anchor
stringlengths 50
3.92k
| positive
stringlengths 55
6.16k
|
|---|---|
Relaxation in Conformal Field Theory, Hawking-Page Transition, and
Quasinormal/Normal Modes: We study the process of relaxation back to thermal equilibrium in
$(1+1)$-dimensional conformal field theory at finite temperature. When the size
of the system is much larger than the inverse temperature, perturbations decay
exponentially with time. On the other hand, when the inverse temperature is
large, the relaxation is oscillatory with characteristic period set by the size
of the system. We then analyse the intermediate regime in two specific models,
namely free fermions, and a strongly coupled large $\tt k$ conformal field
theory which is dual to string theory on $(2+1)$-dimensional anti-de Sitter
spacetime. In the latter case, there is a sharp transition between the two
regimes in the ${\tt k}=\infty$ limit, which is a manifestation of the
gravitational Hawking-Page phase transition. In particular, we establish a
direct connection between quasinormal and normal modes of the gravity system,
and the decaying and oscillating behaviour of the conformal field theory.
|
Novel all loop actions of interacting CFTs: Construction, integrability
and RG flows: We construct the all loop effective action representing, for small couplings,
simultaneously self and mutually interacting current algebra CFTs realized by
WZW models. This non-trivially generalizes our previous works where such
interactions were, at the linear level, not simultaneously present. For the two
coupling case we prove integrability and calculate the coupled RG flow
equations. We also consider non-Abelian T-duality type limits. Our models
provide concrete realisations of integrable flows between exact CFTs and
exhibit several new features which we discuss in detail.
|
Asymmetrical braneworlds and the charged lepton mass spectrum: A braneworld mechanism for explaining the mass spectrum of the charged
leptons is proposed. Based on the existence of an asymmetric warp factor for a
$5+1$-dim braneworld scenario, the proper fractions between the masses of the
electron, muon and tauon are achieved. As a straightforward consequence, our
results coincide with the Koide's mass formula.
|
Light-sheets and AdS/CFT: One may ask whether the CFT restricted to a subset b of the AdS boundary has
a well-defined dual restricted to a subset H(b) of the bulk geometry. The
Poincare patch is an example, but more general choices of b can be considered.
We propose a geometric construction of H. We argue that H should contain the
set C of causal curves with both endpoints on b. Yet H should not reach so far
from the boundary that the CFT has insufficient degrees of freedom to describe
it. This can be guaranteed by constructing a superset of H from light-sheets
off boundary slices and invoking the covariant entropy bound in the bulk. The
simplest covariant choice is L, the intersection of L^+ and L^-, where L^+
(L^-) is the union of all future-directed (past-directed) light-sheets. We
prove that C=L, so the holographic domain is completely determined by our
assumptions: H=C=L. In situations where local bulk operators can be constructed
on b, H is closely related to the set of bulk points where this construction
remains unambiguous under modifications of the CFT Hamiltonian outside of b.
Our construction leads to a covariant geometric RG flow. We comment on the
description of black hole interiors and cosmological regions via AdS/CFT.
|
On Classical Solutions of 4d Supersymmetric Higher Spin Theory: We present a simple construction of solutions to the supersymmetric higher
spin theory based on solutions to bosonic theories. We illustrate this for the
case of the Didenko-Vasiliev solution in arXiv:0906.3898, for which we have
found a striking simplification where the higher-spin connection takes the
vacuum value. Studying these solutions further, we check under which conditions
they preserve some supersymmetry in the bulk, and when they are compatible with
the boundary conditions conjectured to be dual to certain 3d SUSY
Chern-Simons-matter theories. We perform the analysis for a variety of theories
with $\mathcal{N}$ = 2, $\mathcal{N}$ = 3, $\mathcal{N}$ = 4 and $\mathcal{N}$
= 6 and find a rich spectrum of $1/4$, $1/3$ and $1/2$-BPS solutions.
|
N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop: We expose simple and practical relations between the integrated four- and
five-point one-loop amplitudes of N >= 4 supergravity and the corresponding
(super-)Yang-Mills amplitudes. The link between the amplitudes is simply
understood using the recently uncovered duality between color and kinematics
that leads to a double-copy structure for gravity. These examples provide
additional direct confirmations of the duality and double-copy properties at
loop level for a sample of different theories.
|
M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory: A self-contained review is given of the matrix model of M-theory. The
introductory part of the review is intended to be accessible to the general
reader. M-theory is an eleven-dimensional quantum theory of gravity which is
believed to underlie all superstring theories. This is the only candidate at
present for a theory of fundamental physics which reconciles gravity and
quantum field theory in a potentially realistic fashion. Evidence for the
existence of M-theory is still only circumstantial---no complete
background-independent formulation of the theory yet exists. Matrix theory was
first developed as a regularized theory of a supersymmetric quantum membrane.
More recently, the theory appeared in a different guise as the discrete
light-cone quantization of M-theory in flat space. These two approaches to
matrix theory are described in detail and compared. It is shown that matrix
theory is a well-defined quantum theory which reduces to a supersymmetric
theory of gravity at low energies. Although the fundamental degrees of freedom
of matrix theory are essentially pointlike, it is shown that higher-dimensional
fluctuating objects (branes) arise through the nonabelian structure of the
matrix degrees of freedom. The problem of formulating matrix theory in a
general space-time background is discussed, and the connections between matrix
theory and other related models are reviewed.
|
Statistics in the Landscape of Intersecting Brane Models: An approach towards a statistical survey of four dimensional supersymmetric
vacua in the string theory landscape is described and illustrated with three
examples of ensembles of intersecting D-brane models. The question whether it
is conceivable to make predictions based on statistical distributions is
discussed. Especially interesting in this context are possible correlations
between low energy observables. As an example we look at correlations between
properties of the gauge sector of intersecting D-brane models and Gepner model
constructions.
|
On wrapping corrections to GKP-like operators: In the recent paper arXiv:1010.5009, Maldacena et al. derive the two loop
expressions for polygonal Wilson loops expectation values, or MHV amplitudes,
by writing them as sums over exchanges of intermediate free particles. The
spectrum of excitations of the flux tube between two null Wilson lines can be
viewed as the spectrum of excitations around the infinite spin limit of finite
twist operators in the sl(2) sector of N=4 SYM or the Gubser-Klebanov-Polyakov
(GKP) string. This regime can be captured exploiting integrability and assuming
that wrapping corrections are negligible compared to asymptotic Bethe Ansatz
contributions. This assumption holds true for the N=4 SYM background GKP
string, but deserves further analysis for excited states. Here, we investigate
GKP cousins by considering various classes of (generalized) twist operators in
beta-deformed N=4 SYM and ABJM theory. We show that the Y-system of
Gromov-Kazakov-Vieira easily leads to accurate large spin expansions of the
wrapping correction at lowest order in weak-coupling perturbation theory. As a
byproduct, we confirm that wrapping corrections are subleading in all the
considered cases.
|
Brane Tilings and Exceptional Collections: Both brane tilings and exceptional collections are useful tools for
describing the low energy gauge theory on a stack of D3-branes probing a
Calabi-Yau singularity. We provide a dictionary that translates between these
two heretofore unconnected languages. Given a brane tiling, we compute an
exceptional collection of line bundles associated to the base of the
non-compact Calabi-Yau threefold. Given an exceptional collection, we derive
the periodic quiver of the gauge theory which is the graph theoretic dual of
the brane tiling. Our results give new insight to the construction of quiver
theories and their relation to geometry.
|
The Tension Spectrum of Cosmic Superstrings in a Warped Deformed
Conifold: This paper has been withdrawn. The interpretation of tension spectrum of
cosmic superstrings in terms of KK momentum is invalid as presented in section
2. A new paper based on calculations of the KK spectrum presented here will be
submitted.
|
Complete N-Point Superstring Disk Amplitude I. Pure Spinor Computation: In this paper the pure spinor formalism is used to obtain a compact
expression for the superstring N-point disk amplitude. The color ordered string
amplitude is given by a sum over (N-3)! super Yang-Mills subamplitudes
multiplied by multiple Gaussian hypergeometric functions. In order to obtain
this result, the cohomology structure of the pure spinor superspace is
exploited to generalize the Berends-Giele method of computing super Yang-Mills
amplitudes. The method was briefly presented in [1], and this paper elaborates
on the details and contains higher-rank examples of building blocks and
associated cohomology objects. But the main achievement of this work is to
identify these field-theory structures in the pure spinor computation of the
superstring amplitude. In particular, the associated set of basis worldsheet
integrals is constructively obtained here and thoroughly investigated together
with the structure and properties of the amplitude in [2].
|
Supersymmetric localization of (higher-spin) JT gravity: a bulk
perspective: We study two-dimensional Jackiw-Teitelboim gravity on the disk topology by
using a BF gauge theory in the presence of a boundary term. The system can be
equivalently written in a supersymmetric way by introducing auxiliary gauginos
and scalars with suitable boundary conditions on the hemisphere. We compute the
exact partition function thanks to supersymmetric localization and we recover
the result obtained from the Schwarzian theory by accurately identifying the
physical scales. The calculation is then easily extended to the higher-spin
generalization of Jackiw-Teitelboim gravity, finding perfect agreement with
previous results. We argue that our procedure can also be applied to
boundary-anchored Wilson line correlators.
|
The Mandelstam-Terning Line Integral in Unparticle Physics -- A Reply to
Galloway, Martin and Stancato: We show that the path ordered Wilson line integral used in 0802.0313 to make
a nonlocal action gauge invariant is mathematically inconsistent. We also show
that it can lead to reasonable gauge field vertexes by the use of a second
mathematically unjustifiable procedure.
|
$DE$-type little strings from glued brane webs: We propose brane web configurations for $D$-type and $E$-type
$\mathcal{N}=(1,0)$ little string theories based on a trivalent or quadrivalent
gluing of 5-brane web diagrams. Tri-/quadri-valent gluing is a powerful way of
computing 5d/6d partition functions for supersymmetric gauge theories based on
the topological vertex. We generalize the gluing techniques to little string
theories by introducing a new compact direction and compute their
supersymmetric partition functions on Omega-deformed $\mathbb{R}^4\times T^2$.
As concrete examples, we consider little string theories arising from Type IIB
NS5-branes probing $D_4$ or $D_5$ singularity. Their effective gauge theory
descriptions as the affine $D_4$ or $D_5$ quiver gauge theory can be realized
with quadrivalent or trivalent gluing, respectively. Based on these gluings of
5-brane webs, we compute their refined partition functions and compare them
with the known results. We extend the computation of the partition function to
little string theory engineered from IIB NS5-branes probing $E_6$ singularity
based on a trivalent gluing. We also discuss the generalization to higher rank
cases and the symmetries of the partition functions.
|
"Massive" Perturbative QCD, regular in the IR limit: The goal of research is to devise a modification of the perturbative QCD that
should be regular in the low-energy region and could serve as a practical means
for the analysis of data below 1 \GeV up to the IR limit. Recent observation of
the four-loop pQCD series "blow-up" in the region below 1 \GeV for the Bjorken
Sum Rule gave an impetus to this attempt. The proposed {\sf "massive analytic
pQCD"} is constructed on the two grounds. The first is the pQCD with only one
parameter added, the effective "glueball mass" $m_{gl}\lesssim 1 \GeV,$ serving
as an IR regulator. The second stems out of the ghost-free Analytic
Perturbation Theory comprising non-power perturbative expansion that makes it
compatible with linear integral transformations. In short, the proposed MAPT
differs from the minimal APT by simple ansatz $Q^2 \to Q^2+m_{gl}^2.$
|
Inflaton as an auxiliary topological field in a QCD-like system: We propose a new scenario for early cosmology, where inflationary de Sitter
phase dynamically occurs. The effect emerges as a result of dynamics of the
topologically nontrivial sectors in expanding universe. Technically the effect
can be described in terms of the auxiliary fields which effectively describe
the dynamics of the topological sectors in a gauge theory. Inflaton in this
framework is an auxiliary topological non-propagating field with no canonical
kinetic term, similar to known topologically ordered phases in condensed matter
systems. We explain many deep questions in this framework using the so-called
weakly coupled "deformed QCD" toy model.While this theory is weakly coupled
gauge theory, it preserves all the crucial elements of strongly interacting
gauge theory, including confinement, nontrivial $\theta$ dependence, degeneracy
of the topological sectors, etc. We discuss a specific realization of these
ideas using a scaled up version of QCD, coined as \qcd, with the scale
M_{PL}\gg \Lbar\gg \sqrt[3]{M_{EW}^2M_{PL}}\sim 10^8 {\mathrm{GeV}}. If no
other fields are present in the system de Sitter phase will be the final
destination of evolution of the universe. If other interactions are present in
the system, the inflationary de Sitter phase lasts for a finite period of time.
The inflation starts from the thermal equilibrium state long after the \qcd
-confinement phase transition at temperature T_{i}\sim
\Lbar\sqrt{\frac{\Lbar}{M_{PL}}}. The end of inflation is triggered by the
coupling with gauge bosons from the Standard Model. The corresponding
interaction is unambiguously fixed by the triangle anomaly. Number of e-folds
in the \qcd-inflation framework is determined by the gauge coupling constant at
the moment of inflation, and estimated as N_{\rm inf}\sim \alpha_s^{-2}\sim
10^2.
|
The Correlahedron: We introduce a new geometric object, the correlahedron, which we conjecture
to be equivalent to stress-energy correlators in planar N=4 super Yang-Mills.
Re-expressing the Grassmann dependence of correlation functions of n chiral
stress-energy multiplets with Grassmann degree 4k in terms of 4(n+k)-linear
bosonic variables, the resulting expressions have an interpretation as volume
forms on a Gr(n+k,4+n+k) Grassmannian, analogous to the expressions for planar
amplitudes via the amplituhedron. The resulting volume forms are to be
naturally associated with the correlahedron geometry. We construct such
expressions in this bosonised space both directly, in general, from Feynman
diagrams in twistor space, and then more invariantly from specific known
correlator expressions in analytic superspace. We give a geometric
interpretation of the action of the consecutive lightlike limit and show that
under this the correlahedron reduces to the squared amplituhedron both as a
geometric object as well as directly on the corresponding volume forms. We give
an explicit easily implementable algorithm via cylindrical decompositions for
extracting the squared amplituhedron volume form from the squared amplituhedron
geometry with explicit examples and discuss the analogous procedure for the
correlators.
|
Exact solutions and spacetime singularities in nonlocal gravity: We give here a list of exact classical solutions of a large class of weakly
nonlocal theories of gravity, which are unitary and super-renormalizable (or
finite) at quantum level. It is explicitly shown that flat and Ricci-flat
spacetimes as well as maximally symmetric manifolds are exact solutions of the
equation of motion. Therefore, well-known physical spacetimes like
Schwarzschild, Kerr, (Anti-) de Sitter serve as solutions for standard matter
content. In dimension higher than four we can also have Anti-de Sitter
solutions in the presence of positive cosmological constant. We pedagogically
show how to obtain these exact solutions. Furthermore, for another version of
the theory, written in the Weyl basis, Friedmann-Robertson-Walker (FRW)
spacetimes are also exact solutions, when the matter content is given by
conformal matter (radiation). We also comment on the presence of singularities
and possible resolution of them in finite and conformally invariant theories.
"Delocalization" is proposed as a way to solve the black hole singularity
problem. In order to solve the problem of cosmological singularities it seems
crucial to have a conformally invariant or asymptotically free quantum
gravitational theory.
|
W-Strings 93: We present a review of the status of $W$ string theories, their physical
spectra, and their interactions. (Based on review talks given at the Trieste
Spring Workshop, and the Strings 93 meeting at Berkeley, May 1993.)
|
Sonoluminescence: Photon production in time dependent analog system: Sonoluminescence is a well known laboratory phenomenon where an oscillating
gas bubble in the appropriate environment periodically emits a flash of light
in the visible frequency range. In this submission, we study the system in the
framework of analog gravity. We model the oscillating bubble in terms of analog
geometry and propose a non-minimal coupling prescription of the electromagnetic
field with the geometry. The geometry behaves as an analogous oscillating time
dependent background in which repeated flux of photons are produced in a wide
frequency range through parametric resonance from quantum vacuum. Due to our
numerical limitation, we could reach the frequency up to $\sim 10^5
~\mbox{m}^{-1}$. However, we numerically fit the spectrum in a polynomial form
including the observed frequency range around $\sim 10^7 ~\mbox{m}^{-1}$. Our
current analysis seems to suggest that parametric resonance in analog
background may play a fundamental role in explaining such phenomena in the
quantum field theory framework.
|
Planck mass and Dilaton field as a function of the noncommutative
parameter: A deformed Bianchi type I metric in noncommutative gauge gravity is obtained.
