
orbifolding procedure (one half is preserved in two special cases), and analyze
metric perturbations in these backgrounds In analogy with the D8-brane we
propose an effective $(\hat{d}-2)$-brane action which acts as a source for the
RS solution. The action consists of a Nambu-Goto piece and a Wess-Zumino term
containing a $(\hat{d}-1)$-form field. It has the standard form of the action
for a BPS extended object, in correspondence with the supersymmetry preserved
by the solution.
|
Derivation of the two Schwarzians effective action for the
Sachdev-Ye-Kitaev spectral form factor: The Sachdev-Ye-Kitaev model spectral form factor exhibits absence of
information loss in the form of a ramp and a plateau, that are typical of
random matrix theory. In a large $N$ collective fields description, the ramp
was reproduced by Saad, Shenker and Stanford \cite{Saad:2018bqo}, by replica
symmetry breaking saddles for a connected component of the analytically
continued to real times thermal partition function two point function. We
derive a two sides Schwarzians effective action for fluctuations around the
ramp critical saddles, by adapting to the two replica system a method by Kitaev
and Suh \cite{Kitaev:2017awl} for studying non linear responses to the
conformal breaking kinetic operator in regular SYK. Our result confirms
\cite{Saad:2018bqo}, where the form of the action was obtained by assuming
locality.
|
Hopf instantons, Chern-Simons vortices, and Heisenberg ferromagnets: The dimensional reduction of the three-dimensional fermion-Chern-Simons model
(related to Hopf maps) of Adam et el. is shown to be equivalent to (i) either
the static, fixed--chirality sector of our non-relativistic spinor-Chern-Simons
model in 2+1 dimensions, (ii) or a particular Heisenberg ferromagnet in the
plane.
|
Special functions as structure constants for new infinite-dimensional
algebras: Novel infinite-dimensional algebras of the Virasoro/Kac-Moody/
Floratos-Iliopoulos type are introduced, which involve special functions in
their structure constants
|
Wrapping interactions and a new source of corrections to the
spin-chain/string duality: Assuming that the world-sheet sigma-model in the AdS/CFT correspondence is an
integrable {\em quantum} field theory, we deduce that there might be new
corrections to the spin-chain/string Bethe ansatz paradigm. These come from
virtual particles propagating around the circumference of the cylinder and
render Bethe ansatz quantization conditions only approximate. We determine the
nature of these corrections both at weak and at strong coupling in the near BMN
limit, and find that the first corrections behave qualitatively as wrapping
interactions at weak coupling.
|
Positive Signs in Massive Gravity: We derive new constraints on massive gravity from unitarity and analyticity
of scattering amplitudes. Our results apply to a general effective theory
defined by Einstein gravity plus the leading soft diffeomorphism-breaking
corrections. We calculate scattering amplitudes for all combinations of tensor,
vector, and scalar polarizations. The high-energy behavior of these amplitudes
prescribes a specific choice of couplings that ameliorates the ultraviolet
cutoff, in agreement with existing literature. We then derive consistency
conditions from analytic dispersion relations, which dictate positivity of
certain combinations of parameters appearing in the forward scattering
amplitudes. These constraints exclude all but a small island in the parameter
space of ghost-free massive gravity. While the theory of the "Galileon" scalar
mode alone is known to be inconsistent with positivity constraints, this is
remedied in the full massive gravity theory.
|
D-branes and matrix factorisations in supersymmetric coset models: Matrix factorisations describe B-type boundary conditions in N=2
supersymmetric Landau-Ginzburg models. At the infrared fixed point, they
correspond to superconformal boundary states. We investigate the relation
between boundary states and matrix factorisations in the Grassmannian
Kazama-Suzuki coset models. For the first non-minimal series, i.e. for the
models of type SU(3)_k/U(2), we identify matrix factorisations for a subset of
the maximally symmetric boundary states. This set provides a basis for the RR
charge lattice, and can be used to generate (presumably all) other boundary
states by tachyon condensation.
|
Heterotic and type I strings from twisted supermembranes: As shown by Ho\v{r}ava and Witten, there are gravitational anomalies at the
boundaries of $M^{10}\times S^1/Z_2$ of 11 dimensional supergravity. They
showed that only 10 dimensional vector multiplets belonging to $E_8$ gauge
group can be consistently coupled to this theory. Thus, the dimensional
reduction of this theory should be the low energy limit of the $E_8\times E_8$
heterotic string. Here we assume that M-theory is a theory of supermembranes
which includes twisted supermembranes. We show that for a target space
$M^{10}\times S^1/Z_2$, in the limit in which $S^1/Z_2$ is small, the effective
action is the $E_8\times E_8$ heterotic string. We also consider supermembranes
on $M^{9}\times S^1\times S^1/Z_2$ and find the dualities expected from 11
dimensional supergravity on this manifold. We show that the requirements for
worldsheet anomaly cancellations at the boundaries of the worldvolume action
are the same requirements imposed on the Ho\v{r}ava-Witten action.
|
Deformations of spacetime and internal symmetries: Algebraic deformations provide a systematic approach to generalizing the
symmetries of a physical theory through the introduction of new fundamental
constants. The applications of deformations of Lie algebras and Hopf algebras
to both spacetime and internal symmetries are discussed. As a specific example
we demonstrate how deforming the classical flavor group $SU(3)$ to the quantum
group $SU_q(3)\equiv U_q(su(3))$ (a Hopf algebra) and taking into account
electromagnetic mass splitting within isospin multiplets leads to new and
exceptionally accurate baryon mass sum rules that agree perfectly with
experimental data.
|
Bosonization of Three Dimensional Non-Abelian Fermion Field Theories: We discuss bosonization in three dimensions of an $SU(N)$ massive Thirring
model in the low-energy regime. We find that the bosonized theory is related
(but not equal) to $SU(N)$ Yang-Mills-Chern-Simons gauge theory. For free
massive fermions bosonization leads, at low energies, to the pure $SU(N)$
(level $k=1$) Chern-Simons theory.
|
Extended No-Scale Structure and $α^{'2}$ Corrections to the Type
IIB Action: We analyse a new ${\cal N}=1$ string tree level correction at ${\cal
O}(\alpha'^2)$ to the K\"ahler potential of the volume moduli of type IIB
Calabi-Yau flux compactification found recently by Grimm, Savelli and
Weissenbacher~\cite{Grimm:2013gma} and its impact on the moduli potential. We
find that it imposes a strong lower bound the Calabi-Yau volume in the Large
Volume Scenario of moduli stabilisation. For KKLT-like scenarios we find that
consistency of the action imposes an upper bound on the flux superpotential
$|W_0|\lesssim 10^{-3}$, while parametrically controlled survival of the KKLT
minimum needs extreme tuning of $W_0$ close to zero. We also analyse the
K\"ahler uplifting mechanism showing that it can operate on Calabi-Yau
manifolds where the new correction is present and dominated by the 4-cycle
controlling the overall volume if the volume is stabilised at values
$\mathcal{V} \gtrsim 10^3$. We discuss the phenomenological implication of
these bounds on $\mathcal{V}$ in the various scenarios.
|
One-loop vacuum amplitude for D-branes in constant electromagnetic field: Following Polchinski's approach we calculate the one-loop vacuum amplitude
for two parallel D-branes connected by open bosonic (neutral or charged)string
in a constant uniform electromagnetic (EM) field. For neutral string, external
EM field contribution appears as multiplier (Born-Infeld type action) of vacuum
amplitude without external EM field. Hence,it gives the alternative way to see
the inducing of Born-Infeld type action for description of D-branes. For
charged string the situation is more complicated, it may indicate the necessity
to modify the induced D-branes action in this case.
|
Principal Bundles, Connections and BRST Cohomology: We review the elementary theory of gauge fields and the Becchi-Rouet-Stora-
Tyutin symmetry in the context of differential geometry. We emphasize the
topological nature of this symmetry and discuss a double Chevalley-Eilenberg
complex for it.
|
$W_\infty$ coherent states and path-integral derivation of bosonization
of non-relativistic fermions in one dimension: We complete the proof of bosonization of noninteracting nonrelativistic
fermions in one space dimension by deriving the bosonized action using
$W_\infty$ coherent states in the fermion path-integral. This action was
earlier derived by us using the method of coadjoint orbits. We also discuss the
classical limit of the bosonized theory and indicate the precise nature of the
truncation of the full theory that leads to the collective field theory.
|
Celestial Diamonds: Conformal Multiplets in Celestial CFT: We examine the structure of global conformal multiplets in 2D celestial CFT.
For a 4D bulk theory containing massless particles of spin
$s=\{0,\frac{1}{2},1,\frac{3}{2},2\}$ we classify and construct all
SL(2,$\mathbb{C}$) primary descendants which are organized into 'celestial
diamonds'. This explicit construction is achieved using a wavefunction-based
approach that allows us to map 4D scattering amplitudes to celestial CFT
correlators of operators with SL(2,$\mathbb{C}$) conformal dimension $\Delta$
and spin $J$. Radiative conformal primary wavefunctions have $J=\pm s$ and give
rise to conformally soft theorems for special values of $\Delta \in
\frac{1}{2}\mathbb{Z}$. They are located either at the top of celestial
diamonds, where they descend to trivial null primaries, or at the left and
right corners, where they descend both to and from generalized conformal
primary wavefunctions which have $|J|\leq s$. Celestial diamonds naturally
incorporate degeneracies of opposite helicity particles via the 2D shadow
transform relating radiative primaries and account for the global and
asymptotic symmetries in gauge theory and gravity.
|
Supersymmetry, p-brane duality and hidden space and time dimensions: A global superalgebra with 32 supercharges and all possible central
extensions is studied in order to extract some general properties of duality
and hidden dimensions in a theory that treats $p$-branes democratically. The
maximal number of dimensions is 12, with signature (10,2), containing one space
and one time dimensions that are hidden from the point of view of perturbative
10-dimensional string theory or its compactifications. When the theory is
compactified on $R^{d-1,1}\otimes T^{c+1,1}$ with $d+c+2=12,$ there are
isometry groups that relate to the hidden dimensions as well as to duality.
Their combined classification schemes provide some properties of
non-perturbative states and their couplings.
|
The Schwinger Dyson equations and the algebra of constraints of random
tensor models at all orders: Random tensor models for a generic complex tensor generalize matrix models in
arbitrary dimensions and yield a theory of random geometries. They support a
1/N expansion dominated by graphs of spherical topology. Their Schwinger Dyson
equations, generalizing the loop equations of matrix models, translate into
constraints satisfied by the partition function. The constraints have been
shown, in the large N limit, to close a Lie algebra indexed by colored rooted
D-ary trees yielding a first generalization of the Virasoro algebra in
arbitrary dimensions. In this paper we complete the Schwinger Dyson equations
and the associated algebra at all orders in 1/N. The full algebra of
constraints is indexed by D-colored graphs, and the leading order D-ary tree
algebra is a Lie subalgebra of the full constraints algebra.
|
Anomalies and time reversal invariance in relativistic hydrodynamics:
the second order and higher dimensional formulations: We present two new results on relativistic hydrodynamics with anomalies and
external electromagnetic fields, "Chiral MagnetoHydroDynamics" (CMHD). First,
we study CMHD in four dimensions at second order in the derivative expansion
assuming the conformal/Weyl invariance. We classify all possible independent
conformal second order viscous corrections to the energy-momentum tensor and to
the U(1) current in the presence of external electric and/or magnetic fields,
and identify eighteen terms that originate from the triangle anomaly. We then
propose and motivate the following guiding principle to constrain the CMHD: the
anomaly--induced terms that are even under the time reversal invariance should
not contribute to the local entropy production rate. This allows us to fix
thirteen out of the eighteen transport coefficients that enter the second order
formulation of CMHD. We also relate one of our second order transport
coefficients to the chiral shear waves. Our second subject is hydrodynamics
with (N+1)-gon anomaly in an arbitrary 2N dimensions. The effects from the
(N+1)-gon anomaly appear in hydrodynamics at (N-1)'th order in the derivative
expansion, and we identify precisely N such corrections to the U(1) current.
The time reversal constraint is powerful enough to allow us to find the
analytic expressions for all transport coefficients. We confirm the validity of
our results (and of the proposed guiding principle) by an explicit
fluid/gravity computation within the AdS/CFT correspondence.
|
Propagation speeds of relativistic conformal fluids from a generalized
relaxation time approximation: We compute the propagation speeds for a conformal real relativistic fluid. We
begin from a kinetic equation in the relaxation time approximation, where the
relaxation time is an arbitrary function of the particle energy in the Landau
frame. We propose a parameterization of the one particle distribution function
designed to contain a second order Chapman-Enskog solution as a particular
case. We derive the hydrodynamic equations applying the moments method to this
parameterized one particle distribution function, and solve for the propagation
speeds of linearized scalar, vector and tensor perturbations. For relaxation
times of the form $\tau=\tau_0(-\beta_{\mu}p^{\mu})^{-a}$, with $-\infty< a<2$,
where $\beta_{\mu}=u_{\mu}/T$ is the temperature vector in the Landau frame, we
show that the Anderson-Witting prescription $a=1$ yields the fastest speeds.
|
Complementary Projection Defects and Decompositions: As put forward in [arXiv:1907.12339] topological quantum field theories can
be projected using so-called projection defects. The projected theory and its
correlation functions can be completely realized within the unprojected one. An
interesting example is the case of topological quantum field theories
associated to IR fixed points of renormalization group flows, which by this
method can be realized inside the theories associated to the UV. In this note
we show that projection defects in triangulated defect categories (such as
defects in 2d topologically twisted N=(2,2) theories) always come with
complementary projection defects, and that the unprojected theory decomposes
into the theories associated to the two projection defects. We demonstrate this
in the context of Landau-Ginzburg orbifold theories.
|
Aspects of Ultra-Relativistic Field Theories via Flat-space Holography: Recently it was proposed that asymptotically flat spacetimes have a
holographic dual which is an ultra-relativistic conformal field theory. In this
paper, we obtain the conformal anomaly for such a theory via the flat-space
holography technique. Furthermore, using flat-space holography we obtain a
C-function for this theory which is monotonically decreasing from the UV to the
IR by employing the null energy condition in the bulk.
|
Moduli destabilization via gravitational collapse: We examine the interplay between gravitational collapse and moduli stability
in the context of black hole formation. We perform numerical simulations of the
collapse using the double null formalism and show that the very dense regions
one expects to find in the process of black hole formation are able to
destabilize the volume modulus. We establish that the effects of the
destabilization will be visible to an observer at infinity, opening up a window
to a region in spacetime where standard model's couplings and masses can differ
significantly from their background values.
|
The AdS/CFT partition function, AdS as a lift of a CFT, and holographic
RG flow from conformal deformations: Conformal deformations manifest in the AdS/CFT correspondence as boundary
conditions on the AdS field. Heretofore, double-trace deformations have been
the primary focus in this context. To better understand multitrace
deformations, we revisit the relationship between the generating AdS partition
function for a free bulk theory and the boundary CFT partition function subject
to arbitrary conformal deformations. The procedure leads us to a formalism that
constructs bulk fields from boundary operators. Using this formalism, we
independently replicate the holographic RG flow narrative to go on to interpret
the brane used to regulate the AdS theory as a renormalization scale. The
scale-dependence of the dilatation spectrum of a boundary theory in the
presence of general deformations can be thus understood on the AdS side using
this formalism.
|
On Supersymmetric Lifshitz Field Theories: We consider field theories that exhibit a supersymmetric Lifshitz scaling
with two real supercharges. The theories can be formulated in the language of
stochastic quantization. We construct the free field supersymmetry algebra with
rotation singlet fermions for an even dynamical exponent $z=2k$ in an arbitrary
dimension. We analyze the classical and quantum $z=2$ supersymmetric
interactions in $2+1$ and $3+1$ spacetime dimensions and reveal a supersymmetry
preserving quantum diagrammatic cancellation. Stochastic quantization indicates
that Lifshitz scale invariance is broken in the $(3+1)$-dimensional quantum
theory.
|
Characteristics of Z(2) multi-kink soliton configurations: In this article, we first briefly review the solution of Z(2) kink solitons.
Then we construct some multi-kink soliton configurations which are static and
show their few features which are actually important to characterize their
stability conditions. Not only that this show also the particle characteristics
of these kink configurations in these solitonic configurations. Then we will
talk about dynamical kinks and show the affect of dynamics in the expression of
force exerted by the neighbouring kink and anti-kink on each other in the
multi-kink configurations. We have also defined an algebra through which we can
write down equivalent ways of writing down multi-kink configuration
mathematically.
|
Recent progress in intersection theory for Feynman integrals
decomposition: High precision calculations in perturbative QFT often require evaluation of
big collection of Feynman integrals. Complexity of this task can be greatly
reduced via the usage of linear identities among Feynman integrals. Based on
mathematical theory of intersection numbers, recently a new method for
derivation of such identities and decomposition of Feynman integrals was
introduced and applied to many non-trivial examples. In this note we discuss
the latest developments in algorithms for the evaluation of intersection
numbers, and their application to the reduction of Feynman integrals.
|
The effect of three matters on KSS bound: In this paper we introduce the black brane solutions in AdS space in
4-dimensional (4D) Einstein-Gauss-Bonnet-Yang-Mills theory in the presence of
string cloud and quintessence. Shear viscosity to entropy density ratio is
computed via fluid-gravity duality, as a transport coefficient for this model.
|
Coupled $\mathcal{N}$ = 2 supersymmetric quantum systems: symmetries and
supervariable approach: We consider specific examples of $\mathcal{N}$ = 2 supersymmetric quantum
mechanical models and list out all the novel symmetries. In each case, we show
the existence of two sets of discrete symmetries that correspond to the Hodge
duality operator of differential geometry. Thus, we are able to provide a proof
of the conjecture which endorses the existence of more than one discrete
symmetry transformation as the analogue of Hodge duality operation. Finally, we
extend our analysis to a more general case and derive on-shell nilpotent
symmetries within the framework of supervariable approach.
|
Separability of a modified Dirac equation in a five-dimensional
rotating, charged black hole in string theory: The aim of this paper is to investigate the separability of a spin-1/2 spinor
field in a five-dimensional rotating, charged black hole constructed by Cvetic
and Youm in string theory, in the case when three U(1) charges are set equal.
This black hole solution represents a natural generalization of the famous
four-dimensional Kerr-Newman solution to five dimensions with the inclusion of
a Chern-Simons term to the Maxwell equation. It is shown that the usual Dirac
equation can not be separated by variables in this general spacetime with two
independent angular momenta. However if one supplements an additional
counterterm into the usual Dirac operator, then the modified Dirac equation for
the spin-1/2 spinor particles is separable in this rotating, charged
Einstein-Maxwell-Chern-Simons black hole background geometry. A first-order
symmetry operator that commutes with the modified Dirac operator has exactly
the same form as that previously found in the uncharged Myers-Perry black hole
case. It is expressed in terms of a rank-three totally antisymmetric tensor and
its covariant derivative. This tensor obeys a generalized Killing-Yano equation
and its square is a second-order symmetric Stackel-Killing tensor admitted by
the five-dimensional rotating, charged black hole spacetime.
|
On the Geometric Interpretation of N = 2 Superconformal Theories: We clarify certain important issues relevant for the geometric interpretation
of a large class of N = 2 superconformal theories. By fully exploiting the
phase structure of these theories (discovered in earlier works) we are able to
clearly identify their geometric content. One application is to present a
simple and natural resolution to the question of what constitutes the mirror of
a rigid Calabi-Yau manifold. We also discuss some other models with unusual
phase diagrams that highlight some subtle features regarding the geometric
content of conformal theories.
|
Meanders and the Temperley-Lieb algebra: The statistics of meanders is studied in connection with the Temperley-Lieb
algebra. Each (multi-component) meander corresponds to a pair of reduced
elements of the algebra. The assignment of a weight $q$ per connected component
of meander translates into a bilinear form on the algebra, with a Gram matrix
encoding the fine structure of meander numbers. Here, we calculate the
associated Gram determinant as a function of $q$, and make use of the
orthogonalization process to derive alternative expressions for meander numbers
as sums over correlated random walks.
|
dS$_2$ Supergravity: We construct two-dimensional supergravity theories endowed with a positive
cosmological constant, that admit de Sitter vacua. We consider the cases of
$\mathcal{N}=1$ as well as $\mathcal{N}=2$ supersymmetry, and couple the
supergravity to a superconformal field theory with the same amount of
supersymmetry. Upon fixing a supersymmetric extension of the Weyl gauge, the
theories are captured, at the quantum level, by supersymmetric extensions of
timelike Liouville theory with $\mathcal{N}=1$ and $\mathcal{N}=2$
supersymmetry respectively. The theories exhibit good ultraviolet properties
and are amenable to a variety of techniques such as systematic loop expansions
and, in the $\mathcal{N}=2$ case, supersymmetric localization. Our
constructions offer a novel path toward a precise treatment of the Euclidean
gravitational path integral for de Sitter, and in turn, the Gibbons-Hawking
entropy of the de Sitter horizon. We argue that the supersymmetric localization
method applied to the $\mathcal{N}=2$ theory must receive contributions from
boundary terms in configuration space. We also discuss how these theories
overcome several obstructions that appear upon combining de Sitter space with
supersymmetry.
|
Effective Action and Phase Transitions in Thermal Yang-Mills Theory on
Spheres: We study the covariantly constant Savvidy-type chromomagnetic vacuum in
finite-temperature Yang-Mills theory on the four-dimensional curved spacetime.