The gauge potential (tetrad fields) and scalar curvature are determined up to
the second order in the noncommutativity parameters. The noncommutativity
correction to the Einstein-Hilbert action is deduced. We obtain the Planck
mass, on noncommutative space-time as a function of the noncommutative
parameter {\theta}, which implies that noncommutativity has modified the
structure and topology of the space-time.
|
Free energy and entropy in Rindler and de Sitter space-times: We investigate the free energy and entropy of the Gaussian massive scalar
field theory in the static de Sitter space-time for arbitrary temperature. For
the inverse temperatures of the form $\beta=2 \pi 2^k, \ \ k\in \mathbf{Z}$, in
curvature units, we find the explicit form of the free energy and its
derivatives with respect to the temperature. There are two types of
contributions to the free energy: one is of the "area type" and can be
attributed to the horizon, while the other is of the "volume type" and is
associated with the interior of the space-time. The latter contribution in the
odd-dimensional case in the limit of the week field (large mass or small Hubble
constant) significantly depends on the temperature. Namely, for $ \beta<2\pi$,
the free energy behaves as $ F^{bulk}_{\beta} \sim e^{- \beta \, m} $, while
for $\beta>2\pi$ it behaves as $ F^{bulk}_{\beta} \sim e^{- 2 \, \pi \, m}$. We
also show that even the leading UV contributions to the free energy
significantly depend on the state of the theory, which is very unusual. We
explain the origin and physical meaning of these observations. As the model
example we consider the situation in the Rindler wedge of the flat space-time.
|
Constraint Dynamics and Gravitons in Three Dimensions: The complete non-linear three-dimensional Einstein gravity with gravitational
Chern-Simons term and cosmological constant are studied in dreibein
formulation. The constraints and their algebras are computed in an explicit
form. From counting the number of first and second class constraints, the
number of dynamical degrees of freedom, which equals to the number of
propagating graviton modes, is found to be 1, "regardless of" the value of
cosmological constant. I note also that the usual equivalence with Chern-Simons
gauge theory does "not" work for general circumstances.
|
Background field dependence from the Slavnov-Taylor identity in
(non-perturbative) Yang-Mills theory: We show that in Yang-Mills theory the Slavnov-Taylor (ST) identity, extended
in the presence of a background gauge connection, allows to fix in a unique way
the dependence of the vertex functional on the background, once the 1-PI
amplitudes at zero background are known. The reconstruction of the background
dependence is carried out by purely algebraic techniques and therefore can be
applied in a non-perturbative scheme (e.g. on the lattice or in the
Schwinger-Dyson approach), provided that the latter preserves the ST identity.
The field-antifield redefinition, which replaces the classical
background-quantum splitting when quantum corrections are taken into account,
is considered on the example of an instanton background in SU(2) Yang-Mills
theory.
|
Deformations of Lifshitz holography with the Gauss-Bonnet term in
($n+1$) dimensions: We investigate deformations of Gauss-Bonnet-Lifshitz holography in $(n+1)$
dimensional spacetime. Marginally relevant operators are dynamically generated
by a momentum scale $\Lambda \sim 0$ and correspond to slightly deformed
Gauss-Bonnet-Lifshitz spacetimes via a holographic picture. To admit
(non-trivial) sub-leading orders of the asymptotic solution for the marginal
mode, we find that the value of the dynamical critical exponent $z$ is
restricted by $z= n-1-2(n-2) \tilde{\alpha}$, where $\tilde{\alpha}$ is the
(rescaled) Gauss-Bonnet coupling constant. The generic black hole solution,
which is characterized by the horizon flux of the vector field and
$\tilde{\alpha}$, is obtained in the bulk, and we explore its thermodynamic
properties for various values of $n$ and $\tilde{\alpha}$.
|
Duality and Self-Duality (Energy Reflection Symmetry) of Quasi-Exactly
Solvable Periodic Potentials: A class of spectral problems with a hidden Lie-algebraic structure is
considered. We define a duality transformation which maps the spectrum of one
quasi-exactly solvable (QES) periodic potential to that of another QES periodic
potential. The self-dual point of this transformation corresponds to the
energy-reflection symmetry found previously for certain QES systems. The
duality transformation interchanges bands at the bottom (top) of the spectrum
of one potential with gaps at the top (bottom) of the spectrum of the other,
dual, potential. Thus, the duality transformation provides an exact mapping
between the weak coupling (perturbative) and semiclassical (nonperturbative)
sectors.
|
A Detailed Study of Bogomol'nyi Equations in Two-Dimensional Generalized
Maxwell-Higgs Model Using \textit{On-Shell} Method: We use a recent {\it on-shell} Bogomol'nyi method, developed
in~\cite{Atmaja:2014fha}, to construct Bogomol'nyi equations of the
two-dimensional generalized Maxwell-Higgs model~\cite{Bazeia:2012uc}. The
formalism can generate a large class of Bogomol'nyi equations parametrized by a
constant $C_0$. The resulting equations are classified into two types,
determined by $C_0=0$ and $C_0\neq0$. We identify that the ones obtained by
Bazeia {\it et al}~\cite{Bazeia:2012uc} are of the type $C_0=0$. We also
reveal, as in the case of ordinary vortex, that this theory does not admit
Bogomol'nyi equations in the Bogomol'nyi-Prasad-Sommerfield limit in its
spectrum. However, when the vacuum energy is lifted up by adding some constant
to the energy density then the existence of such equation is possible. Another
possibility whose energy is equal to the vacuum is also discussed in brief. As
a future of the \textit{on-shell} method, we find another new Bogomol'nyi
equations, for $C_0\neq0$, which are related to a non-trivial function defined
as a difference between energy density of potential term of the scalar field
and kinetic term of the gauge field.
|
Information geometry encoded in bulk geometry: We study how information geometry is described by bulk geometry in the
gauge/gravity correspondence. We consider a quantum information metric that
measures the distance between the ground states of a CFT and a theory obtained
by perturbing the CFT. We find a universal formula that represents the quantum
information metric in terms of back reaction to the AdS bulk geometry.
|
Duality for massive spin two theories in arbitrary dimensions: Using the parent Lagrangian approach we construct a dual formulation, in the
sense originally proposed by Curtright and Freund, of a massive spin two
Fierz-Pauli theory in arbitrary dimensions $D$. This is achieved in terms of a
mixed symmetry tensor $T_{A[B_{1}B_{2}... B_{D-2}]}$, without the need of
auxiliary fields. The relation of this method with an alternative formulation
based on a gauge symmetry principle proposed by Zinoviev is elucidated. We show
that the latter formulation in four dimensions, with a given gauge fixing
together with a definite sequence of auxiliary fields elimination via their
equations of motion, leads to the parent Lagrangian already considered by West
completed by a Fierz-Pauli mass term, which in turns yields the
Curtright-Freund action. This motivates our generalization to arbitrary
dimensions leading to the corresponding extension of the four dimensional
result. We identify the transverse true degrees of freedom of the dual theory
and verify that their number is in accordance with those of the massive
Fierz-Pauli field.
|
Causal three-point functions and nonlinear second-order hydrodynamic
coefficients in AdS/CFT: In the context of $\mathcal{N}=4$ SYM, we compute the finite 't Hooft
coupling $\lambda$ correction to the non-linear second-order hydrodynamic
coefficient $\lambda_3$ from a Kubo formula based on fully retarded three-point
functions using AdS/CFT. Although $\lambda_3$ is known to vanish in the
infinite 't Hooft coupling limit, we find that the finite $\lambda$ correction
is non-zero. We also present a set of Kubo formulae for the non-linear
coefficients $\lambda_{1,2,3}$, which is more convenient than the one that has
appeared recently elsewhere.
|
Open & Closed vs. Pure Open String Disk Amplitudes: We establish a relation between disk amplitudes involving N_o open and N_c
closed strings and disk amplitudes with only N_o+2N_c open strings. This map,
which represents a sort of generalized KLT relation on the disk, reveals
important structures between open & closed and pure open string disk
amplitudes: it relates couplings of brane and bulk string states to pure brane
couplings.
On the string world-sheet this becomes a non-trivial monodromy problem, which
reduces the disk amplitude of N_o open and N_c closed strings to a sum of many
color ordered partial subamplitudes of N_o+2N_c open strings. This sum can be
further reduced to a sum over (N_o+2N_c-3)! subamplitudes of N=N_o+2N_c open
strings only. Hence, the computation of disk amplitudes involving open and
closed strings is reduced to computing these subamplitudes in the open string
sector.
In this sector we find a string theory generalization and proof of the
Kleiss-Kuijf and Bern-Carrasco-Johanson relations: All order alpha' identities
between open string subamplitudes are derived, which reproduce these
field-theory relations in the limit alpha'->0. These identities allow to reduce
the number of independent subamplitudes of an open string N-point amplitude to
(N-3)!. This number is identical to the dimension of a minimal basis of
generalized Gaussian hypergeometric functions describing the full N-point open
string amplitude.
|
Energy-dependent topological anti-de Sitter black holes in Gauss-Bonnet
Born-Infeld gravity: Employing higher curvature corrections to Einstein--Maxwell gravity has
garnered a great deal of attention motivated by the high energy regime in
quantum nature of black hole physics. In addition, one may employ gravity's
rainbow to encode quantum gravity effects into the black hole solutions. In
this paper, we regard an energy dependent static spacetime with various
topologies and study its black hole solutions in the context of Gauss--Bonnet
Born--Infeld (GB--BI) gravity. We study thermodynamic properties and examine
the first law of thermodynamics. Using suitable local transformation, we endow
the Ricci--flat black hole solutions with a global rotation and study the
effects of rotation on thermodynamic quantities. We also investigate thermal
stability in canonical ensemble through calculating the heat capacity. We
obtain the effects of various parameters on the horizon radius of stable black
holes. Finally, we discuss second order phase transition in the extended phase
space thermodynamics and investigate the critical behavior.
|
On solvable models of type IIB superstring in NS-NS and R-R plane wave
backgrounds: We consider type IIB string in the two plane-wave backgrounds which may be
interpreted as special limits of the AdS_3 x S^3 metric supported by either the
NS-NS or R-R 3-form field. The NS-NS plane-wave string model is equivalent to a
direct generalization of the Nappi-Witten model, with its spectrum being
similar to that of strings in constant magnetic field. The R-R model can be
solved in the light-cone gauge, where the Green-Schwarz action describes 4
massive and 4 massless copies of free bosons and fermions. We find the spectra
of the two string models and study the asymptotic density of states. We also
discuss a more general class of exactly solvable plane-wave models with reduced
supersymmetry which is obtained by adding twists in two spatial 2-planes.
|
An N=2 gauge theory and its supergravity dual: We study flows on the scalar manifold of N=8 gauged supergravity in five
dimensions which are dual to certain mass deformations of N=4 super Yang--Mills
theory. In particular, we consider a perturbation of the gauge theory by a mass
term for the adjoint hyper-multiplet, giving rise to an N=2 theory. The exact
solution of the 5-dim gauged supergravity equations of motion is found and the
metric is uplifted to a ten-dimensional background of type-IIB supergravity.
Using these geometric data and the AdS/CFT correspondence we analyze the
spectra of certain operators as well as Wilson loops on the dual gauge theory
side. The physical flows are parametrized by a single non-positive constant and
describe part of the Coulomb branch of the N=2 theory at strong coupling. We
also propose a general criterion to distinguish between `physical' and
`unphysical' curvature singularities. Applying it in many backgrounds arising
within the AdS/CFT correspondence we find results that are in complete
agreement with field theory expectations.
|
Heisenberg versus the Covariant String: A Poincar\'e multiplet of mass eigenstates $\bigl(P^2 - m^2\bigr)\Psi = 0$
cannot be a subspace of a space with a $D$-vector position operator
$X=(X_0,\dots X_{D-1})$: the Heisenberg algebra $[P^m, X_n] = i \delta^m{}_n$
implies by a simple argument that each Poincar\'e multiplet of definite mass
vanishes.
The same conclusion follows from the Stone-von Neumann theorem.
In a quantum theory the constraint of an absolutely continuous spectrum to a
lower dimensional submanifold yields zero even if Dirac's treatment of the
corresponding classical constraint defines a symplectic submanifold with a
consistent corresponding quantum model. Its Hilbert space is not a subspace of
the unconstrained theory. Hence the operator relations of the unconstrained
model need not carry over to the constrained model.
Our argument excludes quantized worldline models of relativistic particles
and the physical states of the covariant quantum string.
We correct misconceptions about the generators of Lorentz transformations
acting on particles.
|
Nonhomogeneous Cooling, Entropic Gravity and MOND Theory: In this paper, by using the holographic principle, a modified equipartition
theorem where we assume that below a critical temperature the energy is not
equally divided on all bits, and the Unruh temperature, we derive MOND theory
and a modified Friedmann equation compatible with MOND theory. Furthermore, we
rederive a modified Newton's law of gravitation by employing an adequate
redefinition of the numbers of bits.
|
Emergent spinor fields from exotic spin structures: The classification of emergent spinor fields according to modified bilinear
covariants is scrutinized, in spacetimes with nontrivial topology, which induce
inequivalent spin structures. Extended Clifford algebras, constructed by
equipping the underlying spacetime with an extended bilinear form with
additional terms coming from the nontrivial topology, naturally yield emergent
extended algebraic spinor fields and their subsequent extended bilinear
covariants, which are constructed and contrasted to the classical spinor
classification. An unexpected duality between the standard and the exotic
spinor field classes is therefore established, showing that a complementary
fusion process among the spinor field classes sets in, when extended Clifford
bundles are addressed in multiply connected spacetimes.
|
Stochastic Motion of Heavy Quarks in Holography: A Theory-Independent
Treatment: Stochastic dynamics play a central role in strongly coupled phenomena. We
present and review a theory independent approach in holography to study such
phenomena. We firstly argue that the heavy quark diffusion occurs in realistic
strongly coupled systems. Then we analyze the quantum and thermal fluctuation,
dissipation and the corresponding Brownian motion of a heavy particle in such
environments for a wide class of theories. The holographic study is based on
the properties of the straight string fluctuations. The observables and
coefficients associated with the stochastic motion depend on a single parameter
which encodes the properties of the different theories. Moreover, certain
Dp-brane fluctuations can be mapped one-to-one to the string fluctuations and
therefore the stochastic brane observables can be read from the string ones.
Then we review the Langevin diffusion of a moving heavy quark in generic
thermal holographic theories. The analysis is based on the properties of the
trailing string and its fluctuations. The string world-sheet has a black hole
horizon and the quark feels an effective temperature different than the
environmental one. The formulas of the effective temperature, the drag force on
the particle and the Langevin coefficients are given in terms of the background
metric elements readily applicable to any theory. At the end we comment on the
backreaction effects on the medium and present results of the Monte Carlo
simulations.
|
Local observed time and redshift in curved spacetime: Using the observed time and spatial intervals defined originally by Einstein
and the observation frame in the vierbein formalism, we propose that in curved
spacetime, for a wave received in laboratories, the observed frequency is the
changing rate of the phase of the wave relative to the local observable time
scale and the momentum the changing rate of the phase relative to the local
observable spatial length scale. The case of Robertson-Walker universe is
especially considered.
|
D-Brane Boundary States in the Pure Spinor Superstring: We study the construction of D-brane boundary states in the pure spinor
formalism for the quantisation of the superstring. This is achieved both via a
direct analysis of the definition of D-brane boundary states in the pure spinor
conformal field theory, as well as via comparison between standard RNS and pure
spinor descriptions of the superstring. Regarding the map between RNS and pure
spinor formulations of the superstring, we shed new light on the tree level
zero mode saturation rule. Within the pure spinor formalism we propose an
explicit expression for the D-brane boundary state in a flat spacetime
background. While the non-zero mode sector mostly follows from a simple
understanding of the pure spinor conformal field theory, the zero mode sector
requires a deeper analysis which is one of the main points in this work. With
the construction of the boundary states at hand, we give a prescription for
calculating scattering amplitudes in the presence of a D-brane. Finally, we
also briefly discuss the coupling to the world-volume gauge field and show that
the D-brane low-energy effective action is correctly reproduced.
|
Weak Scale in Heterotic String: We investigate the possibility of lowering the string scale in four
dimensional heterotic models possessing a non-perturbative extension of the
gauge group. In particular, we consider a class of compactifications in which
the perturbative gauge sector is massive, and all the gauge bosons are
non-perturbative, with a coupling independent on the Planck and string scales.
|
Renormalization in Nonrelativistic Quantum Mechanics: The importance and usefulness of renormalization are emphasized in
nonrelativistic quantum mechanics. The momentum space treatment of both
two-body bound state and scattering problems involving some potentials singular
at the origin exhibits ultraviolet divergence. The use of renormalization
techniques in these problems leads to finite converged results for both the
exact and perturbative solutions. The renormalization procedure is carried out
for the quantum two-body problem in different partial waves for a minimal
potential possessing only the threshold behavior and no form factors. The
renormalized perturbative and exact solutions for this problem are found to be
consistent with each other. The useful role of the renormalization group
equations for this problem is also pointed out.
|
Matrix Model and Time-like Linear Dilaton Matter: We consider a matrix model description of the 2d string theory whose matter
part is given by a time-like linear dilaton CFT. This is equivalent to the c=1
matrix model with a deformed, but very simple fermi surface. Indeed, after a
Lorentz transformation, the corresponding 2d spacetime is a conventional linear
dilaton background with a time-dependent tachyon field. We show that the tree
level scattering amplitudes in the matrix model perfectly agree with those
computed in the world-sheet theory. The classical trajectories of fermions
correspond to the decaying D-branes in the time-like linear dilaton CFT. We
also discuss the ground ring structure. Furthermore, we study the properties of
the time-like Liouville theory by applying this matrix model description. We
find that its ground ring structure is very similar to that of the minimal
string.
|
Permutation branes and linear matrix factorisations: All the known rational boundary states for Gepner models can be regarded as
permutation branes. On general grounds, one expects that topological branes in
Gepner models can be encoded as matrix factorisations of the corresponding
Landau-Ginzburg potentials. In this paper we identify the matrix factorisations
associated to arbitrary B-type permutation branes.
|
The Perturbative Calculation of the Spin-Spin Correlation Function in
the Two Dimensional Ising Model: Using the variational formula for operator product coefficients a method for
perturbative calculation of the short-distance expansion of the Spin-Spin
correlation function in the two dimensional Ising model is presented. Results
of explicit calculation up to third order agree with known results from the
scaling limit of the lattice calculation.
|
Hydrodynamic Vortices and their Gravity Duals: In this talk we review analytical and numerical studies of hydrodynamic
vortices in conformal fluids and their gravity duals. We present two
conclusions. First, (3+1)-dimensional turbulence is within the range of
validity of the AdS/hydrodynamics correspondence. Second, the local equilibrium
of the fluid is equivalent to the ultralocality of the holographic
correspondence, in the sense that the bulk data at a given point is determined,
to any given precision, by the boundary data at a single point together with a
fixed number of derivatives. With this criterion we see that the cores of hot
and slow (3+1)-dimensional conformal generalizations of Burgers vortices are
everywhere in local equilibrium and their gravity duals are thus easily found.