Motivated by the fact that a positive spatial curvature acts as an effective
gluon mass we consider the compact Euclidean spacetime $S^1\times S^1\times
S^2$, with the radius of the first circle determined by the temperature
$a_1=(2\pi T)^{-1}$. We show that covariantly constant Yang-Mills fields on
$S^2$ cannot be arbitrary but are rather a collection of monopole-antimonopole
pairs. We compute the heat kernels of all relevant operators exactly and show
that the gluon operator on such a background has negative modes for any compact
semi-simple gauge group. We compute the infrared regularized effective action
and apply the result for the computation of the entropy and the heat capacity
of the quark-gluon gas. We compute the heat capacity for the gauge group SU(2N)
for a field configuration of $N$ monopole-antimonopole pairs. We show that in
the high-temperature limit the heat capacity is well defined in the infrared
limit and exhibits a typical behavior of second-order phase transition $\sim
(T-T_c)^{-3/2}$ with the critical temperature $T_c=(2\pi a)^{-1}$, where $a$ is
the radius of the 2-sphere $S^2$.
|
Minimal Affinizations of Representations of Quantum Groups: the rank 2
case: We define the notion of a minimal affinization of an irreducible
representation of $U_q(g)$. We prove that minimal affinizations exist and
establish their uniqueness in the rank 2 case.
|
Can fusion coefficients be calculated from the depth rule ?: The depth rule is a level truncation of tensor product coefficients expected
to be sufficient for the evaluation of fusion coefficients. We reformulate the
depth rule in a precise way, and show how, in principle, it can be used to
calculate fusion coefficients. However, we argue that the computation of the
depth itself, in terms of which the constraints on tensor product coefficients
is formulated, is problematic. Indeed, the elements of the basis of states
convenient for calculating tensor product coefficients do not have a
well-defined depth! We proceed by showing how one can calculate the depth in an
`approximate' way and derive accurate lower bounds for the minimum level at
which a coupling appears. It turns out that this method yields exact results
for $\widehat{su}(3)$ and constitutes an efficient and simple algorithm for
computing $\widehat{su}(3)$ fusion coefficients.
|
Gauge symmetries decrease the number of Dp-brane dimensions: It is known that the presence of antisymmetric background field $B_{\mu\nu}$
leads to noncommutativity of Dp-brane manifold. Addition of the linear dilaton
field in the form $\Phi(x)=\Phi_0+a_\mu x^\mu$, causes the appearance of the
commutative Dp-brane coordinate $x=a_\mu x^\mu$. In the present article we show
that for some particular choices of the background fields, $a^2\equiv
G^{\mu\nu}a_\mu a_\nu=0$ and $\tilde a^2\equiv [ (G-4BG^{-1}B)^{-1}\
]^{\mu\nu}a_\mu a_\nu=0$, the local gauge symmetries appear in the theory. They
turn some Neuman boundary conditions into the Dirichlet ones, and consequently
decrease the number of the Dp-brane dimensions.
|
Localizing gravity on Maxwell gauged CP1 model in six dimensions: We shall consider about a 3-brane embedded in six-dimensional space-time with
a negative bulk cosmological constant. The 3-brane is constructed by a
topological soliton solution living in two-dimensional axially symmetric
transverse subspace. Similar to most previous works of six-dimensional soliton
models, our Maxwell gauged CP1 brane model can also achieve to localize gravity
around the 3-brane. The CP1 field is described by a scalar doublet and derived
from O(3) sigma model by projecting it onto two-dimensional complex space. In
that sense, our framework is more effective than other solitonic brane models
concerning with gauge theory. We shall also discuss about linear stability
analysis for our new model by fluctuating all fields.
|
Statistics of the Composite Systems: The commutation relations of the composite fields are studied in the 3, 2 and
1 space dimensions. It is shown that the field of an atom consisting of a
nucleus and an electron fields satisfies, in the space-like asymptotic limit,
the canonical commutation relations within the sub-Fock-space of the atom. The
composite anyon fields are shown to satisfy the proper anyonic commutation
relations with the additive phase exponents. Then, (quasi)particle pictures of
the anyons are clarified. The hierarchy of the fractional quantum Hall effect
is rather simply nderstood by utilizing the (quasi)particle charactors of the
anyons. The commutation relations of the scalar object in the
Schwinger(Thirring) model are mentioned briefly.
|
Gravitational Constrained Instantons: We find constrained instantons in Einstein gravity with and without a
cosmological constant. These configurations are not saddle points of the
Einstein-Hilbert action, yet they contribute to non-perturbative processes in
quantum gravity. In some cases we expect that they give the dominant
contribution from spacetimes with certain fixed topologies. With negative
cosmological constant, these metrics describe wormholes connecting two
asymptotic regions. We find many examples of such wormhole metrics and for
certain symmetric configurations establish their perturbative stability. We
expect that the Euclidean versions of these wormholes encode the energy level
statistics of AdS black hole microstates. In the de Sitter and flat space
settings we find new homogeneous and isotropic bounce and big bang/crunch
cosmologies.
|
O(d,d,Z) Transformations as Automorphisms of the Operator Algebra: We implement the O(d,d,Z) transformations of T-duality as automorphisms of
the operator algebras of Conformal Field Theories. This extends these
transformations to arbitrary field configurations in the deformation class.
|
From tree- to loop-simplicity in affine Toda theories I: Landau
singularities and their subleading coefficients: Various features of the even order poles appearing in the S-matrices of
simply-laced affine Toda field theories are analysed in some detail. In
particular, the coefficients of first- and second-order singularities appearing
in the Laurent expansion of the S-matrix around a general $2N^{\rm th}$ order
pole are derived in a universal way using perturbation theory at one loop. We
show how to cut loop diagrams contributing to the pole into particular products
of tree-level graphs that depend on the on-shell geometry of the loop; in this
way, we recover the coefficients of the Laurent expansion around the pole
exploiting tree-level integrability properties of the theory. The analysis is
independent of the particular simply-laced theory considered, and all the
results agree with those obtained in the conjectured bootstrapped S-matrices of
the ADE series of theories.
|
The $β$-function of supersymmetric theories from vacuum supergraphs:
a three-loop example: We verify a method which allows to obtain the $\beta$-function of
supersymmetric theories regularized by higher covariant derivatives by
calculating only specially modified vacuum supergraphs. With the help of this
method for a general renormalizable ${\cal N}=1$ supersymmetric gauge theory a
part of the three-loop $\beta$-function depending on the Yukawa couplings is
constructed in the general $\xi$-gauge. The result is written in the form of an
integral of double total derivatives with respect to the loop momenta. It is
demonstrated that all gauge dependent terms cancel each other in agreement with
the general statements. Taking into account that the result in the Feynman
gauge (found earlier) coincides with the one obtained by the standard
technique, this fact confirms the correctness of the considered method by a
highly nontrivial multiloop calculation.
|
Combinatorial Factorization: The simplest integrands in the CHY formulation of scattering amplitudes are
constructed using the so-called Parke-Taylor functions. Parke-Taylor functions
also turn out to belong to a large class of rational functions known as MHV
leading singularities. In fact, Parke-Taylor functions correspond to planar MHV
leading singularities. In this note we study the behavior of CHY integrands
constructed using non-planar MHV leading singularities under collinear and
multi-particle factorization limits. General $n$-particle MHV leading
singularities are completely characterized by a set of $(n-2)$ triples of
particle labels. We give a simple operation on this combinatorial data which
"factors" the list into two sets of triples defining two lower point MHV
leading singularities. The fact that general MHV leading singularities form a
closed set under "multi-particle factorizations" is surprising from their gauge
theoretic origin.
|
Nonlinear corrections in basic problems of electro- and magneto-statics
in the vacuum: We find third-power nonlinear corrections to the Coulomb and other static
electric fields, as well as to the electric and magnetic dipole fields, as we
work within QED with no background field. The nonlinear response function we
base our consideration on is the fourth-rank polarization tensor, calculated
within the local (infrared) approximation of the effective action. Therefore,
the results are applicable to weakly varying fields. It is established that the
nonlinear correction to magnetic moment of some baryons just matches, in the
order of magnitude, the existing gap between its experimental and theoretical
values.
|
Double Scaling Limits, Airy Functions and Multicritical Behaviour in
O(N) Vektor Sigma Models: O(N) vector sigma models possessing catastrophes in their action are studied.
Coupling the limit N --> infinity with an appropriate scaling behaviour of the
coupling constants, the partition function develops a singular factor. This is
a generalized Airy function in the case of spacetime dimension zero and the
partition function of a scalar field theory for positive spacetime dimension.
|
Higher charge calorons with non-trivial holonomy: The full ADHM-Nahm formalism is employed to find exact higher charge caloron
solutions with non-trivial holonomy, extended beyond the axially symmetric
solutions found earlier. Particularly interesting is the case where the
constituent monopoles, that make up these solutions, are not necessarily
well-separated. This is worked out in detail for charge 2. We resolve the
structure of the extended core, which was previously localized only through the
singularity structure of the zero-mode density in the far field limit. We also
show that this singularity structure agrees exactly with the abelian charge
distribution as seen through the abelian component of the gauge field. As a
by-product zero-mode densities for charge 2 magnetic monopoles are found.
|
Exceptional Chern-Simons-Matter Dualities: We use conformal embeddings involving exceptional affine Kac-Moody algebras
to derive new dualities of three-dimensional topological field theories. These
generalize the familiar level-rank duality of Chern-Simons theories based on
classical gauge groups to the setting of exceptional gauge groups. For
instance, one duality sequence we discuss is $(E_{N})_{1}\leftrightarrow
SU(9-N)_{-1}$. Others such as $SO(3)_{8}\leftrightarrow PSU(3)_{-6},$ are
dualities among theories with classical gauge groups that arise due to their
embedding into an exceptional chiral algebra. We apply these equivalences
between topological field theories to conjecture new boson-boson Chern-Simons
matter dualities. We also use them to determine candidate phase diagrams of
time-reversal invariant $G_{2}$ gauge theory coupled to either an adjoint
fermion, or two fundamental fermions.
|
Bootstrapping six-gluon scattering in planar ${\cal N}=4$
super-Yang-Mills theory: We describe the hexagon function bootstrap for solving for six-gluon
scattering amplitudes in the large $N_c$ limit of ${\cal N}=4$ super-Yang-Mills
theory. In this method, an ansatz for the finite part of these amplitudes is
constrained at the level of amplitudes, not integrands, using boundary
information. In the near-collinear limit, the dual picture of the amplitudes as
Wilson loops leads to an operator product expansion which has been solved using
integrability by Basso, Sever and Vieira. Factorization of the amplitudes in
the multi-Regge limit provides additional boundary data. This bootstrap has
been applied successfully through four loops for the maximally helicity
violating (MHV) configuration of gluon helicities, and through three loops for
the non-MHV case.
|
New Gauge Invariant Formulation of the Chern-Simons Gauge Theory: A new gauge invariant formulation of the relativistic scalar field
interacting with Chern-Simons gauge fields is considered. This formulation is
consistent with the gauge fixed formulation. Furthermore we find that canonical
(Noether) Poincar\'e generators are not gauge invariant even on the constraints
surface and do not satisfy the (classical) Poincar\'e algebra. It is the
improved generators, constructed from the symmetric energy-momentum tensor,
which are (manifestly) gauge invariant and obey the classical Poincar\'e
algebra.
|
The QED(0+1) model and a possible dynamical solution of the strong CP
problem: The QED(0+1) model describing a quantum mechanical particle on a circle with
minimal electromagnetic interaction and with a potential -M cos(phi - theta_M),
which mimics the massive Schwinger model, is discussed as a prototype of
mechanisms and infrared structures of gauge quantum field theories in positive
gauges. The functional integral representation displays a complex measure, with
a crucial role of the boundary conditions, and the decomposition into theta
sectors takes place already in finite volume. In the infinite volume limit, the
standard results are reproduced for M=0 (massless fermions), but one meets
substantial differences for M not = 0: for generic boundary conditions,
independently of the lagrangean angle of the topological term, the infinite
volume limit selects the sector with theta = theta_M, and provides a natural
"dynamical" solution of the strong CP problem. In comparison with previous
approaches, the strategy discussed here allows to exploit the consequences of
the theta-dependence of the free energy density, with a unique minimum at theta
= theta_M.
|
An Introduction to the Worldline Technique for Quantum Field Theory
Calculations: These two lectures give a pedagogical introduction to the ``string-inspired''
worldline technique for perturbative calculations in quantum field theory. This
includes an overview over the present range of its applications. Several
examples are calculated in detail, up to the three-loop level. The emphasis is
on photon scattering in quantum electrodynamics.