On the other hand local equilibrium breaks down in the core of singular
(2+1)-dimensional vortices, but the holographic correspondence with Einstein
gravity may be used to define the boundary field theory in the region in which
the hydrodynamic description fails.
|
Operator bases, $S$-matrices, and their partition functions: Relativistic quantum systems that admit scattering experiments are
quantitatively described by effective field theories, where $S$-matrix
kinematics and symmetry considerations are encoded in the operator spectrum of
the EFT. In this paper we use the $S$-matrix to derive the structure of the EFT
operator basis, providing complementary descriptions in (i) position space
utilizing the conformal algebra and cohomology and (ii) momentum space via an
algebraic formulation in terms of a ring of momenta with kinematics implemented
as an ideal. These frameworks systematically handle redundancies associated
with equations of motion (on-shell) and integration by parts (momentum
conservation).
We introduce a partition function, termed the Hilbert series, to enumerate
the operator basis--correspondingly, the $S$-matrix--and derive a matrix
integral expression to compute the Hilbert series. The expression is general,
easily applied in any spacetime dimension, with arbitrary field content and
(linearly realized) symmetries.
In addition to counting, we discuss construction of the basis. Simple
algorithms follow from the algebraic formulation in momentum space. We
explicitly compute the basis for operators involving up to $n=5$ scalar fields.
This construction universally applies to fields with spin, since the operator
basis for scalars encodes the momentum dependence of $n$-point amplitudes.
We discuss in detail the operator basis for non-linearly realized symmetries.
In the presence of massless particles, there is freedom to impose additional
structure on the $S$-matrix in the form of soft limits. The most na\"ive
implementation for massless scalars leads to the operator basis for pions,
which we confirm using the standard CCWZ formulation for non-linear
realizations.
|
Exact expressions for $n$-point maximal $U(1)_Y$-violating integrated
correlators in $SU(N)$ $\mathcal{N}=4$ SYM: The exact expressions for integrated maximal $U(1)_Y$ violating (MUV)
$n$-point correlators in $SU(N)$ ${\mathcal N}=4$ supersymmetric Yang--Mills
theory are determined. The analysis generalises previous results on the
integrated correlator of four superconformal primaries and is based on
supersymmetric localisation. The integrated correlators are functions of $N$
and $\tau=\theta/(2\pi)+4\pi i/g_{_{YM}}^2$, and are expressed as
two-dimensional lattice sums that are modular forms with holomorphic and
anti-holomorphic weights $(w,-w)$ where $w=n-4$. The correlators satisfy
Laplace-difference equations that relate the $SU(N+1)$, $SU(N)$ and $SU(N-1)$
expressions and generalise the equations previously found in the $w=0$ case.
The correlators can be expressed as infinite sums of Eisenstein modular forms
of weight $(w,-w)$. For any fixed value of $N$ the perturbation expansion of
this correlator is found to start at order $( g_{_{YM}}^2 N)^w$. The
contributions of Yang--Mills instantons of charge $k>0$ are of the form $q^k\,
f(g_{_{YM}})$, where $q=e^{2\pi i \tau}$ and $f(g_{_{YM}})= O(g_{_{YM}}^{-2w})$
when $g_{_{YM}}^2 \ll 1$. Anti-instanton contributions have charge $k<0$ and
are of the form $\bar q^{|k|} \, \hat f(g_{_{YM}})$, where $\hat f(g_{_{YM}}) =
O(g_{_{YM}}^{2w})$ when $g_{_{YM}}^2 \ll 1$. Properties of the large-$N$
expansion are in agreement with expectations based on the low energy expansion
of flat-space type IIB superstring amplitudes. We also comment on the
identification of $n$-point free-field MUV correlators with the integrands of
$(n-4)$-loop perturbative contributions to the four-point correlator. In
particular, we emphasise the important r\^ole of $SL(2, \mathbb{Z})$-covariance
in the construction.
|
Non-Perturbative Particle Dynamics: We construct a non-perturbative, single-valued solution for the metric and
the motion of two interacting particles in ($2+1$)-Gravity, by using a Coulomb
gauge of conformal type. The method provides the mapping from multivalued (
minkowskian ) coordinates to single-valued ones, which solves the non-abelian
monodromies due to particles's momenta and can be applied also to the general
N-body case.
|
On generalized Melvin solutions for Lie algebras of rank 3: Generalized Melvin solutions for rank-$3$ Lie algebras $A_3$, $B_3$ and $C_3$
are considered. Any solution contains metric, three Abelian 2-forms and three
scalar fields. It is governed by three moduli functions $H_1(z),H_2(z),H_3(z)$
($z = \rho^2$ and $\rho$ is a radial variable), obeying three differential
equations with certain boundary conditions imposed. These functions are
polynomials with powers $(n_1,n_2, n_3) = (3,4,3), (6,10,6), (5,8,9)$ for Lie
algebras $A_3$, $B_3$, $C_3$, respectively. The solutions depend upon
integration constants $q_1, q_2, q_3 \neq 0$.
The power-law asymptotic relations for polynomials at large $z$ are governed
by integer-valued $3 \times 3$ matrix $\nu$, which coincides with twice the
inverse Cartan matrix $2 A^{-1}$ for Lie algebras $B_3$ and $C_3$, while in the
$A_3$ case $\nu = A^{-1} (I + P)$, where $I$ is the identity matrix and $P$ is
a permutation matrix, corresponding to a generator of the $\mathbb{Z}_2$-group
of symmetry of the Dynkin diagram. The duality identities for polynomials and
asymptotic relations for solutions at large distances are obtained. 2-form flux
integrals over a $2$-dimensional disc of radius $R$ and corresponding Wilson
loop factors over a circle of radius $R$ are presented.
|
Finite Density Effect in the Gross-Neveu Model in a Weakly Curved
$R^1\times S^2$ Spacetime: The three-dimensional Gross-Neveu model in $R^{1} \times S^{2}$ spacetime is
considered at finite particles number density. We evaluate an effective
potential of the composite scalar field $\sigma(x)$, which is expressed in
terms of a scalar curvature $R$ and nonzero chemical potential $\mu$. We then
derive the critical values of $(R,\mu)$ at which the system undergoes the first
order phase transition from the phase with broken chiral invariance to the
symmetric phase.
|
A ${\bf Z_2}$ Structure in the Configuration Space of Yang-Mills
Theories: We argue for the presence of a ${\bf Z}_2$ topological structure in the space
of static gauge-Higgs field configurations of $SU(2n)$ and $SO(2n)$ Yang-Mills
theories. We rigorously prove the existence of a ${\bf Z}_2$ homotopy group of
mappings from the 2-dim. projective sphere ${\bf R}P^2$ into $SU(2n)/{\bf Z}_2$
and $SO(2n)/{\bf Z}_2$ Lie groups respectively. Consequently the symmetric
phase of these theories admits infinite surfaces of odd-parity static and
unstable gauge field configurations which divide into two disconnected sectors
with integer Chern-Simons numbers $n$ and $n+1/2$ respectively. Such a ${\bf
Z}_2$ structure persists in the Higgs phase of the above theories and accounts
for the existence of $CS=1/2$ odd-parity saddle point solutions to the field
equations which correspond to spontaneous symmetry breaking mass scales.
|
AdS/CFT and Randall-Sundrum Model Without a Brane: We reformulate the Randall-Sundrum (RS) model on the compactified AdS by
adding a term proportional to the area of the boundary to the usual gravity
action with a negative cosmological constant and show that gravity can still be
localized on the boundary without introducing singular brane sources. The
boundary conditions now follow from the field equations, which are obtained by
letting the induced metric vary on the boundary. This approach gives similar
modes that are obtained in [1] and clarifies the complementarity of the RS and
the AdS/CFT pictures. Normalizability of these modes is checked by an
inner-product in the space of linearized perturbations. The same conclusions
hold for a massless scalar field in the bulk.
|
Ring wormholes via duality rotations: We apply duality rotations and complex transformations to the Schwarzschild
metric to obtain wormhole geometries with two asymptotically flat regions
connected by a throat. In the simplest case these are the well-known wormholes
supported by phantom scalar field. Further duality rotations remove the scalar
field to yield less well known vacuum metrics of the oblate Zipoy-Voorhees-Weyl
class, which describe ring wormholes. The ring encircles the wormhole throat
and can have any radius, whereas its tension is always negative and should be
less than $-c^4/4G$. If the tension reaches the maximal value, the geometry
becomes exactly flat, but the topology remains non-trivial and corresponds to
two copies of Minkowski space glued together along the disk encircled by the
ring. The geodesics are straight lines, and those which traverse the ring get
to the other universe. The ring therefore literally produces a hole in space.
Such wormholes could perhaps be created by negative energies concentrated in
toroidal volumes, for example by vacuum fluctuations.
|
Thouless energy in QCD and effects of diffusion modes on level
correlations of Dirac operator: The correlations of the QCD Dirac eigenvalues are studied with use of an
extended chiral random matrix model. The inclusion of spatial dependence which
the original model lacks enables us to investigate the effects of diffusion
modes. We get analytical expressions of level correlation functions with
non-universal behavior caused by diffusion modes which is characterized by
Thouless energy. Pion mode is shown to be responsible for these diffusion
effects when QCD vacuum is considered a disordered medium.
|
Partition functions of chiral gauge theories on the two dimensional
torus and their duality properties: Two different families of abelian chiral gauge theories on the torus are
investigated: the aim is to test the consistency of two-dimensional anomalous
gauge theories in the presence of global degrees of freedom for the gauge
field. An explicit computation of the partition functions shows that unitarity
is recovered in particular regions of parameter space and that the effective
dynamics is described in terms of fermionic interacting models. For the first
family, this connection with fermionic models uncovers an exact duality which
is conjectured to hold in the nonabelian case as well.
|
Cohomology and Decomposition of Tensor Product Representations of
SL(2,R): We analyze the decomposition of tensor products between infinite dimensional
(unitary) and finite-dimensional (non-unitary) representations of SL(2,R).
Using classical results on indefinite inner product spaces, we derive explicit
decomposition formulae, true modulo a natural cohomological reduction, for the
tensor products.
|
Classical dynamical $r$-matrices for the Chern-Simons formulation of
generalised 3d gravity: Classical dynamical $r$-matrices arise naturally in the combinatorial
description of the phase space of Chern-Simons theories, either through the
inclusion of dynamical sources or through a gauge-fixing procedure involving
two punctures. Here we consider classical dynamical $r$-matrices for the family
of Lie algebras which arise in the Chern-Simons formulation of 3d gravity, for
any value of the cosmological constant. We derive differential equations for
classical dynamical $r$-matrices in this case, and show that they can be viewed
as generalised complexifications, in a sense which we define, of the equations
governing dynamical $r$-matrices for $\mathfrak{su}(2)$ and
$\mathfrak{sl}(2,\mathbb{R})$. We obtain explicit families of solutions and
relate them, via Weierstrass factorisation, to solutions found by Feher, Gabor,
Marshall, Palla and Pusztai in the context of chiral WZWN models.
|
Low-Energy Kahler Potentials in Supersymmetric Gauge Theories with
(ALMOST) Flat Directions: We derive the supersymmetric low-energy effective theory of the D-flat
directions of a supersymmetric gauge theory. The Kahler potential of Affleck,
Dine and Seiberg is derived by applying holomorphic constraints which
manifestly maintain supersymmetry. We also present a simple procedure for
calculating all derivatives of the Kahler potential at points on the flat
direction manifold. Together with knowledge of the superpotential, these are
sufficient for a complete determination of the spectrum and the interactions of
the light degrees of freedom. We illustrate the method on the example of a
chiral abelian model, and comment on its application to more complicated
calculable models with dynamical supersymmetry breaking.
|
Born-Infeld Gravity with a Unique Vacuum and a Massless Graviton: We construct an n-dimensional Born-Infeld type gravity theory that has the
same properties as Einstein's gravity in terms of the vacuum and particle
content: Namely, the theory has a unique viable vacuum (maximally symmetric
solution) and a single massless unitary spin-2 graviton about this vacuum. The
BI gravity, in some sense, is the most natural, minimal generalization of
Einstein's gravity with a better UV behavior, and hence, is a potentially
viable proposal for low energy quantum gravity. The Gauss-Bonnet combination
plays a non-trivial role in the construction of the theory. As an extreme
example, we consider the infinite dimensional limit where an interesting
exponential gravity arises.
|
Nonlinear Magnetohydrodynamics from Gravity: We apply the recently established connection between nonlinear fluid dynamics
and AdS gravity to the case of the dyonic black brane in AdS_4. This yields the
equations of fluid dynamics for a 2+1 dimensional charged fluid in a background
magnetic field. We construct the gravity solution to second order in the
derivative expansion. From this we find the fluid dynamical stress tensor and
charge current to second and third order in derivatives respectively, along
with values for the associated transport coefficients.
|
A minimalistic pure spinor sigma-model in AdS: The $b$-ghost of the pure spinor formalism in a general curved background is
not holomorphic. For such theories, the construction of the string measure
requires the knowledge of the action of diffeomorphisms on the BV phase space.
We construct such an action for the pure spinor sigma-model in $AdS_5\times
S^5$. From the point of view of the BV formalism, this sigma-model belongs to
the class of theories where the expansion of the Master Action in antifields
terminates at the quadratic order. We show that it can be reduced to a simpler
degenerate sigma-model, preserving the AdS symmetries. We construct the action
of the algebra of worldsheet vector fields on the BV phase space of this
minimalistic sigma-model, and explain how to lift it to the original model.
|
Decompactification near the horizon and non-vanishing entropy: Intersecting D-brane configurations are related to black holes in D=4. Using
the standard way of compactification only the Reissner-Nordstr{\o}m black hole
is non-singular. In this paper we argue, that also the other black holes are
non-singular if i) we compactify over a periodic array and ii) we allow the
string metric after reaching a critical curvature to choose the dual geometry.
Effectively this means that near the horizon the solution completely
decompactifies and chooses a non-singular D-brane configuration.
|
Holographic Entropy Production: The suspicion that gravity is holographic has been supported mainly by a
variety of specific examples from string theory. In this paper, we propose that
such a holography can actually be observed in the context of Einstein's gravity
and at least a class of generalized gravitational theories, based on a definite
holographic principle where neither is the bulk space-time required to be
asymptotically AdS nor the boundary to be located at conformal infinity,
echoing Wilson's formulation of quantum field theory. After showing the general
equilibrium thermodynamics from the corresponding holographic dictionary, in
particular, we provide a rather general proof of the equality between the
entropy production on the boundary and the increase of black hole entropy in
the bulk, which can be regarded as strong support to this holographic
principle. The entropy production in the familiar holographic
superconductors/superfluids is investigated as an important example, where the
role played by the holographic renormalization is explained.
|
Fluid-gravity and membrane-gravity dualities - Comparison at subleading
orders: In this note we have compared two different perturbation techniques that
could be used to generate solutions of Einstein's equations in presence of
negative cosmological constant. One of these two methods is derivative
expansion and the other is an expansion in inverse powers of dimension. Both
the techniques generate space-time with a singularity shielded by a dynamical
event horizon. We have shown that in the appropriate regime of parameter space
and with appropriate choice of coordinates, the metrics and corresponding
horizon dynamics, generated by these two different techniques, are exactly
equal to the order the solutions are known both sides. This work is essentially
extension of \cite{prevwork} where the authors have shown the equivalence of
the two techniques up to the first non-trivial order.
|
The particle number in Galilean holography: Recently, gravity duals for certain Galilean-invariant conformal field
theories have been constructed. In this paper, we point out that the spectrum
of the particle number operator in the examples found so far is not a necessary
consequence of the existence of a gravity dual. We record some progress towards
more realistic spectra. In particular, we construct bulk systems with
asymptotic Schrodinger symmetry and only one extra dimension. In examples, we
find solutions which describe these Schrodinger-symmetric systems at finite
density. A lift to M-theory is used to resolve a curvature singularity. As a
happy byproduct of this analysis, we realize a state which could be called a
holographic Mott insulator.
|
On the Integrability of the Bukhvostov-Lipatov Model: The integrability of the Bukhvostov-Lipatov four-fermion model is
investigated. It is shown that the classical model possesses a current of
Lorentz spin 3, conserved both in the bulk and on the half-line for specific
types of boundary actions. It is then established that the conservation law is
spoiled at the quantum level -- a fact that might indicate that the quantum
Bukhvostov-Lipatov model is not integrable, contrary to what was previously
believed.
|
Supersymmetry in the Non-Commutative Plane: The supersymmetric extension of a model introduced by Lukierski, Stichel and
Zakrewski in the non-commutative plane is studied. The Noether charges
associated to the symmetries are determined. Their Poisson algebra is
investigated in the Ostrogradski--Dirac formalism for constrained Hamiltonian
systems. It is shown to provide a supersymmetric generalization of the Galilei
algebra with a two-dimensional central extension.
|
Supersymmetric theories on squashed five-sphere: We construct supersymmetric theories on the SU(3)xU(1) symmetric squashed
five-sphere with 2, 4, 6, and 12 supercharges. We first determine the Killing
equation by dimensional reduction from 6d, and use Noether procedure to
construct actions. The supersymmetric Yang-Mills action is straightforwardly
obtained from the supersymmetric Chern-Simons action by using a supersymmetry
preserving constant vector multiplet.
|
Black Holes, Dark Wormholes and Solitons in f(T) Gravities: By choosing an appropriate vielbein basis, we obtain a class of
spherically-symmetric solutions in $f(T)$ gravities. The solutions are
asymptotic to Minkowski spacetimes with leading falloffs the same as those of
the Schwarzschild black hole. In general, these solutions have branch-cut
singularities in the middle. For appropriately chosen $f(T)$ functions,
extremal black holes can also emerge. Furthermore, we obtain wormhole
configurations whose spatial section is analogous to an Ellis wormhole, but
$-g_{tt}$ runs from 0 to 1 as the proper radial coordinate runs from $-\infty$
to $+\infty$. Thus a signal sent from $-\infty$ to $+\infty$ through the
wormhole will be infinitely red-shifted. We call such a spacetime configuration
a dark wormhole. By introducing a bare cosmological constant $\Lambda_0$, we
construct smooth solitons that are asymptotic to local AdS with an effective
$\Lambda_{\rm eff}$. In the middle of bulk, the soliton metric behaves like the
AdS of bare $\Lambda_0$ in global coordinates. We also embed AdS planar and
Lifshitz black holes in $f(T)$ gravities. Finally we couple the Maxwell field
to the $f(T)$ theories and construct electrically-charged solutions.
|
On Geometric Transitions in String Compactifications: We reconsider the study of the geometric transitions and brane/flux dualities
in various dimensions. We first give toric interpretations of the topology
changing transitions in the Calabi-Yau conifold and the $Spin(7)$ manifold. The
latter, for instance, can be viewed as three intersecting Calabi-Yau conifolds
according to $\cp^2$ toric graph. Orbifolds of such geometries are given in
terms of del Pezzo complex surfaces. Second we propose a four-dimensional
F-theory interpretation of type IIB geometric transitions on the Calabi-Yau
conifold. This gives a dual description of the M-theory flop in terms of toric
mirror symmetry. In two dimensions, we study the geometric transition in a
singular $Spin(7)$ manifold constructed as a cone on SU(3)/U(1). In particular,
we discuss brane/flux duality in such a compactification in both type IIA and
type IIB superstrings. These examples preserve one supercharge and so have
${\cal N}= 1/2$ supersymmetry in two dimensions. Then, an interpretation in
terms of F-theory is given.
|
Worldline Path Integrals for Fermions with Scalar, Pseudoscalar and
Vector Couplings: A systematic derivation is given of the worldline path integrals for the
effective action of a multiplet of Dirac fermions interacting with general
matrix-valued classical background scalar, pseudoscalar, and vector gauge
fields. The first path integral involves worldline fermions with antiperiodic
boundary conditions on the worldline loop and generates the real part of the
one loop (Euclidean) effective action. The second path integral involves
worldline fermions with periodic boundary conditions and generates the
imaginary part of the (Euclidean) effective action, i.e. the phase of the
fermion functional determinant. Here we also introduce a new regularization for
the phase of functional determinants resembling a heat-kernel regularization.
Compared to the known special cases, our worldline Lagrangians have a number of
new interaction terms; the validity of some of these terms is checked in
perturbation theory. In particular, we obtain the leading order contribution
(in the heavy mass expansion) to the Wess-Zumino-Witten term, which generates
the chiral anomaly.
|
Duality Symmetries for N=2 Supersymmetric QCD with Vanishing
beta-Functions: We construct the duality groups for N=2 Supersymmetric QCD with gauge group
SU(2n+1) and N_f=4n+2 hypermultiplets in the fundamental representation. The
groups are generated by two elements $S$ and $T$ that satisfy a relation
$(STS^{-1}T)^{2n+1}=1$. Thus, the groups are not subgroups of $SL(2,Z)$. We
also construct automorphic functions that map the fundamental region of the
group generated by $T$ and $STS$ to the Riemann sphere. These automorphic
functions faithfully represent the duality symmetry in the Seiberg-Witten
curve.
|
Schwinger-Dyson approach to Liouville Field Theory: We discuss Liouville field theory in the framework of Schwinger-Dyson
approach and derive a functional equation for the three-point structure
constant. We argue the existence of a second Schwinger-Dyson equation on the
basis of the duality between the screening charge operators and obtain a second
functional equation for the structure constant. We discuss the utility of the
two functional equations to fix the structure constant uniquely.
|
Back Reaction to Rotating Detector: It has been a puzzle that rotating detector may respond even in the
appropriate vacuum defined via canonical quantization. We solve this puzzle by
taking back reaction of the detector into account. The influence of the back
reaction, even in the detector's mass infinite limit, appears in the response
function. It makes the detector possible to respond in the vacuum if the
detector is rotating, though the detector in linear uniform motion never
respond in the vacuum as expected from Poincare invariance.
|
Conformal Invariance in the Long-Range Ising Model: We consider the question of conformal invariance of the long-range Ising
model at the critical point. The continuum description is given in terms of a
nonlocal field theory, and the absence of a stress tensor invalidates all of
the standard arguments for the enhancement of scale invariance to conformal
invariance. We however show that several correlation functions, computed to
second order in the epsilon expansion, are nontrivially consistent with
conformal invariance. We proceed to give a proof of conformal invariance to all
orders in the epsilon expansion, based on the description of the long-range
Ising model as a defect theory in an auxiliary higher-dimensional space. A
detailed review of conformal invariance in the d-dimensional short-range Ising
model is also included and may be of independent interest.
|
On three-point functions in ABJM and the latitude Wilson loop: I consider three-point functions of twist-one operators in ABJM at weak
coupling. I compute the structure constant of correlators involving one
twist-one un-protected operator and two protected ones for a few finite values
of the spin, up to two-loop order. As an application I enforce a limit on the
gauge group ranks, in which I relate the structure constant for three chiral
primary operators to the expectation value of a supersymmetric Wilson loop.
Such a relation is then used to perform a successful five-loop test on the
matrix model conjectured to describe the supersymmetric Wilson loop.
|
Perturbations of General Relativity to All Orders and the General
$n^{\rm th}$ Order Terms: We derive all-order expressions for perturbations of the Einstein-Hilbert
action and the Einstein equation with the general $n$-th order terms. To this
end, we employ Cheung and Remmen's perturbation conventions both in tensor
density and the usual metric tensor formalisms, including the Einstein-dilaton
theory. Remarkably, we find minimal building blocks that generate the entire
perturbations for each of our formulations. We show that the number of terms of
perturbations grows linearly as the order of perturbations increases. We regard
our results as the reference and discuss how to derive perturbations in other
conventions from the reference. As a consistency check, we compute graviton
scattering amplitudes using the perturbiner method based on the perturbative
Einstein equation. Finally we discuss how to generalise the results to curved
backgrounds and incorporate additional matter.
|
Basic quantizations of $D=4$ Euclidean, Lorentz, Kleinian and
quaternionic $\mathfrak{o}^{\star}(4)$ symmetries: We construct firstly the complete list of five quantum deformations of $D=4$
complex homogeneous orthogonal Lie algebra $\mathfrak{o}(4;\mathbb{C})\cong
\mathfrak{o}(3;\mathbb{C})\oplus \mathfrak{o}(3;\mathbb{C})$, describing
quantum rotational symmetry of four-dimensional complex space-time, in
particular we provide the corresponding universal quantum $R$-matrices. Further
applying four possible reality conditions we obtain all sixteen Hopf-algebraic
quantum deformations for the real forms of $\mathfrak{o}(4;\mathbb{C})$:
Euclidean $\mathfrak{o}(4)$, Lorentz $\mathfrak{o}(3,1)$, Kleinian
$\mathfrak{o}(2,2)$ and quaternionic $\mathfrak{o}^{\star}(4)$. For
$\mathfrak{o}(3,1)$ we only recall well-known results obtained previously by
the authors, but for other real Lie algebras (Euclidean, Kleinian,
quaternionic) as well as for the complex Lie algebra
$\mathfrak{o}(4;\mathbb{C})$ we present new results.
|
Review of Open Superstring Field Theory: I review the construction of an action for open superstring field theory
which does not suffer from the contact term problems of other approaches. This
action resembles a Wess-Zumino-Witten action and can be constructed in a
manifestly D=4 super-Poincar\'e covariant manner. This review is based on
lectures given at the ICTP Latin-American String School in Mexico City and the
Komaba 2000 Workshop in Tokyo.
|
Nontrivial realization of the space-time translations in the theory of
quantum fields: In standard quantum field theory, the one-particle states are classified by
unitary representations of the Poincar\'e group, whereas the causal fields'
classification employs the finite dimensional (non-unitary) representations of
the (homogeneous) Lorentz group. A natural question arises - why the fields are
not allowed to transform nontrivially under translations? We investigate this
issue by considering the fields that transform under the full representation of
the Poincar\'e group. It follows that such fields can be consistently
constructed, although the Lagrangians that describe them necessarily exhibit
explicit dependence on the space-time coordinates. The two examples of the
Poincar\'e-spinor and the Poincar\'e-vector fields are considered in details.
The inclusion of Yang--Mills type interactions is considered on the simplest
example of the U(1) gauge theory. The generalization to the non-abelian case is
straightforward so long as the action of the gauge group on fields is
independent of the action of the Poincar\'e group. This is the case for all the
known interactions but gravity.
|
Interpolation of partial and full supersymmetry breakings in $\cal{N} =
2$ supergravity: We discuss an $\cal{N}=2$ supergravity model that interpolates the full and
the partial supersymmetry breakings. In particular, we find the conditions for
an $\cal{N}=0$ Minkowski vacuum, which is continuously connected to the
partial-breaking ($\cal{N}=1$ preserving) one. The model contains multiple
(Abelian) vector multiplets and a single hypermultiplet, and is constructed by
employing the embedding tensor technique. We compute the mass spectrum on the
Minkowski vacuum, and find some non-trivial mass relations among the massive
fields. Our model allows us to choose the two supersymmetry-breaking scales
independently, and to discuss the cascade supersymmetry breaking for the
applications to particle phenomenology and cosmology.
|
Strong/weak duality symmetries for Jacobi--Gordon field theory through
elliptic functions: By using the scheme of Jacobi elliptic functions with their duality
symmetries we present a formulation of the Jacobi- Gordon field theory that
will manifest the strong/weak coupling duality at classical level; for certain
continuous limits for the elliptic modulus the model will reduce to the
standard sin/sinh Gordon field theories, for which such a strong/weak duality
is known only at the level of the S-matrix. It is shown that the so called
self-dual point for the standard sin/sinh Gordon field theory that divides the
strong and the weak coupling regimes, corresponds only to one point of a set of
fixed points under the duality transformations for the elliptic functions. The
potentials constructed in terms of elliptic functions have a critical behavior
near that self-dual point, showing a change of topology; in the weak coupling
regime the vacuum topology implies that there exists the possibility of
formation of topological defects, and in the strong regime coupling there no
exists the possibility of formation of those defects. Furthermore, the
equations of motion can be solved in exact form in terms of the inverse
elliptic functions; in a case the kink-like solitons asso\-cia\-ted with the
maxima of the potential can decay to cusp-like solitons associated with the
minima. The polynomial expansions of the generalized models show a critical
behavior at certain self-dual points; such points define the regions where the
spontaneous symmetry breaking scenarios are po\-ssi\-ble. By invoking the
duality symmetries for the elliptic functions, an explicit relation between the
original potentials and their dual versions are constructed; with this
relationship,
an approaching to a specific self-dual point is considered for our
generalized models.
|
Higgs phases at non-zero density from holography: We show how Higgs phases at non-zero density can be described using a simple
analytic method for gauge theories possessing a holographic dual. We introduce
co-dimension one branes in a bottom-up gravity dual that are sources of form
flux, such that the effective curvature radius is changed when the brane is
crossed. This mimics the expected flow produced by color branes nucleating in a
top-down model.
|
Semiclassical short strings in AdS_5 x S^5: We present results for the one-loop correction to the energy of a class of
string solutions in AdS_5 x S^5 in the short string limit. The computation is
based on the observation that, as for rigid spinning string elliptic solutions,
the fluctuation operators can be put into the single-gap Lame' form. Our
computation reveals a remarkable universality of the form of the energy of
short semiclassical strings. This may help to understand better the structure
of the strong coupling expansion of the anomalous dimensions of dual gauge
theory operators.
|
A Correction to the Hamiltonian of the QCD String with Quarks due to the
Rigidity Term: A correction to the Hamiltonian of the quark-antiquark system, arising due to
the rigidity term in the gluodynamics string effective action, is obtained.
This correction contains additional contributions to the orbital momentum of
the system and several higher derivative operators. With the help of the
derived Hamiltonian a rigid string-induced term in the Hamiltonian of the
relativistic quark model is evaluated for the case of large masses of a quark
and antiquark.
|
Feshbach-Villars oscillator (FVO) in Kaluza-Klein Theory (KKT): This research investigates the relativistic quantum dynamics of spin-0 scalar
massive charged particles via the relativistic Feshbach-Villars oscillator in
the background of the Kaluza-Klein Theory. We solve the Feshbach-Villars
equation in the abckground of a cosmic string spec-time in the context of the
Kaluza-Klein and presented the eigenvalue solution. Afterward, we rewrite this
system in the case of the Feshbach-Villars quantum oscillator and obtain the
eigenvalue analytically. Finally, we study the interaction of the
Feshbach-Villars equation and oscillator in a cosmic dislocation in the
Som-Raychaudhuri in the context of the Kaluza-Klein Theory and solve the wave
equation analytically. We analyze the influence of topological defect in the
quantification of energy and wave function of the Feshbach-Villars oscillator
and with the external fields in the last one
|
Celestial $w_{1+\infty}$ Symmetries from Twistor Space: We explain how twistor theory represents the self-dual sector of four
dimensional gravity in terms of the loop group of Poisson diffeomorphisms of
the plane via Penrose's non-linear graviton construction. The symmetries of the
self-dual sector are generated by the corresponding loop algebra
$Lw_{1+\infty}$ of the algebra $w_{1+\infty}$ of these Poisson diffeomorphisms.
We show that these coincide with the infinite tower of soft graviton symmetries
in tree-level perturbative gravity recently discovered in the context of
celestial amplitudes. We use a twistor sigma model for the self-dual sector
which describes maps from the Riemann sphere to the asymptotic twistor space
defined from characteristic data at null infinity ${\mathcal I}$. We show that
the OPE of the sigma model naturally encodes the Poisson structure on twistor
space and gives rise to the celestial realization of $Lw_{1+\infty}$. The
vertex operators representing soft gravitons in our model act as currents
generating the wedge algebra of $w_{1+\infty}$ and produce the expected
celestial OPE with hard gravitons of both helicities. We also discuss how the
two copies of $Lw_{1+\infty}$, one for each of the self-dual and anti-self-dual
sectors, are represented in the OPEs of vertex operators of the 4d ambitwistor
string.
|
Towards Classification of $\mathcal{N}=1$ and $\mathcal{N}=0$ Flipped
$SU(5)$ Asymmetric $\mathbb{Z}_2 \times \mathbb{Z}_2$ Heterotic String
Orbifolds: The free fermionic classification method provides a powerful tool to
investigate string vacua, which led to the discovery of spinor--vector duality
and exophobic string models. We extend the classification methodology to both
$\mathcal{N}=1$ and $\mathcal{N}=0$ Flipped $SU(5)$ $\mathbb{Z}_2 \times
\mathbb{Z}_2$ heterotic string orbifolds with asymmetric shifts. The impact of
the asymmetric assignments on the phenomenological characteristics of these
models is investigated. Of particular interest is the analysis of untwisted
moduli fixing for various choices of asymmetric boundary conditions. Two
classes of vacua with different characteristics are systematically investigated
with help from SAT/SMT algorithms, which are shown to increase search
efficiency by up to two orders of magnitude, as well as providing useful tools
to find contradictions between various phenomenological criteria. The general
form of the partition function for the space of models is explained and given
for two specific example models for different choices of asymmetric boundary
conditions. Additionally, the distribution of one-loop cosmological constant
contributions for samples in the two different classes of models are depicted
and discussed.
|
Lower-dimensional pure-spinor superstrings: We study to what extent it is possible to generalise Berkovits' pure-spinor
construction in d=10 to lower dimensions. Using a suitable definition of a
``pure'' spinor in d=4,6, we propose models analogous to the d=10 pure-spinor
superstring in these dimensions. Similar models in d=2,3 are also briefly
discussed.
|
Gauged twistor formulation of a massive spinning particle in four
dimensions: We present a gauged twistor model of a free massive spinning particle in
four-dimensional Minkowski space. This model is governed by an action, referred
to here as the gauged generalized Shirafuji (GGS) action, that consists of
twistor variables, auxiliary variables, and $U(1)$ and $SU(2)$ gauge fields on
the one-dimensional parameter space of a particle's worldline. The GGS action
remains invariant under reparametrization and the local $U(1)$ and $SU(2)$
transformations of the relevant variables, although the $SU(2)$ symmetry is
nonlinearly realized. We consider the canonical Hamiltonian formalism based on
the GGS action in the unitary gauge by following Dirac's recipe for constrained
Hamiltonian systems. It is shown that just sufficient constraints for the
twistor variables are consistently derived by virtue of the gauge symmetries of
the GGS action. In the subsequent quantization procedure, these constraints
turn into simultaneous differential equations for a twistor function. We
perform the Penrose transform of this twistor function to define a massive
spinor field of arbitrary rank, demonstrating that the spinor field satisfies
generalized Dirac-Fierz-Pauli equations with $SU(2)$ indices. We also
investigate the rank-one spinor fields in detail to clarify the physical
meanings of the $U(1)$ and $SU(2)$ symmetries.
|
Transport Coefficients at Zero Temperature from Extremal Black Holes: Using the AdS/CFT correspondence we study transport coefficients of a
strongly-coupled (2 +1)-dimensional field theory at {\it zero} temperature and
finite charge density. The field theory under consideration is dual to the
extremal Reissner-Nordstrom AdS_4 black hole in the bulk. We show that, like
the cases of scalar and spinor operators studied in \cite{Faulkner:2009wj}, the
correlators of charge (vector) current and energy-momentum (tensor) operators
exhibit scaling behavior at low frequency. The existence of such low frequency
behavior is related to the fact that the near-horizon geometry of the extremal
black hole background has an AdS_2 factor. We carefully calculate the shear
viscosity (at zero temperature) and show that the ratio of the shear viscosity
to the entropy density takes the value of 1/4\pi. Because of the AdS_2 factor,
we argue that this result stays the same for all d-dimensional boundary field
theories dual to the extremal Reissner-Nordstrom AdS_{d+1} black holes. Also,
we compute the charge conductivity at zero temperature. The limiting behavior
of the conductivity for small frequencies is also attributed to the near
horizon AdS_2 factor and is argued to hold regardless of the dimension of the
zero-temperature boundary field theory. Finally, using the extremal dyonic
AdS_4 black hole as the background, we extract the conductivity in the presence
of a constant magnetic field.
|
Note About Integrability and Gauge Fixing for Bosonic String on
AdS(5)xS(5): This short note is devoted to the study of the integrability of the bosonic
string on AdS(5)xS(5) in the uniform light-cone gauge. We construct Lax
connection for gauge fixed theory and we argue that it is flat.
|
Information Loss in Black Holes: The question of whether information is lost in black holes is investigated
using Euclidean path integrals. The formation and evaporation of black holes is
regarded as a scattering problem with all measurements being made at infinity.