|
A-D hypersurface of $su(n)$ $\mathcal{N}=2$ supersymmetric gauge theory
with $N_f = 2n-2$ flavors: In the previous letter, arXiv:2210.16738[hep-th], we found a set of flavor
mass relations as constraints that the $\beta$-deformed $A_{n-1}$ quiver matrix
model restores the maximal symmetry in the massive scaling limit and reported
the existence of Argyres-Douglas critical hypersurface. In this letter, we
derive the concrete conditions on moduli parameters which maximally degenerates
the Seiberg-Witten curve while maintaining the flavor mass relations. These
conditions define the A-D hypersurface.
|
Compactified Quantum Fields. Is there Life Beyond the Cut-off Scale?: A consistent definition of high dimensional compactified quantum field theory
without breaking the Kaluza-Klein tower is proposed. It is possible in the
limit when the size of compact dimensions is of the order of the cut off. This
limit is nontrivial and depends on the geometry of compact dimensions. Possible
consequences are discussed for the scalar model.
|
Partition function of massless scalar field in Schwarzschild background: Using thermal value of zeta function instead of zero temperature, the
partition function of quantized fields in arbitrary stationary backgrounds was
found to be independent of undetermined regularization constant in
even-dimension and the long drawn problem associated with the trace anomaly
effect had been removed. Here, we explicitly calculate the expression for the
coincidence limit so that the technique may be applied in some specific
problems. A particular problem dealt with here is to calculate the partition
function of massless scalar field in Schwarzschild background.
|
The AdS/CFT Correspondence for the Massive Rarita-Schwinger Field: The complete solution to the massive Rarita-Schwinger field equation in
anti-de Sitter space is constructed, and used in the AdS/CFT correspondence to
calculate the correlators for the boundary conformal field theory. It is found
that when no condition is imposed on the field solution, there appear two
different boundary conformal field operators, one coupling to a
Rarita-Schwinger field and the other to a Dirac field. These two operators are
seen to have different scaling dimensions, with that of the spinor-coupled
operator exhibiting non-analytic mass dependence.
|
Partition Functions of Reduced Matrix Models with Classical Gauge Groups: We evaluate partition functions of matrix models which are given by
topologically twisted and dimensionally reduced actions of d=4 N=1 super
Yang-Mills theories with classical (semi-)simple gauge groups, SO(2N), SO(2N+1)
and USp(2N). The integrals reduce to those over the maximal tori by
semi-classical approximation which is exact in reduced models. We carry out
residue calculus by developing a diagrammatic method, in which the action of
the Weyl groups and therefore counting of multiplicities are explained
obviously.
|
Classical integrability of chiral $QCD_{2}$ and classical curves: In this letter, classical chiral $QCD_{2}$ is studied in the lightcone gauge
$A_{-}=0$. The once integrated equation of motion for the current is shown to
be of the Lax form, which demonstrates an infinite number of conserved
quantities. Specializing to gauge group SU(2), we show that solutions to the
classical equations of motion can be identified with a very large class of
curves. We demonstrate this correspondence explicitly for two solutions. The
classical fermionic fields associated with these currents are then obtained.
|
Non-singular black holes from gravity-matter-brane lagrangians: We consider self-consistent coupling of bulk Einstein-Maxwell-Kalb-Ramond
system to codimension-one charged lightlike p-brane with dynamical (variable)
tension (LL-brane). The latter is described by a manifestly
reparametrization-invariant world-volume action significantly different from
the ordinary Nambu-Goto one. We show that the LL-brane is the appropriate
gravitational and charge source in the Einstein-Maxwell-Kalb-Ramond equations
of motion needed to generate a self-consistent solution describing non-singular
black hole. The latter consists of de Sitter interior region and exterior
Reissner-Nordstroem region glued together along their common horizon (it is the
inner horizon from the Reissner-Nordstroem side). The matching horizon is
automatically occupied by the LL-brane as a result of its world-volume
lagrangian dynamics, which dynamically generates the cosmological constant in
the interior region and uniquely determines the mass and charge parameters of
the exterior region. Using similar techniques we construct a self-consistent
wormhole solution of Einstein-Maxwell system coupled to electrically neutral
LL-brane, which describes two identical copies of a non-singular black hole
region being the exterior Reissner-Nordstroem region above the inner horizon,
glued together along their common horizon (the inner Reissner-Nordstroem one)
occupied by the LL-brane. The corresponding mass and charge parameters of the
two black hole "universes" are explicitly determined by the dynamical LL-brane
tension. This also provides an explicit example of Misner-Wheeler "charge
without charge" phenomenon. Finally, this wormhole solution connecting two
non-singular black holes can be transformed into a special case of
Kantowski-Sachs bouncing cosmology solution.
|
Geometry of dynamics and phase transitions in classical lattice phi^4
theories: We perform a microcanonical study of classical lattice phi^4 field models in
3 dimensions with O(n) symmetries. The Hamiltonian flows associated to these
systems that undergo a second order phase transition in the thermodynamic limit
are here investigated. The microscopic Hamiltonian dynamics neatly reveals the
presence of a phase transition through the time averages of conventional
thermodynamical observables. Moreover, peculiar behaviors of the largest
Lyapunov exponents at the transition point are observed. A Riemannian
geometrization of Hamiltonian dynamics is then used to introduce other relevant
observables, that are measured as functions of both energy density and
temperature. On the basis of a simple and abstract geometric model, we suggest
that the apparently singular behaviour of these geometric observables might
probe a major topological change of the manifolds whose geodesics are the
natural motions.
|
New relations between analyticity, Regge trajectories, Veneziano
amplitude, and Moebius transformations: In this paper we use the analyticity properties of the scattering amplitude
in the context of the conformal mapping techniques. The Schwarz-Christoffel and
Riemann-Schwarz functions are used to map the upper half -plane onto a
triangle. We use the known asymptotic and threshold behaviors of the scattering
amplitude to establish a connection between the values of the Regge trajectory
functions and the angles of the triangle. This geometrical interpretation
allows a link between values of the Regge trajectory functions and the
generators of the invariance group of Moebius transformations associated with
the underlying automorphic function. The formalism provides useful new
relations between analyticity, geometry, Regge trajectory functions, Veneziano
model, groups of Moebius transformations and automorphic functions. It is hoped
that they will provide avenues for further work.
|
A covariant entropy conjecture on cosmological dynamical horizon: We here propose a covariant entropy conjecture on cosmological dynamical
horizon. After the formulation of our conjecture, we test its validity in
adiabatically expanding universes with open, flat and closed spatial geometry,
where our conjecture can also be viewed as a cosmological version of the
generalized second law of thermodynamics in some sense.
|
The time-dependent non-Abelian Aharonov-Bohm effect: In this article, we study the time-dependent Aharonov-Bohm effect for
non-Abelian gauge fields. We use two well known time-dependent solutions to the
Yang-Mills field equations to investigate the Aharonov-Bohm phase shift. For
both of the solutions, we find a cancellation between the phase shift coming
from the non-Abelian "magnetic" field and the phase shift coming from the
non-Abelian "electric" field, which inevitably arises in time-dependent cases.
We compare and contrast this cancellation for the time-dependent non-Abelian
case to a similar cancellation which occurs in the time-dependent Abelian case.
We postulate that this cancellation occurs generally in time-dependent
situations for both Abelian and non-Abelian fields.
|
An Elliptic Superpotential for Softly Broken N=4 Supersymmetric
Yang-Mills Theory: An exact superpotential is derived for the N=1 theories which arise as
massive deformations of N=4 supersymmetric Yang-Mills (SYM) theory. The
superpotential of the SU(N) theory formulated on R^{3}\times S^{1} is shown to
coincide with the complexified potential of the N-body elliptic Calogero-Moser
Hamiltonian. This superpotential reproduces the vacuum structure predicted by
Donagi and Witten for the corresponding four-dimensional theory and also
transforms covariantly under the S-duality group of N=4 SYM. The analysis
yields exact formulae with interesting modular properties for the condensates
of gauge-invariant chiral operators in the four-dimensional theory.
|
Electric-magnetic deformations of D=4 gauged supergravities: We discuss duality orbits and symplectic deformations of D=4 gauged
supergravity theories, with focus on N$\ge$2. We provide a general constructive
framework for computing symplectic deformations starting from a reference
gauging, and apply it to many interesting examples. We prove that no continuous
deformations are allowed for Fayet-Iliopoulos gaugings of the N=2 STU model and
in particular that any $\omega$ deformation is classically trivial. We further
show that although in the N=6 truncation of SO(8) maximal supergravity the
$\omega$ parameter can be dualized away, in the 'twin' N=2 truncation $\omega$
is preserved and a second, new deformation appears. We further provide a full
classification and appropriate duality orbits of certain N=4 gauged
supergravities, including all inequivalent SO(4)$^2$ gaugings and several
non-compact forms.
|
Objective and subjective time in anthropic reasoning: The original formulation of the (weak) anthropic principle was prompted by a
question about objective time at a macroscopic level, namely the age of the
universe when ``anthropic'' observers such as ourselves would be most likely to
emerge. Theoretical interpretation of what one observes requires the theory to
indicate what is expected, which will commonly depend on where, and
particularly when, the observation can be expected to occur. In response to the
question of where and when, the original version of the anthropic principle
proposed an {it a priori} probability weighting proportional to the number of
``anthropic'' observers present. The present discussion takes up the question
of the time unit characterising the biological clock controlling our subjective
internal time, using a revised alternative to a line of argument due to Press,
who postulated that animal size is limited by the brittleness of bone. On the
basis of a static support condition depending on the tensile strength of flesh
rather than bone, it is reasoned here that our size should be subject to a
limit inversely proportional to the terrestrial gravitation field g, which is
itself found to be proportional (with a factor given by the 5/2 power of the
fine structure constant) to the gravitational coupling constant.This provides
an animal size limit that will in all cases be of the order of a thousandth of
the maximum mountain height, which will itself be of the order of a thousandth
of the planetary radius. The upshot, via the (strong) anthropic principle, is
that the need for brains, and therefore planets, that are large in terms of
baryon number may be what explains the weakness of gravity relative to
electromagnetism.
|
Higgs Mechanism in String Theory: In first-quantized string theory, spacetime symmetries are described by inner
automorphisms of the underlying conformal field theory. In this paper we use
this approach to illustrate the Higgs effect in string theory. We consider
string propagation on M^{24,1} \times S^1, where the circle has radius R, and
study SU(2) symmetry breaking as R moves away from its critical value. We find
a gauge-covariant equation of motion for the broken-symmetry gauge bosons and
the would-be Goldstone bosons. We show that the Goldstone bosons can be
eliminated by an appropriate gauge transformation. In this unitary gauge, the
Goldstone bosons become the longitudinal components of massive gauge bosons.
|
Factorization of unitarity and black hole firewalls: Unitary black hole evaporation necessarily involves a late-time superposition
of decoherent states, including states describing distinct spacetimes (e.g.,
different center of mass trajectories of the black hole). Typical analyses of
the black hole information problem, including the argument for the existence of
firewalls, assume approximate unitarity ("factorization of unitarity") on each
of the decoherent spacetimes. This factorization assumption is non-trivial, and
indeed may be incorrect. We describe an ansatz for the radiation state that
violates factorization and which allows unitarity and the equivalence principle
to coexist (no firewall). Unitarity without factorization provides a natural
realization of the idea of black hole complementarity.