This seems to be well formulated only in asymptotically AdS spacetimes. The
path integral over metrics with trivial topology is unitary and information
preserving. On the other hand, the path integral over metrics with non-trivial
topologies leads to correlation functions that decay to zero. Thus at late
times only the unitary information preserving path integrals over trivial
topologies will contribute. Elementary quantum gravity interactions do not lose
information or quantum coherence.
|
Super Coherent States, Boson-Fermion Realizations and Representations of
Superalgebras: Super coherent states are useful in the explicit construction of
representations of superalgebras and quantum superalgebras. In this
contribution, we describe how they are used to construct (quantum)
boson-fermion realizations and representations of (quantum) superalgebras. We
work through a few examples: $osp(1|2)$ and its quantum version
$U_t[osp(1|2)]$, $osp(2|2)$ in the non-standard and standard bases and
$gl(2|2)$ in the non-standard basis. We obtain free boson-fermion realizations
of these superalgebras. Applying the boson-fermion realizations, we explicitly
construct their finite-dimensional representations. Our results are expected to
be useful in the study of current superalgebras and their corresponding
conformal field theories.
|
A defect in holographic interpretations of tensor networks: We initiate the study of how tensor networks reproduce properties of static
holographic space-times, which are not locally pure anti-de Sitter. We consider
geometries that are holographically dual to ground states of defect, interface
and boundary CFTs and compare them to the structure of the requisite MERA
networks predicted by the theory of minimal updates. When the CFT is deformed,
certain tensors require updating. On the other hand, even identical tensors can
contribute differently to estimates of entanglement entropies. We interpret
these facts holographically by associating tensor updates to turning on
non-normalizable modes in the bulk. In passing, we also clarify and complement
existing arguments in support of the theory of minimal updates, propose a novel
ansatz called rayed MERA that applies to a class of generalized interface CFTs,
and analyze the kinematic spaces of the thin wall and AdS3-Janus geometries.
|
Fermion Determinants: The current status of bounds on and limits of fermion determinants in two,
three and four dimensions in QED and QCD is reviewed. A new lower bound on the
two-dimensional QED determinant is derived. An outline of the demonstration of
the continuity of this determinant at zero mass when the background magnetic
field flux is zero is also given.
|
Exotic twisted equivariant cohomology of loop spaces, twisted
Bismut-Chern character and T-duality: We define exotic twisted $S^1$-equivariant cohomology for the loop space $LZ$
of a smooth manifold $Z$ via the invariant differential forms on $LZ$ with
coefficients in the (typically non-flat) holonomy line bundle of a gerbe, with
differential an equivariantly flat superconnection. We introduce the twisted
Bismut-Chern character form, a loop space refinement of the twisted Chern
character form, which represent classes in the completed periodic exotic
twisted $S^1$-equivariant cohomology of $LZ$. We establish a localisation
theorem for the completed periodic exotic twisted $S^1$-equivariant cohomology
for loop spaces and apply it to establish T-duality in a background flux in
type II String Theory from a loop space perspective.
|
Conformal Symmetry and the Three Point Function for the Gravitational
Axial Anomaly: This work presents a first study of a radiative calculation for the
gravitational axial anomaly in the massless Abelian Higgs model. The two loop
contribution to the anomalous correlation function of one axial current and two
energy-momentum tensors, <A_alpha(z) T_\mu\nu(y) T_\rho\sigma(x)>, is computed
at an order that involves only internal matter fields. Conformal properties of
massless field theories are used in order to perform the Feynman diagram
calculations in the coordinate space representation. The two loop contribution
is found not to vanish, due to the presence of two independent tensor
structures in the anomalous correlator.
|
Romans-mass-driven flows on the D2-brane: The addition of supersymmetric Chern-Simons terms to ${\cal N}=8$
super-Yang-Mills theory in three-dimensions is expected to make the latter flow
into infrared superconformal phases. We address this problem holographically by
studying the effect of the Romans mass on the D2-brane near-horizon geometry.
Working in a consistent, effective four-dimensional setting provided by $D=4$
${\cal N}=8$ supergravity with a dyonic $\textrm{ISO(7)}$ gauging, we verify
the existence of a rich web of supersymmetric domain walls triggered by the
Romans mass that interpolate between the (four-dimensional description of the)
D2-brane and various superconformal phases. We also construct domain walls for
which both endpoints are superconformal. While most of our results are
numerical, we provide analytic results for the $\textrm{SU}(3)\times
\textrm{U}(1)$-invariant flow into an ${\cal N}=2$ conformal phase recently
discovered.
|
Superfield Effective Action in the Noncommutative Wess-Zumino Model: We introduce the concept of superfield effective action in noncommutative N=1
supersymmetric field theories containing chiral superfields. One and two loops
low-energy contributions to the effective action are found for the
noncommutative Wess-Zumino model. The one loop Kahlerian effective potential
coincides with its commutative counterpart. We show that the two loops
nonplanar contributions to the Kahlerian effective potential are leading in the
case of small noncommutativity. The structure of the leading chiral corrections
to the effective action and the behaviour of the chiral effective potential in
the limit of large noncommutativity are also investigated.
|
NS-NS Sector of Closed Superstring Field Theory: We give a construction for a general class of vertices in superstring field
theory which include integration over bosonic moduli as well as the required
picture changing insertions. We apply this procedure to find a covariant action
for the NS-NS sector of Type II closed superstring field theory.
|
Stimulated emission of particles by 1+1 dimensional black holes: The stimulated emission of massless bosons by a relativistic and the CGHS
black hole are studied for real and complex scalar fields. The radiations
induced by one-particle and thermal states are considered and their thermal
properties investigated near the horizon. These exhibit both thermal and
non-thermal properties for the two black-hole models.
|
E-string Quantum Curve: In this work we study the quantisation of the Seiberg-Witten curve for the
E-string theory compactified on a two-torus. We find that the resulting
operator expression belongs to the class of elliptic quantum curves. It can be
rephrased as an eigenvalue equation with eigenvectors corresponding to
co-dimension 2 defect operators and eigenvalues to co-dimension 4 Wilson
surfaces wrapping the elliptic curve, respectively. Moreover, the operator we
find is a generalised version of the van Diejen operator arising in the study
of elliptic integrable systems. Although the microscopic representation of the
co-dimension 4 defect only furnishes an $\mathrm{SO}(16)$ flavour symmetry in
the UV, we find an enhancement in the IR to representations in terms of affine
$E_8$ characters. Finally, using the Nekrasov-Shatashvili limit of the E-string
BPS partition function, we give a path integral derivation of the quantum
curve.
|
Scale-dependent (2+1) - dimensional electrically charged black holes in
Einstein-power-Maxwell theory: In this work we extend and generalize our previous work on the scale
dependence at the level of the effective action of black holes in the presence
of non-linear electrodynamics. In particular, we consider the
Einstein-power-Maxwell theory without a cosmological constant in (2+1)
dimensions, assuming a scale dependence of both the gravitational and the
electromagnetic coupling and we investigate in detail how the scale--dependent
scenario affects the horizon and thermodynamic properties of the classical
black holes for any value of the power parameter. In addition, we solve the
corresponding effective field equations imposing the "null energy condition" in
order to obtain analytical solutions. The implications of quantum corrections
are also briefly discussed.
|
Effects of quantum deformation on the spin-1/2 Aharonov-Bohm problem: In this letter we study the Aharonov-Bohm problem for a spin-1/2 particle in
the quantum deformed framework generated by the $\kappa$-Poincar\'{e}-Hopf
algebra. We consider the nonrelativistic limit of the $\kappa$-deformed Dirac
equation and use the spin-dependent term to impose an upper bound on the
magnitude of the deformation parameter $\varepsilon$. By using the self-adjoint
extension approach, we examine the scattering and bound state scenarios. After
obtaining the scattering phase shift and the $S$-matrix, the bound states
energies are obtained by analyzing the pole structure of the latter. Using a
recently developed general regularization prescription [Phys. Rev. D.
\textbf{85}, 041701(R) (2012)], the self-adjoint extension parameter is
determined in terms of the physics of the problem. For last, we analyze the
problem of helicity conservation.
|
Scale Symmetry and Weinberg's No-go Theorem in the Cosmological Constant
Problem: We complete the proof of Weinberg's no-go theorem on the cosmological
constant problem in classical gravity when the theory has a (global) scale
symmetry. Stimulated with this proof, we explore a solution to the cosmological
constant problem by the help of renormalization group equations. We find that
the manifestly scale invariant regularization method provides a physically
plausible solution to the cosmological constant problem, in particular, to the
issue of radiative instability of the cosmological constant.
|
From the Superparticle Path Integral to Superfield Theory: We investigate the hitherto unexplored relation between the superparticle
path integral and superfield theory. Requiring that the path integral has the
global symmetries of the classical action and obeys the natural composition
property of path integrals, and also that the discretized action has the
correct naive continuum limit, we find a viable discretization of the (D=3,N=2)
free superparticle action. The resulting propagator is not the usual superfield
one. We extend the discretization to include the coupling to an external gauge
supermultiplet and use this to show the equivalence to superfield theory. This
is possible since we are able to reformulate the superfield perturbation theory
in terms of our new propagator.
|
On Complexity for Higher Derivative Gravities: Using "complexity=action" proposal we study complexity growth of certain
gravitational theories containing higher derivative terms. These include
critical gravity in diverse dimensions. One observes that the complexity growth
for neutral black holes saturates the proposed bound when the results are
written in terms of physical quantities of the model. We will also study
effects of shock wave to the complexity growth where we find that the presence
of massive spin-2 mode slows down the rate of growth.
|
Cancellation of Global Anomalies in Spontaneously Broken Gauge Theories: We discuss the generalization to global gauge anomalies of the familiar
procedure for the cancellation of local gauge anomalies in effective theories
of spontaneously broken symmetries. We illustrate this mechanism in a recently
proposed six-dimensional extension of the standard model.
|
star-Cohomology, Connes-Chern Characters, and Anomalies in General
Translation-Invariant Noncommutative Yang-Mills: Topological structure of translation-invariant noncommutative Yang-Mills
theories are studied by means of a cohomology theory, so called
star-cohomology, which plays an intermediate role between de Rham and cyclic
(co)homology theory for noncommutative algebras and gives rise to a
cohomological formulation comparable to Seiberg-Witten map.
|
Abelian solutions of the KP equation: We introduce the notion of abelian solutions of KP equations and show that
all of them are algebro-geometric.
|
Feynman Diagrams and a Combination of the Integration by Parts (IBP) and
the Integration by Fractional Expansion (IBFE) Techniques: In this paper we show how to improve and extend the Integration by Fractional
Expansion technique (IBFE) by applying it to certain families of scalar massive
Feynman diagrams. The strategy is based on combining this method together with
the Integration by Parts technique (IBP). In particular, we want to calculate
certain Feynman diagrams which have a triangle loop as a subgraph. The main
idea is to use IBP in this subgraph in order to simplify the topology of the
original diagram in which it is immersed, using then, in a second step, the
IBFE technique. The result we have obtained, after the application of both
techniques, represents a simplification in the complexity of the solution,
compared with having used only the IBFE technique.
|
Instanton R-matrix and W-symmetry: We study the relation between $\mathcal{W}_{1+\infty}$ algebra and
Arbesfeld-Schiffmann-Tsymbaliuk Yangian using the Maulik-Okounkov R-matrix. The
central object linking these two pictures is the Miura transformation. Using
the results of Nazarov and Sklyanin we find an explicit formula for the mixed
R-matrix acting on two Fock spaces associated to two different asymptotic
directions of the affine Yangian. Using the free field representation we
propose an explicit identification of Arbesfeld-Schiffmann-Tsymbaliuk
generators with the generators of Maulik-Okounkov Yangian. In the last part we
use the Miura transformation to give a conformal field theoretic construction
of conserved quantities and ladder operators in the quantum mechanical rational
and trigonometric Calogero-Sutherland models on which a vector representation
of the Yangian acts.
|
The embedding tensor of Scherk-Schwarz flux compactifications from
eleven dimensions: We study the Scherk-Schwarz reduction of D=11 supergravity with background
fluxes in the context of a recently developed framework pertaining to D=11
supergravity. We derive the embedding tensor of the associated four-dimensional
maximal gauged theories directly from eleven dimensions by exploiting the
generalised vielbein postulates, and by analysing the couplings of the full set
of 56 electric and magnetic gauge fields to the generalised vielbeine. The
treatment presented here will apply more generally to other reductions of
$D=11$ supergravity to maximal gauged theories in four dimensions.
|
The Swampland, Quintessence and the Vacuum Energy: It has recently been conjectured that string theory does not admit de Sitter
vacua, and that quintessence explains the current epoch of accelerated cosmic
expansion. A proposed, key prediction of this scenario is time-varying
couplings in the dark sector, induced by the evolving quintessence field. We
note that cosmological models with varying couplings suffer from severe
problems with quantum corrections, beyond those shared by all quintessence
models. The vacuum energy depends on all masses and couplings of the theory,
and even small variations of parameters can lead to overwhelmingly large
corrections to the effective potential. We find that quintessence models with
varying parameters can be realised in consistent quantum theories by either: 1)
enforcing exceptional levels of fine-tuning; 2) realising some unknown
mechanism that cancels all undesirable contributions to the effective potential
with unprecedented accuracy; or 3) ensuring that the quintessence field couples
exclusively to very light states, and does not backreact on heavy fields.
|
Brane Condensation and Confinement: We study the static quantum potential for a theory of anti-symmetric tensor
fields that results from the condensation of topological defects, within the
framework of the gauge-invariant but path-dependent variables formalism. Our
calculations show that the interaction energy is the sum of a Yukawa and a
linear potentials, leading to the confinement of static probe charges.
|
Regular braneworlds with bulk fluids: We review studies on the singularity structure and asymptotic analysis of a
3-brane (flat or curved) embedded in a five-dimensional bulk filled with a
`perfect fluid' with an equation of state with the `pressure' and the `density'
of the fluid depending on the fifth space coordinate. Regular solutions
satisfying positive energy conditions in the bulk exist only in the cases of a
flat brane with an EoS parameter equal to -1, or of AdS branes for EoS
parameter values in suitable intervals. More cases can be found by gluing two
regular branches of solutions at the position of the brane. However, only the
case of a flat brane with an EoS parameter equal to -1 leads to finite Planck
mass on the brane and thus localises gravity. In a more recent work, we showed
that a way to rectify the previous findings and obtain a solution for a flat
brane in a finite range of the EoS parameter, which is both free from
finite-distance singularities and compatible with the physical conditions of
energy and finiteness of four-dimensional Planck mass, is by introducing a bulk
fluid component that satisfies a nonlinear equation of state.
|
Quantum Field Theory of Fluids: The quantum theory of fields is largely based on studying perturbations
around non-interacting, or free, field theories, which correspond to a
collection of quantum-mechanical harmonic oscillators. The quantum theory of an
ordinary fluid is `freer', in the sense that the non-interacting theory also
contains an infinite collection of quantum-mechanical free particles,
corresponding to vortex modes. By computing a variety of correlation functions
at tree- and loop-level, we give evidence that a quantum perfect fluid can be
consistently formulated as a low-energy, effective field theory. We speculate
that the quantum behaviour is radically different to both classical fluids and
quantum fields, with interesting physical consequences for fluids in the low
temperature regime.
|
Supersymmetry and Polytopes: We make an imaginative comparison between the Minimal Supersymmetric Standard
Model and the 24-cell polytope in four dimensions, the Octacube.
|
Effective action of bosonic string theory at order $ α'^2 $: Recently, it has been shown that the gauge invariance requires the minimum
number of independent couplings for $B$-field, metric and dilaton at order
$\alpha'^2$ to be 60. In this paper we fix the corresponding 60 parameters in
string theory by requiring the couplings to be invariant under the global
T-duality transformations. The Riemann cubed terms are exactly the same as the
couplings that have been found by the S-matrix calculations.
|
Self-Dual Fields on Self-Dual Backgrounds and the Double Copy: We explore the double copy for self-dual gauge and gravitational fields on
self-dual background spacetimes. We consider backgrounds associated to
solutions of the second Plebanski equation and describe results with different
gauge-fixing conditions. Finally we discuss the kinematic and $w$-algebras and
the double copy, identifying modified Poisson structures and kinematic
structure constants in the presence of the self-dual background. The self-dual
plane wave and Eguchi-Hanson spacetimes are studied as examples and their
respective $w$-algebras derived.
|
Dynamics of Dirichlet-Neumann Open Strings on D-branes: Method for computing scattering amplitudes of open strings with Dirichlet
boundary on one end and Neumann boundary condition on the other is described.
Vertex operator for these states are constructed using twist fields which have
been studied previously in the context of Ashkin-Teller model and strings on
orbifolds. Using these vertex operators, we compute the three- and four-point
scattering amplitudes for (5,9) strings on 5-branes and 9-branes. In the low
energy limit, these amplitudes are found to be in exact agreement with the
field theory amplitudes for supersymmetric Yang-Mills coupled to
hypermultiplets in 6-dimensions. We also consider the 1-brane 5-brane system
and compute the amplitude for a pair of (1,5) strings to collide and to escape
the brane as a closed string. (1,5) strings are found to be remarkably
selective in their coupling to massless closed strings in NS-NS sector; they
only couple to the dilaton.
|
The Atiyah Class and Complex Structure Stabilization in Heterotic
Calabi-Yau Compactifications: Holomorphic gauge fields in N=1 supersymmetric heterotic compactifications
can constrain the complex structure moduli of a Calabi-Yau manifold. In this
paper, the tools necessary to use holomorphic bundles as a mechanism for moduli
stabilization are systematically developed. We review the requisite deformation
theory -- including the Atiyah class, which determines the deformations of the
complex structure for which the gauge bundle becomes non-holomorphic and,
hence, non-supersymmetric. In addition, two equivalent approaches to this
mechanism of moduli stabilization are presented. The first is an efficient
computational algorithm for determining the supersymmetric moduli space, while
the second is an F-term potential in the four-dimensional theory associated
with vector bundle holomorphy. These three methods are proven to be rigorously
equivalent. We present explicit examples in which large numbers of complex
structure moduli are stabilized. Finally, higher-order corrections to the
moduli space are discussed.
|
The Angular Tension of Black Holes: Angular tension is an ADM charge that contributes a work term to the first
law of black hole mechanics when the range of an angular coordinate is varied
and leads to a new Smarr formula for stationary black holes. A phase diagram
for singly-spinning D=5 black holes shows that angular tension resolves the
degeneracies between spherical black holes and (dipole) black rings and
captures the physics of the black ring balance condition. Angular tension
depends on the behavior of the metric at rotational axes and we speculate on
its relation to rod/domain structure characterizations of higher dimensional
black holes and black hole uniqueness theorems.
|
Resolution of Gauss' law in Yang-Mills theory by Gauge Invariant
Projection: Topology and Magnetic Monopoles: An efficient way of resolving Gauss' law in Yang-Mills theory is presented by
starting from the projected gauge invariant partition function and integrating
out one spatial field variable. In this way one obtains immediately the
description in terms of unconstrained gauge invariant variables which was
previously obtained by explicitly resolving Gauss' law in a modified axial
gauge. In this gauge, which is a variant of 't Hooft's Abelian gauges, magnetic
monopoles occur. It is shown how the Pontryagin index of the gauge field is
related to the magnetic charges. It turns out that the magnetic monopoles are
sufficient to account for the non-trivial topological structure of the theory.
|
Heat kernel of non-minimal gauge field kinetic operators on Moyal plane: We generalize the Endo formula originally developed for the computation of
the heat kernel asymptotic expansion for non-minimal operators in commutative
gauge theories to the noncommutative case. In this way, the first three
non-zero heat trace coefficients of the non-minimal U(N) gauge field kinetic
operator on the Moyal plane taken in an arbitrary background are calculated. We
show that the non-planar part of the heat trace asymptotics is determined by
U(1) sector of the gauge model. The non-planar or mixed heat kernel
coefficients are shown to be gauge-fixing dependent in any dimension of
space-time. In the case of the degenerate deformation parameter the lowest
mixed coefficients in the heat expansion produce non-local gauge-fixing
dependent singularities of the one-loop effective action that destroy the
renormalizability of the U(N) model at one-loop level. The twisted-gauge
transformation approach is discussed.
|
Gauge Invariance and Noncommutativity: The role of the gauge invariance in noncommutative field theory is discussed.
A basic introduction to noncommutative geometry and noncommutative field theory
is given. Background invariant formulation of Wilson lines is proposed. Duality
symmetries relating various noncommutative gauge models are being discussed.
|
Non-renormalizable Interactions: A Self-Consistency Manifesto: The renormalization procedure is proved to be a rigorous way to get finite
answers in a renormalizable class of field theories. We claim, however, that it
is redundant if one reduces the requirement of finiteness to S-matrix elements
only and does not require finiteness of intermediate quantities like the
off-shell Green functions. We suggest a novel view on the renormalization
procedure. It is based on the usual BPHZ R-operation, which is equally
applicable to any local QFT, renormalizable or not. The key point is the
replacement of the multiplicative renormalization, used in renormalizable
theories, by an operation when the renormalization constants depend on the
fields and momenta that have to be integrated inside the subgraphs. This
approach does not distinguish between renormalizable and non-renormalizable
interactions and provides the basis for getting finite scattering amplitudes in
both cases. The arbitrariness of the subtraction procedure is fixed by imposing
a normalization condition on the scattering amplitude as a whole rather than on
an infinite series of new operators appearing in non-renormalizable theories.
Using the property of locality of counter-terms, we get recurrence relations
connecting leading, subleading, etc., UV divergences in all orders of PT in any
local theory. This allows one to get generalized RG equations that have an
integro-differential form and sum up the leading logarithms. This way one can
cure the problem of violation of unitarity in non-renormalizable theories by
summing up the leading asymptotics. We illustrate the basic features of our
approach by several examples.
Our main statement is that non-renormalizable theories are self-consistent,
they can be well treated within the usual BPHZ R-operation, and the
arbitrariness can be fixed to a finite number of parameters just as in the
renormalizable case.
|
Challenges for Superstring Cosmology: We consider whether current notions about superstring theory below the Planck
scale are compatible with cosmology. We find that the anticipated form for the
dilaton interaction creates a serious roadblock for inflation and makes it
unlikely that the universe ever reaches a state with zero cosmological constant
and time-independent gravitational constant.
|
Cosmology as Geodesic Motion: For gravity coupled to N scalar fields with arbitrary potential V, it is
shown that all flat (homogeneous and isotropic) cosmologies correspond to
geodesics in an (N+1)-dimensional `augmented' target space of Lorentzian
signature (1,N), timelike if V>0, null if V=0 and spacelike if V<0.
Accelerating cosmologies correspond to timelike geodesics that lie within an
`acceleration subcone' of the `lightcone'. Non-flat (k=-1,+1) cosmologies are
shown to evolve as projections of geodesic motion in a space of dimension
(N+2), of signature (1,N+1) for k=-1 and signature (2,N) for k=+1. This
formalism is illustrated by cosmological solutions of models with an
exponential potential, which are comprehensively analysed; the late-time
behviour for other potentials of current interest is deduced by comparison.
|
Eigenbranes in Jackiw-Teitelboim gravity: It was proven recently that JT gravity can be defined as an ensemble of L x L
Hermitian matrices. We point out that the eigenvalues of the matrix correspond
in JT gravity to FZZT-type boundaries on which spacetimes can end. We then
investigate an ensemble of matrices with 1<<N<<L eigenvalues held fixed. This
corresponds to a version of JT gravity which includes N FZZT type boundaries in
the path integral contour and which is found to emulate a discrete quantum
chaotic system. In particular this version of JT gravity can capture the
behavior of finite-volume holographic correlators at late times, including
erratic oscillations.
|
Bound states in bottomless potentials: We consider classical and quantum dynamics on potentials that are
asymptotically unbounded from below. By explicit construction we find that
quantum bound states can exist in certain bottomless potentials. The classical
dynamics in these potentials is novel. Only a set of zero measure of classical
trajectories can escape to infinity. All other trajectories get trapped as they
get further out into the asymptotic region.
|
Spacetime Subsystem Symmetries: One characteristic feature of many fractonic lattice models, and a defining
property of the exotic field theories developed to describe them, are subsystem
symmetries including a conservation of not just net electric charge but also
electric dipole moments or charges living on submanifolds. So far all such
theories were based on internal subsystem symmetries. In this work we
generalize the notion of subsystem symmetries to system with subsystem
spacetime symmetries with locally conserved energies.
|
Axionic Festina Lente: The swampland conjecture known as Festina Lente (FL) imposes a lower bound on
the mass of all charged particles in a quasi-de Sitter space. In this paper, we
propose the aFL (axionic Festina Lente) bound, an extension of FL to axion-like
particles arising from type II string theory. We find that the product of the
instanton action and the axion decay constant is bounded from below by the
vacuum energy. This is achieved indirectly, using dimensional reduction on
Calabi-Yau threefolds, and translating the FL result for dipoles into a purely
geometric bound. We discuss axionic black holes evolution, and aFL constraints
on Euclidean wormholes, showing that the gravitational arguments leading to the
FL bound for U$(1)$ charged particles cannot be directly applied to axions.
Moreover, we discuss phenomenological implications of the aFL bound, including
constraints on string inflation models and the axion-photon coupling via
kinetic mixing.
|
New maverick coset theories: We present new examples of maverick coset conformal field theories. They are
closely related to conformal embeddings and exceptional modular invariants.
|
UV-IR coupling in higher derivative gravity: We discuss the possible existence of new generic vacuum solutions of
Robertson-Walker form in higher derivative gravity theories in four dimensions.
These solutions illustrate how a dynamical coupling between very low and very
high frequency modes can occur when the cosmological constant is small.
|
Fake Supergravity and Domain Wall Stability: We review the generalized Witten-Nester spinor stability argument for flat
domain wall solutions of gravitational theories. Neither the field theory nor
the solution need be supersymmetric. Nor is the space-time dimension
restricted. We develop the non-trivial extension required for AdS-sliced domain
walls and apply this to show that the recently proposed "Janus" solution of
Type IIB supergravity is stable non-perturbatively for a broad class of
deformations. Generalizations of this solution to arbitrary dimension and a
simple curious linear dilaton solution of Type IIB supergravity are byproducts
of this work.
|
Geometry of four-dimensional Killing spinors: The supersymmetric solutions of N=2, D=4 minimal ungauged and gauged
supergravity are classified according to the fraction of preserved
supersymmetry using spinorial geometry techniques. Subject to a reasonable
assumption in the 1/2-supersymmetric time-like case of the gauged theory, we
derive the complete form of all supersymmetric solutions. This includes a
number of new 1/4- and 1/2-supersymmetric possibilities, like gravitational
waves on bubbles of nothing in AdS_4.
|
Eikonal model analysis of elastic proton-proton collisions at 52.8 GeV
and 8 TeV: Under the influence of standardly used description of Coulomb-hadronic
interference proposed by West and Yennie the protons have been interpreted as
transparent objects; elastic events have been interpreted as more central than
inelastic ones. It will be shown that using eikonal model the protons may be
interpreted in agreement with usual ontological conception; elastic processes
being more peripheral than inelastic ones. The corresponding results (differing
fundamentally from the suggested hitherto models) will be presented by
analyzing the most ample elastic data set measured at the ISR energy of 52.8
GeV and the LHC energy of 8 TeV. Detailed analysis of measured differential
cross section will be performed and possibility of peripheral behavior on the
basis of eikonal model will be presented. The impact of recently established
electromagnetic form factors on determination of quantities specifying hadron
interaction determined from the fits of experimental elastic data will be
analyzed. The influence of some other assumptions on proton characteristics
derived from elastic hadronic amplitude determined on the basis of experimental
data will be studied, too.
|
A local non-Abelian gauge invariant action stemming from the nonlocal
operator F 1/D^2 F: We report on the nonlocal gauge invariant operator of dimension two, F 1/D^2
F. We are able to localize this operator by introducing a suitable set of
(anti)commuting antisymmetric tensor fields. Starting from this, we succeed in
constructing a local gauge invariant action containing a mass parameter, and we
prove the renormalizability to all orders of perturbation theory of this action
in the linear covariant gauges using the algebraic renormalization technique.
We point out the existence of a nilpotent BRST symmetry. Despite the additional
(anti)commuting tensor fields and coupling constants, we prove that our model
in the limit of vanishing mass is equivalent with ordinary massless Yang-Mills
theories by making use of an extra symmetry in the massless case. We also
present explicit renormalization group functions at two loop order in the MSbar
scheme.
|
Magnetically Charged Calorons with Non-Trivial Holonomy: Instantons in pure Yang-Mills theories on partially periodic space
$\mathbb{R}^3\times S^1$ are usually called calorons. The background
periodicity brings on characteristic features of calorons such as non-trivial
holonomy, which plays an essential role for confinement/deconfinement
transition in pure Yang-Mills gauge theory. For the case of gauge group
$SU(2)$, calorons can be interpreted as composite objects of two constituent
"monopoles" with opposite magnetic charges. There are often the cases that the
two monopole charges are unbalanced so that the calorons possess net magnetic
charge in $\mathbb{R}^3$. In this paper, we consider several mechanism how such
net magnetic charges appear for certain types of calorons through the ADHM/Nahm
construction with explicit examples. In particular, we construct analytically
the gauge configuration of the $(2,1)$-caloron with $U(1)$-symmetry, which has
intrinsically magnetic charge.
|
Variational Calculation of Effective Classical Potential at $T \neq 0$
to Higher Orders: Using the new variational approach proposed recently for a systematic
improvement of the locally harmonic Feynman-Kleinert approximation to path
integrals we calculate the partition function of the anharmonic oscillator for
all temperatures and coupling strength with high accuracy.
|
Solutions with intersecting p-branes related to Toda chains: Solutions in multidimensional gravity with m p-branes related to Toda-like
systems (of general type) are obtained. These solutions are defined on a
product of n+1 Ricci-flat spaces M_0 x M_1 x...x M_n and are governed by one
harmonic function on M_0. The solutions are defined up to the solutions of
Laplace and Toda-type equations and correspond to null-geodesics of the
(sigma-model) target-space metric. Special solutions relating to A_m Toda
chains (e.g. with m =1,2) are considered.
|
BRST Operator for Superconformal Algebras with Quadratic Nonlinearity: We construct the quantum BRST operators for a large class of superconformal
and quasi--superconformal algebras with quadratic nonlinearity. The only free
parameter in these algebras is the level of the (super) Kac-Moody sector. The
nilpotency of the quantum BRST operator imposes a condition on the level. We
find this condition for (quasi) superconformal algebras with a Kac-Moody sector
based on a simple Lie algebra and for the $Z_2\times Z_2$--graded
superconformal algebras with a Kac-Mody sector based on the superalgebra
$osp(N\vert 2M)$ or $s\ell(N+2\vert N)$.
|
The Swampland at Large Number of Space-Time Dimensions: We discuss some aspects of swampland constraints - especially the swampland
distance conjecture - in a large number of space-time dimensions $D$. We
analyze Kaluza-Klein (KK) states at large $D$ and find that some KK spectra
possess an interesting dependence on $D$. On the basis of these observations we
propose a new large dimension conjecture. We apply it to KK states of
compactifications to anti-de Sitter backgrounds where it predicts an upper
bound on the dimension of space-time as a function of its characteristic
radius. We also apply our conjecture to black hole spacetimes, whose entropies
have a $D$-dependence very similar to that of the KK spectrum.
|
Dynamical Instability of Holographic QCD at Finite Density: In this paper we study the dynamical instability of Sakai-Sugimoto's
holographic QCD model at finite baryon density. In this model, the baryon
density, represented by the smeared instanton on the worldvolume of the probe
D8-\overline{D8} mesonic brane, sources the worldvolume electric field, and
through the Chern-Simons term it will induces the instability to form a chiral
helical wave. This is similar to Deryagin-Grigoriev-Rubakov instability to form
the chiral density wave for large N_c QCD at finite density. Our results show
that this kind of instability occurs for sufficiently high baryon number
densities. The phase diagram of holographic QCD will thus be changed from the
one which is based only on thermodynamics. This holographic approach provides
an effective way to study the phases of QCD at finite density, where the
conventional perturbative QCD and lattice simulation fail.
|
Resonance spectrum of a bulk fermion on branes: It is known that there are two mechanisms for localizing a bulk fermion on a
brane, one is the well-known Yukawa coupling and the other is the new coupling
proposed in [Phys. Rev. D 89, 086001 (2014)]. In this paper, we investigate
localization and resonance spectrum of a bulk fermion on the same branes with
the two localization mechanisms. It is found that both the two mechanisms can
result in a volcano-like effective potential of the fermion Kaluza-Klein modes.
The left-chiral fermion zero mode can be localized on the brane and there exist
some discrete massive fermion Kaluza-Klein modes that quasilocalized on the
brane (also called fermion resonances). The number of the fermion resonances
increases linearly with the coupling parameter.
|
NSR Open Super-string in the proper-time gauge I: Free Field Theory: We study the Neveu-Schwarz-Ramond (NSR) open super-string theory in the
proper-time gauge. The string field action is obtained by evaluating the
Polyakov string path integral. In this study, we focus on the open-string
free-field action, which corresponds to the string path integral on a strip.