|
Local Grand Unification in the Heterotic Landscape: We consider the possibility that the unification of the electroweak
interactions and the strong force arises from string theory, at energies
significantly lower than the string scale. As a tool, an effective grand
unified field theory in six dimensions is derived from an anisotropic orbifold
compactification of the heterotic string. It is explicitly shown that all
anomalies cancel in the model, though anomalous Abelian gauge symmetries are
present locally at the boundary singularities. In the supersymmetric vacuum
additional interactions arise from higher-dimensional operators. We develop
methods that relate the couplings of the effective theory to the location of
the vacuum, and find that unbroken discrete symmetries play an important role
for the phenomenology of orbifold models. An efficient algorithm for the
calculation of the superpotential to arbitrary order is developed, based on
symmetry arguments. We furthermore present a correspondence between bulk fields
of the orbifold model in six dimensions, and the moduli fields that arise from
compactifying four internal dimensions on a manifold with non-trivial gauge
background.
|
Gauged Double Field Theory: We find necessary and sufficient conditions for gauge invariance of the
action of Double Field Theory (DFT) as well as closure of the algebra of gauge
symmetries. The so-called weak and strong constraints are sufficient to satisfy
them, but not necessary. We then analyze compactifications of DFT on twisted
double tori satisfying the consistency conditions. The effective theory is a
Gauged DFT where the gaugings come from the duality twists. The action,
bracket, global symmetries, gauge symmetries and their closure are computed by
twisting their analogs in the higher dimensional DFT. The non-Abelian heterotic
string and lower dimensional gauged supergravities are particular examples of
Gauged DFT.
|
M-Theory: We construct an eleven-dimensional superspace with superspace coordinates and
formulate a finite M-theory using non-anticommutative geometry. The conjectured
M-theory has the correct eleven-dimensional supergravity low energy limit. We
consider the problem of finding a stable finite M-theory which has de Sitter
space as a natural ground state, and the problem of eliminating possible future
horizons.
|
Non-minimally coupled vector curvaton: It is shown that a massive Abelian vector boson field can generate the
curvature perturbation in the Universe, when coupled non-minimally to gravity,
through an RA^2 coupling. The vector boson acts as a curvaton field imposing
the curvature perturbation after the end of inflation, without generating a
large-scale anisotropy. The parameter space of the model is fully explored,
obtaining the relevant bounds on the inflation scale and the decay constant of
the vector curvaton.
|
Generalization of Faddeev--Popov Rules in Yang--Mills Theories: N=3,4
BRST Symmetries: The Faddeev-Popov rules for quantization of theory with gauge group are
generalized for case of nvariance of quantum actions, $S_N$, on N-parametric
Abelian SUSY transformations with odd parameters $\lambda_p$, p=1,..,N and
anticommuting generators $s_p$, for N=3,4 implying substitution of ghost fields
N-plet, $C^p$ multipled on $\lambda_p$, instead of the parameter, $\xi$, of
gauge transformations. Total configuration spaces for quantum theory of the
same classical model coincide for N=3 ,4 cases. For N=3 transformations the
superspace of irrep includes in addition 3 ghost $C^p$, 3 even $B^{pq}$ and odd
$\hat{B}$ fields for p,q=1-3. It is shown for quantum action $S_{3}$ the
gauge-fixing by adding to classical action of N=3-exact term requires 1
antighost $\bar{C}$, 3 even $B^{p}$ 3 odd $\hat{B}{}^p$ and Nakanishi--Lautrup
fields. Action of N=3 transformations on the latter fields is found. The
transformations appear by N=3 BRST ones for the vacuum functional, $Z_3(0) $.
It is shown, the configuration space appears by irrep superspace for fields
$\Phi_4$ for N=4- transformations containing in addition to $A^\mu$: (4+6+4+1)
ghost-antighost $C^r$, even $B^{rs}$, odd $\hat{B}{}^r $ fields and B. Action
$S_4$ is constructed by adding to classical action of N=4-exact with gauge
boson $F_4$ as compared to gauge fermion $\Psi_3$ for N=3 case. Procedure is
valid for any admissible gauge. The equivalence with $N=1$ BRST-invariant
quantization method is explicitly found. Finite N=3,4 BRST transformations are
derived from algebraic transformations. Respective Jacobians for
field-dependent parameters are calculated. They imply the presence of
corresponding modified Ward identity to be reduced to new (usual) Ward
identities for constant parameters and describe the problem of
gauge-dependence. Introduction into diagrammatic Feynman techniques for N=3,4
cases is suggested.
|
The Self-Dual String and Anomalies in the M5-brane: We study the anomalies of a charge $Q_2$ self-dual string solution in the
Coulomb branch of $Q_5$ M5-branes. Cancellation of these anomalies allows us to
determine the anomaly of the zero-modes on the self-dual string and their
scaling with $Q_2$ and $Q_5$. The dimensional reduction of the five-brane
anomalous couplings then lead to certain anomalous couplings for D-branes.
|
On the N=1 super Liouville four-point functions: We construct the four-point correlation functions containing the top
component of the supermultiplet in the Neveu-Schwarz sector of the N=1 SUSY
Liouville field theory. The construction is based on the recursive
representation for the NS conformal blocks. We test our results in the case
where one of the fields is degenerate with a singular vector on the level 3/2.
In this case, the correlation function satisfies a third-order ordinary
differential equation, which we derive. We numerically verify the crossing
symmetry relations for the constructed correlation functions in the
nondegenerate case.
|
Finite Quantum Fluctuations About Static Field Configurations: We develop an unambiguous and practical method to calculate one-loop quantum
corrections to the energies of classical time-independent field configurations
in renormalizable field theories. We show that the standard perturbative
renormalization procedure suffices here as well. We apply our method to a
simplified model where a charged scalar couples to a neutral "Higgs" field, and
compare our results to the derivative expansion.
|
Nonsingular 2-D Black Holes and Classical String Backgrounds: We study a string-inspired classical 2-D effective field theory with {\it
nonsingular} black holes as well as Witten's black hole among its static
solutions. By a dimensional reduction, the static solutions are related to the
$(SL(2,R)_{k}\otimes U(1))/U(1)$ coset model, or more precisely its
$O\bigl((\alpha')^{0}\bigr)$ approximation known as the 3-D charged black
string. The 2-D effective action possesses a propagating degree of freedom, and
the dynamics are highly nontrivial. A collapsing shell is shown to bounce into
another universe without creating a curvature singularity on its path, and the
potential instability of the Cauchy horizon is found to be irrelevent in that
some of the infalling observers never approach the Cauchy horizon. Finally a
$SL(2,R)_{k}/U(1)$ nonperturbative coset metric, found and advocated by R.
Dijkgraaf et.al., is shown to be nonsingular and to coincide with one of the
charged spacetimes found above. Implications of all these geometries are
discussed in connection with black hole evaporation.
|
On the Consistence Conditions to Braneworlds Sum Rules in Scalar-Tensor
Gravity for Arbitrary Dimensions: We derive an one-parameter family of consistence conditions to braneworlds in
the Brans-Dicke gravity. The sum rules are constructed in a completely general
frame and they reproduce the conditions already obtained in General Relativity
theory just by using a right limit of the Brans-Dicke parameter.
|
Resonances in the one-dimensional Dirac equation in the presence of a
point interaction and a constant electric field: We show that the energy spectrum of the one-dimensional Dirac equation in the
presence of a spatial confining point interaction exhibits a resonant behavior
when one includes a weak electric field. After solving the Dirac equation in
terms of parabolic cylinder functions and showing explicitly how the resonant
behavior depends on the sign and strength of the electric field, we derive an
approximate expression for the value of the resonance energy in terms of the
electric field and delta interaction strength.
|
Thermal resonating Hartree-Bogoliubov theory based on the projection
method: We propose a rigorous thermal resonating mean-field theory (Res-MFT). A state
is approximated by superposition of multiple MF wavefunctions (WFs) composed of
non-orthogonal Hartree-Bogoliubov (HB) WFs. We adopt a Res-HB subspace spanned
by Res-HB ground and excited states. A partition function (PF) in a SO(2N)
coherent state representation |g> (N:Number of single-particle states) is
expressed as Tr(e^{-\beta H})=2^{N-1} \int <g|e^{-\beta H}|g>dg (\beta=1/k_BT).
Introducing a projection operator P to the Res-HB subspace, the PF in the
Res-HB subspace is given as Tr(Pe^{-\beta H}), which is calculated within the
Res-HB subspace by using the Laplace transform of e^{-\beta H} and the
projection method. The variation of the Res-HB free energy is made, which leads
to a thermal HB density matrix W_{Res}^{thermal} expressed in terms of a
thermal Res-FB operator F_{Res}^{thermal} as
W_{Res}^{thermal}={1_{2N}+exp(\beta F_{Res}^{thermal})}^{-1}. A calculation of
the PF by an infinite matrix continued fraction is cumbersome and a procedure
of tractable optimization is too complicated. Instead, we seek for another
possible and more practical way of computing the PF and the Res-HB free energy
within the Res-MFT.
|
Super-Calogero-Moser-Sutherland systems and free super-oscillators : a
mapping: We show that the supersymmetric rational Calogero-Moser-Sutherland (CMS)
model of A_{N+1}-type is equivalent to a set of free super-oscillators, through
a similarity transformation. We prescribe methods to construct the complete
eigen-spectrum and the associated eigen-functions, both in supersymmetry
preserving as well as supersymmetry breaking phases, from the free
super-oscillator basis. Further we show that a wide class of super-Hamiltonians
realizing dynamical OSp(2|2) supersymmetry, which also includes all types of
rational super-CMS as a small subset, are equivalent to free super-oscillators.
We study BC_{N+1}-type super-CMS model in some detail to understand the
subtleties involved in this method.
|
Geometrical interpretation of D-branes in gauged WZW models: We show that one can construct D-branes in parafermionic and WZW theories
(and their orbifolds) which have very natural geometrical interpretations, and
yet are not automatically included in the standard Cardy construction of
D-branes in rational conformal field theory. The relation between these
theories and their T-dual description leads to an analogy between these
D-branes and the familiar A-branes and B-branes of N=2 theories.
|
Galilean Geometry in Condensed Matter Systems: We present a systematic means to impose Galilean invariance within field
theory. We begin by defining the most general background geometries consistent
with Galilean invariance and then turn to applications within effective field
theory, fluid dynamics, and the quantum Hall effect.
|
Configurational Entropy in Brane-world Models: A New Approach to
Stability: In this work we investigate the entropic information on thick brane-worlds
scenarios and its consequences. The brane-world entropic information is studied
for the sine-Gordon model is and hence the brane-world entropic information
measure is shown an accurate way for providing the most suitable values for the
bulk AdS curvature. Besides, the brane-world configurational entropy is
employed to demonstrate a high organisational degree in the structure of the
system configuration, for large values of a parameter of the sine-Gordon model
but the one related to the AdS curvature. The Gleiser and Stamatopoulos
procedure is finally applied in order to achieve a precise correlation between
the energy of the system and the brane-world configurational entropy.
|
Thermal corrections to the Casimir energy in a Lorentz-breaking scalar
field theory: In this paper, we investigate the thermal effect on the Casimir energy
associated with a massive scalar quantum field confined between two large
parallel plates in a CPT-even, aether-like Lorentz-breaking scalar field
theory. In order to do that we consider a nonzero chemical potential for the
scalar field assumed to be in thermal equilibrium at some finite temperature.