Depending on the periodicity of the fermion fields, the open super-string has
two sectors: The Neveu-Schwarz (NS) and Ramond (R) sectors. We can impose the
gauge conditions to fix the (super-) reparametrization invariance on the
two-dimensional metric and its super-partner on the string world sheet to
secure the covariance, in contrast to the light-cone gauge condition.
Accordingly, the proper-time emerges in the NS sector and both proper-time and
its super-partner appear in the R-sector. Integration leads to free-string
field actions in both sectors.
|
Macroscopic strings as heavy quarks: Large-N gauge theory and anti-de
Sitter supergravity: We study some aspects of Maldacena's large $N$ correspondence between N=4
superconformal gauge theory on D3-brane and maximal supergravity on AdS_5xS_5
by introducing macroscopic strings as heavy (anti)-quark probes. The
macroscopic strings are semi-infinite Type IIB strings ending on D3-brane
world-volume. We first study deformation and fluctuation of D3-brane when a
macroscopic BPS string is attached. We find that both dynamics and boundary
conditions agree with those for macroscopic string in anti-de Sitter
supergravity. As by-product we clarify how Polchinski's Dirichlet / Neumann
open string boundary conditions arise dynamically. We then study non-BPS
macroscopic string anti-string pair configuration as physical realization of
heavy quark Wilson loop. We obtain quark-antiquark static potential from the
supergravity side and find that the potential exhibits nonanalyticity of
square-root branch cut in `t Hooft coupling parameter. We put forward the
nonanalyticity as prediction for large-N gauge theory at strong `t Hooft
coupling limit. By turning on Ramond-Ramond zero-form potential, we also study
theta-vacuum angle dependence of the static potential. We finally discuss
possible dynamical realization of heavy N-prong string junction and of large-N
loop equation via local electric field and string recoil thereof. Throughout
comparisons of the AdS-CFT correspondence, we find crucial role played by
`geometric duality' between UV and IR scales on directions perpendicular to
D3-brane and parallel ones, explaining how AdS5 spacetime geometry emerges out
of four-dimensional gauge theory at strong coupling.
|
Study of the AdS$_2$/CFT$_1$ Correspondence with the Contribution from
the Weyl Anomaly: In this paper we will consider the Almheiri-Polchinski model of the AdS$_2$
back reaction coupled with Liouville field, which is necessary for quantum
consistency. In this model, the Liouville field is determined classically by a
bulk conformal transformation. The boundary time is also reparametrized by this
transformation. It is shown that the on-shell action on the boundary for the
gravity sector is given by a bulk integral containing the Liouville field. This
integral stems from Weyl anomaly and is SL(2,R) invariant. A prescription is
given for computing correlation functions of the operators dual to massless
scalars. The generating function of the correlation functions of these
operators is given by a sum of matter action and the bulk integral containing
the Liouville field. The latter integral leads to extra contributions to
$n(\geq 6)$ point functions.
|
Topological mass generation in gapless systems: Mass generation of gauge fields can be universally described by topological
couplings in gapped systems, such as the Abelian Higgs model in $(3+1)$
dimensions and the Maxwell-Chern-Simons theory in $(2+1)$ dimensions. These
systems also exhibit the spontaneous breaking of higher-form $\mathbb{Z}_k$
symmetries and topological orders for level $k \geq 2$. In this paper, we
consider topological mass generation in gapless systems. As a paradigmatic
example, we study the axion electrodynamics with level $k$ in $(3+1)$
dimensions in background fields that hosts both gapped and gapless modes. We
argue that the gapped mode is related to those in fully gapped systems in lower
dimensions via dimensional reduction. We show that this system exhibits the
spontaneous breaking of a higher-form $\mathbb{Z}_k$ symmetry despite the
absence of the conventional topological order. In the case of the background
magnetic field, we also derive the low-energy effective theory of the gapless
mode with the quadratic dispersion relation and show that it satisfies the
chiral anomaly matching.
|
Carroll Expansion of General Relativity: We study the small speed of light expansion of general relativity, utilizing
the modern perspective on non-Lorentzian geometry. This is an expansion around
the ultra-local Carroll limit, in which light cones close up. To this end, we
first rewrite the Einstein-Hilbert action in pre-ultra-local variables, which
is closely related to the 3+1 decomposition of general relativity. At leading
order in the expansion, these pre-ultra-local variables yield Carroll geometry
and the resulting action describes the electric Carroll limit of general
relativity. We also obtain the next-to-leading order action in terms of Carroll
geometry and next-to-leading order geometric fields. The leading order theory
yields constraint and evolution equations, and we can solve the evolution
analytically. We furthermore construct a Carroll version of Bowen-York initial
data, which has associated conserved boundary linear and angular momentum
charges. The notion of mass is not present at leading order and only enters at
next-to-leading order. This is illustrated by considering a particular
truncation of the next-to-leading order action, corresponding to the magnetic
Carroll limit, where we find a solution that describes the Carroll limit of a
Schwarzschild black hole. Finally, we comment on how a cosmological constant
can be incorporated in our analysis.
|
Feynman rules in N=2 projective Superspace II: Massive hypermultiplets: Manifest N=2 supersymmetric hypermultiplet mass terms can be introduced in
the projective N=2 superspace formalism. In the case of complex
hypermultiplets, where the gauge covariantized spinor derivatives have an
explicit representation in terms of gauge prepotentials, it is possible to
interpret such masses as vacuum expectation values of an Abelian vector
multiplet. The duality transformation that relates the N=2 off-shell projective
description of the hypermultiplet to the on-shell description involving two N=1
chiral superfields allows us to obtain the massive propagators of the N=1
complex linear fields in the projective hypermultiplet. The N=1 massive
propagators of the component superfields in the projective hypermultiplet
suggest a possible ansatz for the N=2 massive propagator, which agrees with an
explicit calculation in N=2 superspace.
|
The Super Period Matrix with Ramond Punctures in the supergravity
formulation: In a very recent preprint, Witten showed how to construct a $g|r \, \times \,
g|r$ super period matrix for super Riemann surfaces of genus $g$ with $2r$
Ramond punctures, which is symmetric in the ${\bf Z}_2$ graded sense. He also
showed how it can be applied to analyze supersymmetry breaking in string
compactifications which are supersymmetric at tree-level. Witten's construction
is in the purely holomorphic formulation of super Riemann surfaces. In this
paper, a construction is given in the formulation of two-dimensional
supergravity. The variations of the super period matrix with respect to
supermoduli deformations are also given, as well as an explicit illustration of
how the super period matrix with two Ramond punctures would emerge from a
degeneration of the super period matrix without punctures in higher genus.
|
On the Integrability of Four Dimensional N=2 Gauge Theories in the Omega
Background: We continue to investigate the relationship between the infrared physics of
N=2 supersymmetric gauge theories in four dimensions and various integrable
models such as Gaudin, Calogero-Moser and quantum spin chains. We prove
interesting dualities among some of these integrable systems by performing
different, albeit equivalent, quantizations of the Seiberg-Witten curve of the
four dimensional theory. We also discuss conformal field theories related to
N=2 4d gauge theories by the Alday-Gaiotto-Tachikawa (AGT) duality and the role
of conformal blocks of those CFTs in the integrable systems. As a consequence,
the equivalence of conformal blocks of rank two Toda and
Novikov-Wess-Zumino-Witten (WZNW) theories on the torus with punctures is
found.
|
Semiclassical Corrections to the Bekenstein-Hawking entropy of the BTZ
Black Hole via Self-Gravitation: Hawking radiation is viewed as a tunnelling process. In this way the effect
of self-gravitation gives rise to semiclassical corrections to the entropy of
the (2+1) BTZ black hole. The modified entropy, due to specific modelling of
the self-gravitation effect, of the (2+1) BTZ black hole is evaluated. To first
order in $\omega$ which is a shell of energy radiated outwards the event
horizon of the BTZ black hole, modified entropy is proportional to the horizon.
In this semiclassical analysis, corrections to the Bekenstein-Hawking formula
$S_{BH}=\mathcal{A}_{H} / 4l_{P}^{2}$ are found to be negative and the
proportionality factor connecting the modified entropy, $S_{bh}$, of the (2+1)
BTZ black hole to the Bekenstein-Hawking entropy, $S_{BH}$, is evaluated to
first order in $\omega$.
|
Non-Perturbative Nekrasov Partition Function from String Theory: We calculate gauge instanton corrections to a class of higher derivative
string effective couplings introduced in [1]. We work in Type I string theory
compactified on K3xT2 and realise gauge instantons in terms of D5-branes
wrapping the internal space. In the field theory limit we reproduce the
deformed ADHM action on a general {\Omega}-background from which one can
compute the non-perturbative gauge theory partition function using
localisation. This is a non-perturbative extension of [1] and provides further
evidence for our proposal of a string theory realisation of the
{\Omega}-background.
|
Stability analysis of non-Abelian electric fields: We study the stability of fluctuations around a homogeneous non-Abelian
electric field background that is of a form that is protected from Schwinger
pair production. Our analysis identifies the unstable modes and we find a
limiting set of parameters for which there are no instabilities. We discuss
potential implications of our analysis for confining strings in non-Abelian
gauge theories.
|
Higher-spin massless S-matrices in four-dimensions: On-shell, analytic S-matrix elements in massless theories are constructed
from a finite set of primitive three-point amplitudes, which are fixed by
Poincare invariance up to an overall numerical constant. We classify \emph{all}
such three-point amplitudes in four-dimensions. Imposing the simplest
incarnation of Locality and Unitarity on four-particle amplitudes constructed
from these three-particle amplitudes rules out all but an extremely small
subset of interactions among higher-spin massless states. Notably, the
equivalence principle, and the Weinberg-Witten theorem, are simple corollaries
of this principle. Further, no massless states with helicity larger than two
may consistently interact with massless gravitons. Chromodynamics,
electrodynamics, Yukawa and $\phi^3$-theories are the only marginal and
relevant interactions between massless states. Finally, we show that
supersymmetry naturally emerges as a consistency condition on four-particle
amplitudes involving spin-3/2 states, which must always interact
gravitationally.
|
Topological charges in 2d N=(2,2) theories and massive BPS states: We study how charges of global symmetries that are manifest in the
ultra-violet definition of a theory are realized as topological charges in its
infra-red effective theory for two-dimensional theories with
$\mathcal{N}=(2,2)$ supersymmetry. We focus on the charges that the states
living on $S^1$ carry. The central charge---or BPS masses---of the
supersymmetry algebra play a crucial role in making this correspondence
precise. We study two examples: $U(1)$ gauge theories with chiral matter, and
world-volume theories of "dynamical surface operators" of 4d $\mathcal{N}=2$
gauge theories. In the former example, we show that the flavor charges of the
theory are realized as topological winding numbers in the effective theory on
the Coulomb branch. In the latter, we show that there is a one-to-one
correspondence between topological charges of the effective theory of the
dynamical surface operator and the electric, magnetic, and flavor charges of
the 4d gauge theory. We also examine the topologically charged massive BPS
states on $S^1$ and discover that the massive BPS spectrum is sensitive to the
radius of the circle in the simplest theory---the free theory of a periodic
twisted chiral field. We clarify this behavior by showing that the massive BPS
spectrum on $S^1$, unlike the BPS ground states, cannot be identified as
elements of a cohomology.
|
Embeddings for Non-Critical Superstrings: It was previously shown that at critical central charge, $N$-extended
superstrings can be embedded in $(N+1)$-extended superstrings. In other words,
$(N=0,c=26)\to (N=1,c=15)\to (N=2,c=6)\to (N=3,c=0) \to (N=4,c=0) $. In this
paper, we show that similar embeddings are also possible for $N$-extended
superstrings at non-critical central charge. For any $x$, the embedding is
$(N=0,c=26+x) \to (N=1,c=15+x) \to (N=2,c=6+x) \to (N=3,c=x) \to (N=4,c=x)$. As
was conjectured by Vafa, the $(N=2,c=9) \to (N=3,c=3)$ embedding can be used to
prove that $N=0$ topological strings are special vaccua of N=1 topological
strings.
|
Gravitational Stability and Screening Effect from D Extra Timelike
Dimensions: We study (3+1)+D dimensional spacetime, where D extra dimensions are
timelike. Compactification of the D timelike dimensions leads to tachyonic
Kaluza-Klein gravitons. We calculate the gravitational self-energies of massive
spherical bodies due to the tachyonic exchange, discuss their stability, and
find that the gravitational force is screened in a certain number of the extra
dimensions. We also derive the exact relationship between the Newton constants
in the full 4+D dimensional spacetime with the D extra times and the ordinary
Newton constant of our 4 dimensional world.
|
Non standard parametrizations and adjoint invariants of classical groups: We obtain local parametrizations of classical non-compact Lie groups where
adjoint invariants under maximal compact subgroups are manifest. Extension to
non compact subgroups is straightforward. As a by-product parametrizations of
the same type are obtained for compact groups. They are of physical interest in
any theory gauge invariant under the adjoint action, typical examples being the
two dimensional gauged Wess-Zumino-Witten-Novikov models where these
coordinatizations become of extreme usefulness to get the background fields
representing the vacuum expectation values of the massless modes of the
associated (super) string theory.
|
The Relativistic Dirac-Morse Problem via SUSY QM: The Morse problem is investigated in relativistic quantum mechanics.
|
The All-Loop Integrand For Scattering Amplitudes in Planar N=4 SYM: We give an explicit recursive formula for the all L-loop integrand for
scattering amplitudes in N=4 SYM in the planar limit, manifesting the full
Yangian symmetry of the theory. This generalizes the BCFW recursion relation
for tree amplitudes to all loop orders, and extends the Grassmannian duality
for leading singularities to the full amplitude. It also provides a new
physical picture for the meaning of loops, associated with canonical operations
for removing particles in a Yangian-invariant way. Loop amplitudes arise from
the "entangled" removal of pairs of particles, and are naturally presented as
an integral over lines in momentum-twistor space. As expected from manifest
Yangian-invariance, the integrand is given as a sum over non-local terms,
rather than the familiar decomposition in terms of local scalar integrals with
rational coefficients. Knowing the integrands explicitly, it is straightforward
to express them in local forms if desired; this turns out to be done most
naturally using a novel basis of chiral, tensor integrals written in
momentum-twistor space, each of which has unit leading singularities. As simple
illustrative examples, we present a number of new multi-loop results written in
local form, including the 6- and 7-point 2-loop NMHV amplitudes. Very concise
expressions are presented for all 2-loop MHV amplitudes, as well as the 5-point
3-loop MHV amplitude. The structure of the loop integrand strongly suggests
that the integrals yielding the physical amplitudes are "simple", and
determined by IR-anomalies. We briefly comment on extending these ideas to more
general planar theories.
|
Revisiting the local potential approximation of the exact
renormalization group equation: The conventional absence of field renormalization in the local potential
approximation (LPA) --implying a zero value of the critical exponent \eta -- is
shown to be incompatible with the logic of the derivative expansion of the
exact renormalization group (RG) equation. We present a LPA with \eta \neq 0
that strictly does not make reference to any momentum dependence. Emphasis is
made on the perfect breaking of the reparametrization invariance in that pure
LPA (absence of any vestige of invariance) which is compatible with the
observation of a progressive smooth restoration of that invariance on
implementing the two first orders of the derivative expansion whereas the
conventional requirement (\eta =0 in the LPA) precluded that observation.
|
On massive gravitons in 2+1 dimensions: The Fierz-Pauli (FP) free field theory for massive spin 2 particles can be
extended, in a spacetime of (1+2) dimensions (3D), to a generally covariant
parity-preserving interacting field theory, in at least two ways. One is "new
massive gravity" (NMG), with an action that involves curvature-squared terms.
Another is 3D "bigravity", which involves non-linear couplings of the FP tensor
field to 3D Einstein-Hilbert gravity. We review the proof of the linearized
equivalence of both "massive 3D gravity" theories to FP theory, and we comment
on their similarities and differences.
|
Seeing behind black hole horizons in SYK: We present an explicit reconstruction of the interior of an AdS$_2$ black
hole in Jackiw-Teitelboim gravity, that is entirely formulated in the dual SYK
model and makes no direct reference to the gravitational bulk. We do this by
introducing a probe "observer" in the right wormhole exterior and using the
prescription of [arXiv:2009.04476] to transport SYK operators along the probe's
infalling worldline and into the black hole interior, using an appropriate SYK
modular Hamiltonian. Our SYK computation recovers the precise proper time at
which signals sent from the left boundary are registered by our observer's
apparatus inside the wormhole. The success of the computation relies on the
universal properties of SYK and we outline a promising avenue for extending it
to higher dimensions and applying it to the computation of scattering
amplitudes behind the horizon.
|
Topological Field Theories induced by twisted R-Poisson structure in any
dimension: We construct a class of topological field theories with Wess-Zumino term in
spacetime dimensions $\ge 2$ whose target space has a geometrical structure
that suitably generalizes Poisson or twisted Poisson manifolds. Assuming a
field content comprising a set of scalar fields accompanied by gauge fields of
degree $(1,p-1,p)$ we determine a generic Wess-Zumino topological field theory
in $p+1$ dimensions with background data consisting of a Poisson 2-vector, a
$(p+1)$-vector $R$ and a $(p+2)$-form $H$ satisfying a specific geometrical
condition that defines a $H$-twisted $R$-Poisson structure of order $p+1$. For
this class of theories we demonstrate how a target space covariant formulation
can be found by means of an auxiliary connection without torsion. Furthermore,
we study admissible deformations of the generic class in special spacetime
dimensions and find that they exist in dimensions 2, 3 and 4. The
two-dimensional deformed field theory includes the twisted Poisson sigma model,
whereas in three dimensions we find a more general structure that we call
bi-twisted $R$-Poisson. This extends the twisted $R$-Poisson structure of order
3 by a non-closed 3-form and gives rise to a topological field theory whose
covariant formulation requires a connection with torsion and includes a twisted
Poisson sigma model in three dimensions as a special case. The relation of the
corresponding structures to differential graded Q-manifolds based on the degree
shifted cotangent bundle $T^{\ast}[p]T^{\ast}[1]M$ is discussed, as well as the
obstruction to them being QP-manifolds due to the Wess-Zumino term.
|
Thermal duality and gravitational collapse in heterotic string theories: The thermal duality of E(8) x E(8) and SO(32) heterotic string theories may
underpin a mechanism that would convert the kinetic energy of infalling matter
during gravitational collapse to form a region of a hot string phase that would
expel gravitational gradients. This phase would be the continuation of a
Ginzburg-Landau like superconductor in the Euclidean regime. In this scenario,
there would be no event horizon or singularity produced in gravitational
collapse. Solutions are presented for excitations of the string vacuum that may
form during gravitational collapse and drive the transition to the hot phase.