The calculations of the energies are developed by using the Abel-Plana
summation formula, and the corresponding results are analyzed in several
asymptotic regimes of the parameters of the system, like mass, separations
between the plates and temperature.
|
Universality and a generalized C-function in CFTs with AdS Duals: We argue that the thermodynamics of conformal field theories with AdS duals
exhibits a remarkable universality. At strong coupling, a Cardy-Verlinde
entropy formula holds even when R-charges or bulk supergravity scalars are
turned on. In such a setting, the Casimir entropy can be identified with a
generalized C-function that changes monotonically with temperature as well as
when non-trivial bulk scalar fields are introduced. We generalize the
Cardy-Verlinde formula to cases where no subextensive part of the energy is
present and further observe that such a formula is valid for the N=4 super
Yang-Mills theory in D=4 even at weak coupling. Finally we show that a
generalized Cardy-Verlinde formula holds for asymptotically flat black holes in
any dimension.
|
Finite-sites corrections to the Casimir energy on a periodic lattice: We show that the vacuum ground state energy for massive scalars on a 1-dim
L-sites periodic lattice can be interpreted as the thermodynamic free energy of
particles at temperature 1/L governed by the Arutyunov-Frolov mirror
Hamiltonian. Although the obligatory zero-point sum-over-frequencies is finite
on the lattice, a renormalization prescription is necessary in order to obtain
a physical sensible result for the lattice Casimir energy. The coefficients of
every term in the large L expansion of the lattice Casimir energy are provided
in terms of modified Bessel functions.
|
Counting supersymmetric branes: Maximal supergravity solutions are revisited and classified, with particular
emphasis on objects of co-dimension at most two. This class of solutions
includes branes whose tension scales with g_s^{-\sigma} for \sigma>2. We
present a group theory derivation of the counting of these objects based on the
corresponding tensor hierarchies derived from E11 and discrete T- and U-duality
transformations. This provides a rationale for the wrapping rules that were
recently discussed for \sigma<4 in the literature and extends them. Explicit
supergravity solutions that give rise to co-dimension two branes are
constructed and analysed.
|
Nonlinear Operator Superalgebras and BFV-BRST Operators for Lagrangian
Description of Mixed-symmetry HS Fields in AdS Spaces: We study the properties of nonlinear superalgebras $\mathcal{A}$ and algebras
$\mathcal{A}_b$ arising from a one-to-one correspondence between the sets of
relations that extract AdS-group irreducible representations $D(E_0,s_1,s_2)$
in AdS$_d$-spaces and the sets of operators that form $\mathcal{A}$ and
$\mathcal{A}_b$, respectively, for fermionic, $s_i=n_i+{1/2}$, and bosonic,
$s_i=n_i$, $n_i \in \mathbb{N}_0$, $i=1,2$, HS fields characterized by a Young
tableaux with two rows. We consider a method of constructing the Verma modules
$V_\mathcal{A}$, $V_{\mathcal{A}_b}$ for $\mathcal{A}$, $\mathcal{A}_b$ and
establish a possibility of their Fock-space realizations in terms of formal
power series in oscillator operators which serve to realize an additive
conversion of the above (super)algebra ($\mathcal{A}$) $\mathcal{A}_b$,
containing a set of 2nd-class constraints, into a converted (super)algebra
$\mathcal{A}_{b{}c}$ = $\mathcal{A}_{b}$ + $\mathcal{A}'_b$ ($\mathcal{A}_c$ =
$\mathcal{A}$ + $\mathcal{A}'$), containing a set of 1st-class constraints
only. For the algebra $\mathcal{A}_{b{}c}$, we construct an exact nilpotent
BFV--BRST operator $Q'$ having nonvanishing terms of 3rd degree in the powers
of ghost coordinates and use $Q'$ to construct a gauge-invariant Lagrangian
formulation (LF) for HS fields with a given mass $m$ (energy $E_0(m)$) and
generalized spin $\mathbf{s}$=$(s_1,s_2)$. LFs with off-shell algebraic
constraints are examined as well.
|
Quantum Mechanical Symmetries and Topological Invariants: We give the definition and explore the algebraic structure of a class of
quantum symmetries, called topological symmetries, which are generalizations of
supersymmetry in the sense that they involve topological invariants similar to
the Witten index. A topological symmetry (TS) is specified by an integer n>1,
which determines its grading properties, and an n-tuple of positive integers
(m_1,m_2,...,m_n). We identify the algebras of supersymmetry, p=2
parasupersymmetry, and fractional supersymmetry of order n with those of the
Z_2-graded TS of type (1,1), Z_2-graded TS of type (2,1), and Z_n-graded TS of
type (1,1,...,1), respectively. We also comment on the mathematical
interpretation of the topological invariants associated with the Z_n-graded TS
of type (1,1,...,1). For n=2, the invariant is the Witten index which can be
identified with the analytic index of a Fredholm operator. For n>2, there are n
independent integer-valued invariants. These can be related to differences of
the dimension of the kernels of various products of n operators satisfying
certain conditions.
|
Complex saddles of the Veneziano amplitude: Saddle point approximation is a useful method to explore high energy
asymptotic behaviors of string scattering amplitudes. We show that, even at
tree-level, there are infinitely many complex saddles contributing to string
scattering amplitudes, and that the complex saddles reproduce their appropriate
poles and zeros. Each complex saddle is interpreted as a semi-classical path of
a string in Lorentzian signature. The poles and zeros of the Veneziano
amplitude are understood as constructive or destructive interference of such
semi-classical paths.
|
Symmetry transformations in Batalin-Vilkovisky formalism: This short note is closely related to Sen-Zwiebach paper on gauge
transformations in Batalin-Vilkovisky theory (hep-th 9309027). We formulate
some conditions of physical equivalence of solutions to the quantum master
equation and use these conditions to give a very transparent analysis of
symmetry transformations in BV-approach. We prove that in some sense every
quantum observable (i.e. every even function $H$ obeying
$\Delta_{\rho}(He^S)=0$) determines a symmetry of the theory with the action
functional $S$ satisfying quantum master equation $\Delta_{\rho}e^S=0$ \end
|
Intersections of Twisted Forms: New Theories and Double Copies: Tree-level scattering amplitudes of particles have a geometrical description
in terms of intersection numbers of pairs of twisted differential forms on the
moduli space of Riemann spheres with punctures. We customize a catalog of
twisted differential forms containing both already known and new differential
forms. By pairing elements from this list intersection numbers of various
theories can be furnished to compute their scattering amplitudes. Some of the
latter are familiar through their CHY description, but others are unknown.
Likewise, certain pairings give rise to various known and novel double-copy
constructions of spin-two theories. This way we find double copy constructions
for many theories, including higher derivative gravity, (partial massless)
bimetric gravity and some more exotic theories. Furthermore, we present a
derivation of amplitude relations in intersection theory.
|
Duality Twists, Orbifolds, and Fluxes: We investigate compactifications with duality twists and their relation to
orbifolds and compactifications with fluxes. Inequivalent compactifications are
classified by conjugacy classes of the U-duality group and result in gauged
supergravities in lower dimensions with nontrivial Scherk-Schwarz potentials on
the moduli space. For certain twists, this mechanism is equivalent to
introducing internal fluxes but is more general and can be used to stabilize
some of the moduli. We show that the potential has stable minima with zero
energy precisely at the fixed points of the twist group. In string theory, when
the twist belongs to the T-duality group, the theory at the minimum has an
exact CFT description as an orbifold. We also discuss more general twists by
nonperturbative U-duality transformations.
|
The Noncommutative U(N) Kalb-Ramond Theory: We present the noncommutative extention of the U(N)
Cremmer-Scherk-Kalb-Ramond theory, displaying its differential form and gauge
structures. The Seiberg-Witten map of the model is also constructed up to
$0(\theta^2)$.
|
Observer-independent quanta of mass and length: It has been observed recently by Giovanni Amelino-Camelia \cite{gac1, gac2}
that the hypothesis of existence of a minimal observer-independent (Planck)
length scale is hard to reconcile with special relativity. As a remedy he
postulated to modify special relativity by introducing an observer-independent
length scale. In this letter we set forward a proposal how one should modify
the principles of special relativity, so as to assure that the values of mass
and length scales are the same for any inertial observer. It turns out that one
can achieve this by taking dispersion relations such that the speed of light
goes to infinity for finite momentum (but infinite energy), proposed e.g., in
the framework of the quantum $\kappa$-Poincar\'e symmetry. It follows that at
the Planck scale the world may be non-relativistic.
|
Rotating regular solutions in Einstein-Yang-Mills-Higgs theory: We construct new axially symmetric rotating solutions of
Einstein-Yang-Mills-Higgs theory. These globally regular configurations possess
a nonvanishing electric charge which equals the total angular momentum, and
zero topological charge, representing a monopole-antimonopole system rotating
around the symmetry axis through their common center of mass.
|
Scale without Conformal Invariance: An Example: We give an explicit example of a model in D=4-epsilon space-time dimensions
that is scale but not conformally invariant, is unitary, and has finite
correlators. The invariance is associated with a limit cycle renormalization
group (RG) trajectory. We also prove, to second order in the loop expansion, in
D=4-epsilon, that scale implies conformal invariance for models of any number
of real scalars. For models with one real scalar and any number of Weyl spinors
we show that scale implies conformal invariance to all orders in perturbation
theory.
|
Integrable light-cone lattice discretizations from the universal
R-matrix: Our goal is to develop a more general scheme for constructing integrable
lattice regularisations of integrable quantum field theories. Considering the
affine Toda theories as examples, we show how to construct such lattice
regularisations using the representation theory of quantum affine algebras.
This requires us to clarify in particular the relations between the light-cone
approach to integrable lattice models and the representation theory of quantum
affine algebras. Both are found to be related in a very natural way, suggesting
a general scheme for the construction of generalised Baxter Q-operators. One of
the main difficulties we need to deal with is coming from the
infinite-dimensionality of the relevant families of representations. It is
handled by means of suitable renormalisation prescriptions defining what may be
called the modular double of quantum affine algebras. This framework allows us
to give a representation-theoretic proof of finite-difference equations
generalising the Baxter equation.
|
Symmetry-resolved Entanglement Entropy, Spectra & Boundary Conformal
Field Theory: We perform a comprehensive analysis of the symmetry-resolved (SR)
entanglement entropy (EE) for one single interval in the ground state of a
$1+1$D conformal field theory (CFT), that is invariant under an arbitrary
finite or compact Lie group, $G$. We utilize the boundary CFT approach to study
the total EE, which enables us to find the universal leading order behavior of
the SREE and its first correction, which explicitly depends on the irreducible
representation under consideration and breaks the equipartition of
entanglement. We present two distinct schemes to carry out these computations.
The first relies on the evaluation of the charged moments of the reduced
density matrix. This involves studying the action of the defect-line, that
generates the symmetry, on the boundary states of the theory. This perspective
also paves the way for discussing the infeasibility of studying symmetry
resolution when an anomalous symmetry is present. The second scheme draws a
parallel between the SREE and the partition function of an orbifold CFT. This
approach allows for the direct computation of the SREE without the need to use
charged moments. From this standpoint, the infeasibility of defining the
symmetry-resolved EE for an anomalous symmetry arises from the obstruction to
gauging. Finally, we derive the symmetry-resolved entanglement spectra for a
CFT invariant under a finite symmetry group. We revisit a similar problem for
CFT with compact Lie group, explicitly deriving an improved formula for $U(1)$
resolved entanglement spectra. Using the Tauberian formalism, we can estimate
the aforementioned EE spectra rigorously by proving an optimal lower and upper
bound on the same. In the abelian case, we perform numerical checks on the
bound and find perfect agreement.
|
Gaugino Condensation and Nonperturbative Superpotentials in Flux
Compactifications: There are two known sources of nonperturbative superpotentials for K\"ahler
moduli in type IIB orientifolds, or F-theory compactifications on Calabi-Yau
fourfolds, with flux: Euclidean brane instantons and low-energy dynamics in D7
brane gauge theories. The first class of effects, Euclidean D3 branes which
lift in M-theory to M5 branes wrapping divisors of arithmetic genus 1 in the
fourfold, is relatively well understood. The second class has been less
explored. In this paper, we consider the explicit example of F-theory on $K3
\times K3$ with flux. The fluxes lift the D7 brane matter fields, and stabilize
stacks of D7 branes at loci of enhanced gauge symmetry. The resulting theories
exhibit gaugino condensation, and generate a nonperturbative superpotential for
K\"ahler moduli. We describe how the relevant geometries in general contain
cycles of arithmetic genus $\chi \geq 1$ (and how $\chi > 1$ divisors can
contribute to the superpotential, in the presence of flux). This second class
of effects is likely to be important in finding even larger classes of models
where the KKLT mechanism of moduli stabilization can be realized. We also
address various claims about the situation for IIB models with a single
K\"ahler modulus.
|
Moduli Space Tilings and Lie-Theoretic Color Factors: A detailed understanding of the moduli spaces $X(k,n)$ of $n$ points in
projective $k-1$ space is essential to the investigation of generalized
biadjoint scalar amplitudes, as discovered by Cachazo, Early, Guevara and
Mizera (CEGM) in 2019. But in math, conventional wisdom says that it is
completely hopeless due to the arbitrarily high complexity of realization
spaces of oriented matroids. In this paper, we nonetheless find a path forward.
We present a Lie-theoretic realization of color factors for color-dressed
generalized biadjoint scalar amplitudes, formulated in terms of certain tilings
of the real moduli space $X(k,n)$ and collections of logarithmic differential
forms, resolving an important open question from recent work by Cachazo, Early
and Zhang. The main idea is to replace the realization space decomposition of
$X(k,n)$ with a large class of overlapping tilings whose topologies are
individually relatively simple. So we obtain a collection of color-dressed
amplitudes, each of which satisfies $U(1)$ decoupling separately. The essential
complexity appears when they are all superposed.
|
Holographic transports from Born-Infeld electrodynamics with momentum
dissipation: We construct the Einstein-axions AdS black hole from Born-Infeld
electrodynamics. Various DC transport coefficients of the dual boundary theory
are computed. The DC electric conductivity depends on the temperature, which is
a novel property comparing to that in RN-AdS black hole. The DC electric
conductivity are positive at zero temperature while the thermal conductivity
vanishes, which implies that the dual system is an electrical metal but thermal
insulator. The effects of Born-Infeld parameter on the transport coefficients
are analyzed. Finally, we study the AC electric conductivity from Born-Infeld
electrodynamics with momentum dissipation. For weak momentum dissipation, the
low frequency behavior satisfies the standard Drude formula and the electric
transport is coherent for various correction parameter. While for stronger
momentum dissipation, the modified Drude formula is applied and we observe a
crossover from coherent to incoherent phase. Moreover, the Born-Infeld
correction amplifies the incoherent behavior. Finally, we study the non-linear
conductivity in probe limit and compare our results with those observed in
(i)DBI model.
|
Collective fields, Calogero-Sutherland model and generalized matrix
models: On the basis of the collective field method, we analyze the
Calogero--Sutherland model (CSM) and the Selberg--Aomoto integral, which
defines, in particular case, the partition function of the matrix models.
Vertex operator realizations for some of the eigenstates (the Jack polynomials)
of the CSM Hamiltonian are obtained. We derive Virasoro constraint for the
generalized matrix models and indicate relations with the CSM operators.
Similar results are presented for the $q$--deformed case (the Macdonald
operator and polynomials), which gives the generating functional of infinitely
many conserved charges in the CSM.
|
N=4 Super Yang-Mills from the Plane Wave Matrix Model: We propose a nonperturbative definition of N=4 super Yang-Mills (SYM). We
realize N=4 SYM on RxS^3 as the theory around a vacuum of the plane wave matrix
model. Our regularization preserves sixteen supersymmetries and the gauge
symmetry. We perform the 1-loop calculation to give evidences that the
superconformal symmetry is restored in the continuum limit.
|
An Exact Solution to the Quantized Electromagnetic Field in
D-dimensional de Sitter Spacetimes: In this work we investigate the quantum theory of light propagating in
$D-$dimensional de Sitter spacetimes. To do so, we use the method of dynamic
invariants to obtain the solution of the time-dependent Schr\"odinger equation.
The quantum behavior of the electromagnetic field in this background is
analyzed. As the electromagnetism loses its conformality in $D\neq4$, we point
that there will be particle production and comoving objects will feel a
Bunch-Davies thermal bath. This may become important in extra dimension physics
and raises the intriguing possibility that precise measurements of the Cosmic
Microwave Background could verify the existence of extra dimensions.
|
The black hole/string transition in AdS$_3$ and confining backgrounds: String stars, or Horowitz-Polchinski solutions, are Euclidean string theory
saddles with a normalizable condensate of thermal winding strings. String stars
were suggested as a possible description of stringy (Euclidean) black holes
close to the Hagedorn temperature. In this work, we continue the study
initiated in arXiv:2202.06966 by investigating the thermodynamic properties of
string stars in asymptotically (thermal) anti-de Sitter backgrounds. First, we
discuss the case of AdS$_3$ with mixed RR and NS-NS fluxes (including the pure
NS-NS system) and comment on a possible BTZ/string transition unique to
AdS$_3$. Second, we present new ``winding-string gas'' saddles for confining
holographic backgrounds such as the Witten model, and determine the subleading
correction to their Hagedorn temperature. We speculate a black brane/string
transition in these models and argue for a possible relation to the deconfined
phase of 3+1 dimensional pure Yang-Mills.
|
Stationary Measure in the Multiverse: We study the recently proposed "stationary measure" in the context of the
string landscape scenario. We show that it suffers neither from the "Boltzmann
brain" problem nor from the "youngness" paradox that makes some other measures
predict a high CMB temperature at present. We also demonstrate a satisfactory
performance of this measure in predicting the results of local experiments,
such as proton decay.
|
D-brane probes on G2 Orbifolds: We consider type IIB string theory on a seven dimensional orbifold with
holonomy in G2. The motivation is to use D1-branes as probes of the geometry.
The low energy theory on the D1-brane is a sigma-model with two real
supercharges (N = (1,1) in two dimensional language). We study in detail the
closed and open string sectors and propose a coupling of the twisted fields to
the brane that modifies the vacuum moduli space so that the singularity at the
origin is removed. Instead of coming from D-terms, which are not present here,
the modification comes from a ``twisted'' mass term for the seven scalar
multiplets on the brane. The proposed mechanism involves a generalization of
the moment map.
|
Bridging two quantum quench problems -- local joining quantum quench and
Möbius quench -- and their holographic dual descriptions: We establish an equivalence between two different quantum quench problems,
the joining local quantum quench and the M\"obius quench, in the context of
$(1+1)$-dimensional conformal field theory (CFT). Here, in the former, two
initially decoupled systems (CFTs) on finite intervals are joined at $t=0$. In
the latter, we consider the system that is initially prepared in the ground
state of the regular homogeneous Hamiltonian on a finite interval and, after
$t=0$, let it time-evolve by the so-called M\"obius Hamiltonian that is
spatially inhomogeneous. The equivalence allows us to relate the time-dependent
physical observables in one of these problems to those in the other. As an
application of the equivalence, we construct a holographic dual of the M\"obius
quench from that of the local quantum quench. The holographic geometry involves
an end-of-the-world brane whose profile exhibits non-trivial dynamics.
|
Vacuum energy and spectral function sum rules: We reformulate the problem of the cancellation of the ultraviolet
divergencies of the vacuum energy, particularly important at the cosmological
level, in terms of a saturation of spectral function sum rules which leads to a
set of conditions on the spectrum of the fundamental theory. We specialize the
approach to both Minkowski and de Sitter space-times and investigate some
examples.
|
D-brane Standard Model-Like and Scalar Dark Matter in Type IIA
Superstring Theory: In light of the present LHC Run II at $\sqrt{s}=13$ $TeV$, string y
standard-like model is studied. Concretely, a singlet $S $ scalar-extended SM
given in terms four stacks of intersecting D6-branes in a type IIA superstring
compactification producing a large gauge symmetry is examined. The involved
scales are dealt with. According to the dark matter relic density, the mass of
the scalar dark matter beyond the SM $m_{S}\lesssim 10^{3}GeV$ and the
corresponding Higgs portal couplings $\lambda _{SH}\lesssim 10^{-8}$ are
approached.
|
Universal hypermultiplet metrics: Some instanton corrections to the universal hypermultiplet moduli space
metric of the type-IIA string theory compactified on a Calabi-Yau threefold
arise due to multiple wrapping of BPS membranes and fivebranes around certain
cycles of Calabi-Yau. The classical universal hypermultipet metric is locally
equivalent to the Bergmann metric of the symmetric quaternionic space
SU(2,1)/U(2), whereas its generic quaternionic deformations are governed by the
integrable SU(infinity) Toda equation. We calculate the exact
(non-perturbative) UH metrics in the special cases of (i) the D-instantons (the
wrapped D2-branes) in the absence of fivebranes, and (ii) the fivebrane
instantons with vanishing charges, in the absence of D-instantons. The
solutions of the first type preserve the U(1)xU(1) classical symmetry, while
they can be interpreted as the gravitational dressing of the hyper-K"ahler
D-instanton solutions. The second type solution preserves the non-abelian SU(2)
classical symmetry, while it can be interpreted as a gradient flow in the
universal hypermultiplet moduli space.
|
Path-Integral Quantization of the (2,2) String: A complete treatment of the (2,2) NSR string in flat (2+2) dimensional
space-time is given, from the formal path integral over N=2 super Riemann
surfaces to the computational recipe for amplitudes at any loop or gauge
instanton number. We perform in detail the superconformal gauge fixing, discuss
the spectral flow, and analyze the supermoduli space with emphasis on the gauge
moduli. Background gauge field configurations in all instanton sectors are
constructed. We develop chiral bosonization on punctured higher-genus surfaces
in the presence of gauge moduli and instantons. The BRST cohomology is
recapitulated, with a new space-time interpretation for picture-changing. We
point out two ways of combining left- and right-movers, which lead to different
three-point functions.
|
Extension to Imaginary Chemical Potential in a Holographic Model: We extend a bottom up holographic model, which has been used in studying the
color superconductivity in QCD, to the imaginary chemical potential ($\mu_I$)
region, and the phase diagram is studied on the $\mu_I$-temperature (T) plane.
The analysis is performed for the case of the probe approximation and for the
background where the back reaction from the flavor fermions are taken into
account. For both cases, we could find the expected Roberge-Weiss (RW)
transitions. In the case of the back-reacted solution, a bound of the color
number $N_c$ is found to produce the RW periodicity. It is given as $N_c\geq
1.2$. Furthermore, we could assure the validity of this extended model by
comparing our result with the one of the lattice QCD near $\mu_I=0$.
|
AC Transport at Holographic Quantum Hall Transitions: We compute AC electrical transport at quantum Hall critical points, as
modeled by intersecting branes and gauge/gravity duality. We compare our
results with a previous field theory computation by Sachdev, and find
unexpectedly good agreement. We also give general results for DC Hall and
longitudinal conductivities valid for a wide class of quantum Hall transitions,
as well as (semi)analytical results for AC quantities in special limits. Our
results exhibit a surprising degree of universality; for example, we find that
the high frequency behavior, including subleading behavior, is identical for
our entire class of theories.
|
Induced action for superconformal higher-spin multiplets using SCFT
techniques: Recently, the interacting $\mathcal{N}=1$ superconformal higher-spin theory
in four dimensions has been proposed within the induced action approach. In
this paper we initiate a program of computing perturbative corrections to the
corresponding action and explicitly evaluate all quadratic terms. This is
achieved by employing standard techniques from superconformal field theory.
|
Open Descendants of NAHE-based free fermionic and Type I Z2^n models: The NAHE-set, that underlies the realistic free fermionic models, corresponds
to Z2XZ2 orbifold at an enhanced symmetry point, with (h_{11},h_{21})=(27,3).
Alternatively, a manifold with the same data is obtained by starting with a
Z2XZ2 orbifold at a generic point on the lattice and adding a freely acting Z2
involution. In this paper we study type I orientifolds on the manifolds that
underly the NAHE-based models by incorporating such freely acting shifts. We
present new models in the Type I vacuum which are modulated by Z2^n for n=2,3.
In the case of n=2, the Z2XZ2 structure is a composite orbifold Kaluza-Klein
shift arrangement. The partition function provides a simpler spectrum with
chiral matter. For n=3, the case discussed is a Z2 modulation of the T6/(Z2 X
Z2) spectrum. The additional projection shows an enhanced closed and open
sector with chiral matter. The brane stacks are correspondingly altered from
those which are present in the Z2 X Z2 orbifold. In addition, we discuss the
models arising from the open sector with and without discrete torsion.
|
Constrained Dynamics of the Coupled Abelian Two-Form: I present the reduction of phase space of the theory of an antisymmetric
tensor potential coupled to an abelian gauge field, using Dirac's procedure.
Duality transformations on the reduced phase space are also discussed.
|
Tadpole diagrams in constant electromagnetic fields: We show how all possible one-particle reducible tadpole diagrams in constant
electromagnetic fields can be constructed from one-particle irreducible
constant-field diagrams. The construction procedure is essentially algebraic
and involves differentiations of the latter class of diagrams with respect to
the field strength tensor and contractions with derivatives of the one-particle
irreducible part of the Heisenberg-Euler effective Lagrangian in constant
fields. Specific examples include the two-loop addendum to the Heisenberg-Euler
effective action as well as a novel one-loop correction to the charged particle
propagator in constant electromagnetic fields discovered recently. As an
additional example, the approach devised in the present article is adopted to
derive the tadpole contribution to the two-loop photon polarization tensor in
constant fields for the first time.
|
Quantum affine algebras and universal R-matrix with spectral parameter,
II: This paper is an extended version of our previous short letter \cite{ZG2} and
is attempted to give a detailed account for the results presented in that
paper. Let $U_q({\cal G}^{(1)})$ be the quantized nontwisted affine Lie algebra
and $U_q({\cal G})$ be the corresponding quantum simple Lie algebra. Using the
previous obtained universal $R$-matrix for $U_q(A_1^{(1)})$ and
$U_q(A_2^{(1)})$, we determine the explicitly spectral-dependent universal
$R$-matrix for $U_q(A_1)$ and $U_q(A_2)$. We apply these spectral-dependent
universal $R$-matrix to some concrete representations. We then reproduce the
well-known results for the fundamental representations and we are also able to
derive for the first time the extreamly explicit and compact formula of the
spectral-dependent $R$-matrix for the adjoint representation of $U_q(A_2)$, the
simplest nontrival case when the tensor product of the representations is {\em
not} multiplicity-free.
|
Solitonic Strings and BPS Saturated Dyonic Black Holes: We consider a six-dimensional solitonic string solution described by a
conformal chiral null model with non-trivial $N=4$ superconformal transverse
part. It can be interpreted as a five-dimensional dyonic solitonic string wound
around a compact fifth dimension. The conformal model is regular with the
short-distance (`throat') region equivalent to a WZW theory. At distances
larger than the compactification scale the solitonic string reduces to a dyonic
static spherically-symmetric black hole of toroidally compactified heterotic
string. The new four-dimensional solution is parameterised by five charges,
saturates the Bogomol'nyi bound and has nontrivial dilaton-axion field and
moduli fields of two-torus. When acted by combined T- and S-duality
transformations it serves as a generating solution for all the static
spherically-symmetric BPS-saturated configurations of the low-energy heterotic
string theory compactified on six-torus. Solutions with regular horizons have
the global space-time structure of extreme Reissner-Nordstrom black holes with
the non-zero thermodynamic entropy which depends only on conserved (quantised)
charge vectors. The independence of the thermodynamic entropy on moduli and
axion-dilaton couplings strongly suggests that it should have a microscopic
interpretation as counting degeneracy of underlying string configurations. This
interpretation is supported by arguments based on the corresponding
six-dimensional conformal field theory. The expression for the level of the WZW
theory describing the throat region implies a renormalisation of the string
tension by a product of magnetic charges, thus relating the entropy and the
number of oscillations of the solitonic string in compact directions.
|
Instantons in Large Order of the Perturbative Series: Behavior of the Euclidean path integral at large orders of the perturbation
series is studied. When the model allows tunneling, the path-integral
functional in the zero instanton sector is known to be dominated by bounce-like
configurations at large order of the perturbative series, which causes
non-convergence of the series. We find that in addition to this bounce the
perturbative functional has a subleading peak at the instanton and
anti-instanton pair, and its sum reproduces the non-perturbative valley.
|
Unconstrained Higher Spins of Mixed Symmetry. II. Fermi Fields: This paper is a sequel of arXiv:0810.4350 [hep-th], and is also devoted to
the local "metric-like" unconstrained Lagrangians and field equations for
higher-spin fields of mixed symmetry in flat space. Here we complete the
previous constrained on-shell formulation of Labastida for Fermi fields,
deriving the corresponding constrained Lagrangians both via the Bianchi
identities and via the requirement of self-adjointness. We also describe two
types of unconstrained Lagrangian formulations: a "minimal" one, containing
higher derivatives of the compensator fields, and another non-minimal one,
containing only one-derivative terms. We identify classes of these systems that
are invariant under Weyl-like symmetry transformations.
|
High temperature AdS black holes are low temperature quantum phonon
gases: We report a precise match between the high temperature $(D+2)$-dimensional
Tangherlini-AdS black hole and the low temperature quantum phonon gas in
$D$-dimensional nonmetallic crystals residing in $(D+1)$-dimensional flat
spacetime. The match is realized by use of the recently proposed restricted
phase space formalism for black hole thermodynamics, and the result can be
viewed as a novel contribution to the AdS/CMT correspondence on a quantitative
level.
|
Spinors Fields in Co-dimension One Braneworlds: In this work we analyze the zero mode localization and resonances of
$1/2-$spin fermions in co-dimension one Randall-Sundrum braneworld scenarios.
We consider delta-like, domain walls and deformed domain walls membranes.
Beyond the influence of the spacetime dimension $D$ we also consider three
types of couplings: (i) the standard Yukawa coupling with the scalar field and
parameter $\eta_1$, (ii) a Yukawa-dilaton coupling with two parameters $\eta_2$
and $\lambda$ and (iii) a dilaton derivative coupling with parameter $h$.
Together with the deformation parameter $s$, we end up with five free parameter
to be considered. For the zero mode we find that the localization is dependent
of $D$, because the spinorial representation changes when the bulk
dimensionality is odd or even and must be treated separately. For case (i) we
find that in odd dimensions only one chirality can be localized and for even
dimension a massless Dirac spinor is trapped over the brane. In the cases (ii)
and (iii) we find that for some values of the parameters, both chiralities can
be localized in odd dimensions and for even dimensions we obtain that the
massless Dirac spinor is trapped over the brane. We also calculated numerically
resonances for cases (ii) and (iii) by using the transfer matrix method. We
find that, for deformed defects, the increasing of $D$ induces a shift in the
peaks of resonances. For a given $\lambda$ with domain walls, we find that the
resonances can show up by changing the spacetime dimensionality. For example,
the same case in $D=5$ do not induces resonances but when we consider $D=10$
one peak of resonance is found. Therefore the introduction of more dimensions,
diversely from the bosonic case, can change drastically the zero mode and
resonances in fermion fields.
|
On Stabilization of Maxwell-BMS Algebra: In this work we present different infinite dimensional algebras which appear
as deformations of the asymptotic symmetry of the three-dimensional
Chern-Simons gravity for the Maxwell algebra. We study rigidity and stability
of the infinite dimensional enhancement of the Maxwell algebra. In particular,
we show that three copies of the Witt algebra and the BMS3+Witt algebra are
obtained by deforming its ideal part. New family of infinite dimensional
algebras are obtained by considering deformations of the other commutators
which we have denoted as M(a,b;c,d) and
\bar{M}(\bar{\alpha},\bar{\beta};\bar{\nu}). Interestingly, for the specific
values a=c=d=0, b=-\frac{1}{2} the obtained algebra M(0,-\frac{1}{2};0,0)
corresponds to the twisted Schrodinger-Virasoro algebra. The central extensions
of our results are also explored. The physical implications and relevance of
the deformed algebras introduced here are discussed along the work.
|
Double Inozemtsev Limits of the Quantum DELL System: In this letter we study various Inozemtsev-type limits of the quantum double
elliptic (DELL) system when both elliptic parameters are sent to zero at
different rates, while the coupling constant is sent to infinity, such that a
certain combination of the three parameters is kept fixed. We find a regime in
which such double Inozemtsev limit of DELL produces the elliptic
Ruijsenaars-Schneider (eRS) Hamiltonians albeit in an unconventional
normalization. We discuss other double scaling limits and anisotropic scaling
of coordinates and momenta. In addition, we provide a formal expression for the
eigenvalues of the eRS Hamiltonians solely in terms of their eigenfunctions.
|
Semiclassical decay of strings with maximum angular momentum: We study the classical breaking of a highly excited (closed or open) string
state on the leading Regge trajectory, represented by a rotating soliton
solution, and we find the resulting solutions for the outgoing two pieces,
describing two specific excited string states. This classical picture
reproduces very accurately the precise analytical relation of the masses $M_1$
and $M_2$ of the decay products found in a previous quantum computation. The
decay rate is naturally described in terms of a semiclassical formula. We also
point out some interesting features of the evolution after the splitting
process.
|
Consistent Anomalies in Translation-Invariant Noncommutative Gauge
Theories: Translation-invariant noncommutative gauge theories are discussed in the
setting of matrix modeled gauge theories. Using the matrix model formulation
the explicit form of consistent anomalies and consistent Schwinger terms for
translation-invariant noncommutative gauge theories are derived.
|
Classical Space-Times from the S Matrix: We show that classical space-times can be derived directly from the S-matrix
for a theory of massive particles coupled to a massless spin two particle. As
an explicit example we derive the Schwarzchild space-time as a series in $G_N$.
At no point of the derivation is any use made of the Einstein-Hilbert action or
the Einstein equations. The intermediate steps involve only on-shell S-matrix
elements which are generated via BCFW recursion relations and unitarity sewing
techniques. The notion of a space-time metric is only introduced at the end of
the calculation where it is extracted by matching the potential determined by
the S-matrix to the geodesic motion of a test particle. Other static
space-times such as Kerr follow in a similar manner. Furthermore, given that
the procedure is action independent and depends only upon the choice of the
representation of the little group, solutions to Yang-Mills (YM) theory can be
generated in the same fashion. Moreover, the squaring relation between the YM
and gravity three point functions shows that the seeds that generate solutions
in the two theories are algebraically related. From a technical standpoint our
methodology can also be utilized to calculate quantities relevant for the
binary inspiral problem more efficiently than the more traditional Feynman
diagram approach.
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.