The proposed mechanism is developed here for the case of approximately
spherical gravitational collapse in 4 uncompactified spacetime dimensions. A
way to reconcile the large entropy apparently produced in this process with
quantum mechanics is briefly discussed. In this scenario, astrophysical objects
such as stellar or galactic cores which have undergone extreme gravitational
collapse would currently be sites of an on-going conversion process to shells
of this high temperature phase. The relationship of this proposal to the
`firewall paradox' is noted.
|
Field Theory on Noncommutative Space-Time and the Deformed Virasoro
Algebra: We consider a field theoretical model on the noncommutative cylinder which
leads to a discrete-time evolution. Its Euclidean version is shown to be
equivalent to a model on the complex $q$-plane. We reveal a direct link between
the model on a noncommutative cylinder and the deformed Virasoro algebra
constructed earlier on an abstract mathematical background. As it was shown,
the deformed Virasoro generators necessarily carry a second index (in addition
to the usual one), whose meaning, however, remained unknown. The present field
theoretical approach allows one to ascribe a clear meaning to this second
index: its origin is related to the noncommutativity of the underlying
space-time. The problems with the supersymmetric extension of the model on a
noncommutative super-space are briefly discussed.
|
Generalized Invariants and Quantum Evolution of Open Fermionic System: Open systems acquire time-dependent coupling constants through interaction
with an external field or environment. We generalize the Lewis-Riesenfeld
invariant theorem to open system of quantum fields after second quantization.
The generalized invariants and thereby the quantum evolution are found
explicitly for time-dependent quadratic fermionic systems. The pair production
of fermions is computed and other physical implications are discussed.
|
Alien Calculus and non perturbative effects in Quantum Field Theory: In many domains of physics, methods are needed to deal with non-perturbative
aspects. I want here to argue that a good approach is to work on the Borel
transforms of the quantities of interest, the singularities of which give
non-perturbative contributions. These singularities in many cases can be
largely determined by using the alien calculus developed by Jean \'Ecalle. My
main example will be the two point function of a massless theory given as a
solution of a renormalization group equation.
|
Nonlinear dynamical Casimir effect at weak nonstationarity: We show that even small nonlinearities significantly affect particle
production in the dynamical Casimir effect at large evolution times. To that
end, we derive the effective Hamiltonian and resum leading loop corrections to
the particle flux in a massless scalar field theory with time-dependent
Dirichlet boundary conditions and quartic self-interaction. To perform the
resummation, we assume small deviations from the equilibrium and employ a kind
of rotating wave approximation. Besides that, we consider a quantum circuit
analog of the dynamical Casimir effect, which is also essentially nonlinear. In
both cases, loop contributions to the number of created particles are
comparable to the tree-level values.
|
Anti-de-Sitter-Maxwell-Yang-Mills black holes thermodynamics from
nonlocal observables point of view: In this paper, we analyze the thermodynamic properties of the Anti de Sitter
black hole in the Einstein-Maxwell-Yang-Mills-AdS gravity (EMYM) via many
approaches and in different thermodynamical ensembles (canonical/ grand
canonical). First, we give a concise overview of this phase structure in the
entropy-thermal diagram for fixed charges then we investigate this
thermodynamical structure in fixed potentials ensemble. The Next relevant step
is recalling the nonlocal observables such as holographic entanglement entropy
and two-point correlation function to show that both observables exhibit a Van
der Waals-like behavior in our numerical accuracy and just near the critical
line as the case of the thermal entropy for fixed charges by checking Maxwell's
equal area law and the critical exponent. In the light of the grand canonical
ensemble, we also find a newly phase structure for such a black hole where the
critical behavior disappears in the thermal picture as well as in the
holographic one.
|
Seiberg-Witten theory for a non-trivial compactification from five to
four dimensions: The prepotential and spectral curve are described for a smooth interpolation
between an enlarged N=4 SUSY and ordinary N=2 SUSY Yang-Mills theory in four
dimensions, obtained by compactification from five dimensions with non-trivial
(periodic and antiperiodic) boundary conditions. This system provides a new
solution to the generalized WDVV equations. We show that this exhausts all
possible solutions of a given functional form.
|
Effective Average Action of Chern-Simons Field Theory: The renormalization of the Chern-Simons parameter is investigated by using an
exact and manifestly gauge invariant evolution equation for the scale-dependent
effective average action.
|
On the spectrum of a matrix model for the D=11 supermembrane
compactified on a torus with non-trivial winding: The spectrum of the Hamiltonian of the double compactified D=11 supermembrane
with non-trivial central charge or equivalently the non-commutative symplectic
super Maxwell theory is analyzed. In distinction to what occurs for the D=11
supermembrane in Minkowski target space where the bosonic potential presents
string-like spikes which render the spectrum of the supersymmetric model
continuous, we prove that the potential of the bosonic compactified membrane
with non-trivial central charge is strictly positive definite and becomes
infinity in all directions when the norm of the configuration space goes to
infinity. This ensures that the resolvent of the bosonic Hamiltonian is
compact. We find an upper bound for the asymptotic distribution of the
eigenvalues.
|
Light-cone form of field dynamics in anti-de Sitter space-time and
AdS/CFT correspondence: Light-cone form of field dynamics in anti-de Sitter space-time is developed.
Using field theoretic and group theoretic approaches the light-cone
representation for generators of anti-de Sitter algebra acting as differential
operators on bulk fields is found. We also present light-cone reformulation of
the boundary conformal field theory representations. Making use of these
explicit representations of AdS algebra as isometry algebra in the bulk and the
algebra of conformal transformations at the boundary a precise correspondence
between the bulk fields and the boundary operators is established.
|
Temperature Independent Renormalization of Finite Temperature Field
Theory: We analyse 4-dimensional massive $\vp^4$ theory at finite temperature T in
the imaginary-time formalism. We present a rigorous proof that this quantum
field theory is renormalizable, to all orders of the loop expansion. Our main
point is to show that the counterterms can be chosen temperature independent,
so that the temperature flow of the relevant parameters as a function of $T$
can be followed. Our result confirms the experience from explicit calculations
to the leading orders. The proof is based on flow equations, i.e. on the
(perturbative) Wilson renormalization group. In fact we will show that the
difference between the theories at T>0 and at T=0 contains no relevant terms.
Contrary to BPHZ type formalisms our approach permits to lay hand on
renormalization conditions and counterterms at the same time, since both appear
as boundary terms of the renormalization group flow. This is crucial for the
proof.
|
String Webs and 1/4 BPS Monopoles: We argue for the existence of many new 1/4 BPS states in N=4 SU(N_c)
Super-Yang-Mills theory with N_c>=3, by constructing them from supersymmetric
string webs whose external strings terminate on parallel D3-branes. The masses
of the string webs are shown to agree with the BPS bound for the corresponding
states in SYM. We identify the curves of marginal stability, at which these
states decay into other BPS states. We find the bosonic and fermionic zero
modes of the string webs, and thereby the degeneracy and spin content of some
of the BPS states. States of arbitrarily high spin are predicted in this
manner, all of which become massless at the conformal point. For N_c>=4 we find
BPS states which transform in long multiplets, and are therefore not protected
against becoming stable non-BPS states as moduli are varied. The mass of these
extremal non-BPS states is constrained as they are connected to BPS states.
Analogous geometric phenomena are anticipated.
|
Mathematical Tools for Calculation of the Effective Action in Quantum
Gravity: We review the status of covariant methods in quantum field theory and quantum
gravity, in particular, some recent progress in the calculation of the
effective action via the heat kernel method. We study the heat kernel
associated with an elliptic second-order partial differential operator of
Laplace type acting on smooth sections of a vector bundle over a Riemannian
manifold without boundary. We develop a manifestly covariant method for
computation of the heat kernel asymptotic expansion as well as new algebraic
methods for calculation of the heat kernel for covariantly constant background,
in particular, on homogeneous bundles over symmetric spaces, which enables one
to compute the low-energy non-perturbative effective action.
|
A Nonperturbative Test of M2-Brane Theory: We discuss non-perturbative effects in the ABJM model due to monopole
instantons. We begin by constructing the instanton solutions in the $U(2)\times
U(2)$ model, explicitly, and computing the Euclidean action. The Wick-rotated
Lagrangian is complex and its BPS monopole instantons are found to be a
delicate version of the usual 't Hooft-Polyakov monopole solutions. They are
generically 1/3 BPS but become 1/2 BPS at special locus in the moduli space of
two M2-branes, yet each instanton carries eight fermionic zero modes,
regardless of the vacuum choice. The low energy effective action induced by
monopole instantons are quartic order in derivatives. The resulting vertices
are nonperturbative in $1/k$, as expected, but are rational functions of the
vacuum moduli. We also analyze the system of two M2-branes in the supergravity
framework and compute the higher order interactions via 11-dimensional
supergraviton exchange. The comparison of the two shows that the instanton
vertices are precisely reproduced by this M2-brane picture, supporting the
proposal that the ABJM model describes multiple M2-branes.
|
N = 2 Supersymmetric QED equivalence of N = 2 Volkov-Akulov model: We show explicitly in two dimensional spacetime (d = 2) that the N = 2
Volkov-Akulov model is equivalent to the spontaneously broken linear
supersymmetry (LSUSY) interacting gauge theory for N = 2 vector and N = 2
scalar supermultiplets. The local gauge interaction of LSUSY is induced by the
specific composite structure of the auxiliary fields and the consequent
transformations.
|
Massive Dual Spin 2 Revisited: We reconsider a massive dual spin 2 field theory in four spacetime
dimensions. We obtain the Lagrangian that describes the lowest order coupling
of the field to the four-dimensional curl of its own energy-momentum tensor. We
then find some static solutions for the dual field produced by other
energy-momentum sources and we compare these to similar static solutions for
non-dual "finite range" gravity. Finally, through use of a nonlinear field
redefinition, we show the theory is the exact dual of the
Ogievetsky-Polubarinov model for a massive spin 2 field.
|
Two interacting scalars system in curved spacetime -- vacuum stability
from the curved spacetime Effective Field Theory (cEFT) perspective: In this article we investigated the influence of the gravity induced higher
dimensional operators on the issue of vacuum stability in a model containing
two interacting scalar fields. As a framework we used the curved spacetime
Effective Field Theory (cEFT) applied to the aforementioned system in which one
of the scalars is heavy. After integrating out the heavy scalar we used the
standard Euclidean approach to the obtained cEFT. Apart from analyzing the
influence of standard operators like the non-minimal coupling to gravity and
the dimension six contribution to the scalar field potential, we also
investigated the rarely discussed dimension six contribution to the kinetic
term and the new gravity induced contribution to the scalar quartic
self-interaction.
|
Strong magnetic field asymptotic behaviour for the fermion-induced
effective energy in the presence of a magnetic flux tube: In Ref. 3, we presented an asymptotic formula for the fermion-induced
effective energy in 3+1 dimensions in the presence of a cylindrically symmetric
inhomogeneous strong magnetic field. However, there are some points which were
not clearly explained. In fact, the arguments, which led us to the asymptotic
formula, are based on a numerical study of the integral of Eq. (10), as we will
see in the main part of this paper. The aim of this work is to present this
study in detail.
|
Searching for Gravity Without a Metric: Recently it has been explicitly shown how a theory with global
$GL(d,\mathbb{R})$ coordinate (affine) invariance which is spontaneously broken
down to its Lorentz subgroup will have as its Goldstone fields enough degrees
of freedom to create a metric and a covariant derivative arXiv:1105.5848. Such
a theory would constitute an effective theory of gravity. So far however, no
explicit theory has been found which exhibits this symmetry breaking pattern,
mainly due to the difficulty of even writing down a $GL(d,\mathbb{R})$
invariant actions in the absence of a metric. In this paper we explicitly
construct an affine generalization of the Dirac action employing infinite
dimensional spinorial representations of the group. This implies that it is
built from an infinite number of spinor Lorentz multiplets. We introduce a
systematic procedure for obtaining $GL(d,\mathbb{R})$ invariant interaction
terms to obtain quite general interacting models. Such models have order
operators whose expectation value can break affine symmetry to Poincar\'{e}
symmetry. We discuss possible interactions and mechanisms for this symmetry
breaking to occur, which would provide a dynamical explanation of the
Lorentzian signature of spacetime.
|
Hawking Radiation Spectra for Scalar Fields by a Higher-Dimensional
Schwarzschild-de-Sitter Black Hole: In this work, we study the propagation of scalar fields in the gravitational
background of a higher-dimensional Schwarzschild-de-Sitter black hole as well
as on the projected-on-the-brane 4-dimensional background. The scalar fields
have also a non-minimal coupling to the corresponding, bulk or brane, scalar
curvature. We perform a comprehensive study by deriving exact numerical results
for the greybody factors, and study their profile in terms of particle and
spacetime properties. We then proceed to derive the Hawking radiation spectra
for a higher-dimensional Schwarzschild-de-Sitter black hole, and we study both
bulk and brane channels. We demonstrate that the non-minimal field coupling,
that creates an effective mass term for the fields, suppresses the energy
emission rates while the cosmological constant assumes a dual role. By
computing the relative energy rates and the total emissivity ratio for bulk and
brane emission, we demonstrate that the combined effect of a large number of
extra dimensions and value of the field coupling gives to the bulk channel the
clear domination in the bulk-brane energy balance.
|
The effect of boundary conditions on dimensionally reduced
field-theoretical models at finite temperature: Here we understand \textit{dimensional reduction} as a procedure to obtain an
effective model in $D-1$ dimensions that is related to the original model in
$D$ dimensions. To explore this concept we use both a self-interacting
fermionic model and self-interacting bosonic model. Furthermore, in both cases,
we consider different boundary conditions in space: periodic, antiperiodic,
Dirichlet and Neumann. For bosonic fields, we get the so defined dimensional
reduction. Taking the simple example of a quartic interaction, we obtain that
the boundary condition (periodic, Dirichlet, Neumann) influence the new
coupling of the reduced model. For fermionic fields, we get the curious result
that the model obtained reducing from $D$ dimensions to $D-1$ dimensions is
distinguishable from taking into account a fermionic field originally in $D-1$
dimensions. Moreover, when one considers antiperiodic boundary condition in
space (both for bosons or fermions) it is found that the dimensional reduction
is not allowed.
|
On the structure of composite black p-brane configurations and related
black holes: We comment on the structure of intersecting black p-brane solutions in string
theory explaining how known solutions can be obtained from Schwarzschild
solution simply by sequences of boosts and dualities. This implies, in
particular, that dimensional reduction in all internal world-volume directions
including time leads to a metric (related by analytic continuation to a
cosmological metric) which does not depend on p-brane charges, i.e. is the same
as the metric following by reduction from a higher-dimensional `neutral'
Schwarzschild black hole.
|
Impact of irrelevant deformations on thermodynamics and transport in
holographic quantum critical states: We study thermodynamic and transport observables of quantum critical states
that arise in the infra-red limit of holographic renormalisation group flows.
Although these observables are expected to exhibit quantum critical scaling,
there are a number of cases in which their frequency and temperature
dependences are in apparent contradiction with scaling theories. We study two
different classes of examples, and show in both cases that the apparent
breakdown of scaling is a consequence of the dependence of observables on an
irrelevant deformation of the quantum critical state. By assigning scaling
dimensions to the near-horizon observables, we formulate improved scaling
theories that are completely consistent with all explicit holographic results
once the dependence on the dangerously irrelevant coupling is properly
accounted for. In addition to governing thermodynamic and transport phenomena
in these states, we show that the dangerously irrelevant coupling also controls
late-time equilibration, which occurs at a rate parametrically slower than the
temperature $1/\tau_{eq}\ll T$. At very late times, transport is
diffusion-dominated, with a diffusivity that can be written simply in terms of
$\tau_{eq}$ and the butterfly velocity, $D\sim v_B^2\tau_{eq}$. We conjecture
that in such cases there exists a long-lived, propagating collective mode with
velocity $v_s$, and in this case the relation $D=v_s^2\tau_{eq}$ holds exactly
in the limit $\tau_{eq} T\gg1$.
|
Entanglement entropies of an interval in the free Schrödinger field
theory on the half line: We study the entanglement entropies of an interval adjacent to the boundary
of the half line for the free fermionic spinless Schr\"odinger field theory at
finite density and zero temperature, with either Neumann or Dirichlet boundary
conditions. They are finite functions of the dimensionless parameter given by
the product of the Fermi momentum and the length of the interval. The
entanglement entropy displays an oscillatory behaviour, differently from the
case of the interval on the whole line. This behaviour is related to the
Friedel oscillations of the mean particle density on the half line at the
entangling point. We find analytic expressions for the expansions of the
entanglement entropies in the regimes of small and large values of the
dimensionless parameter. They display a remarkable agreement with the curves
obtained numerically. The analysis is extended to a family of free fermionic
Lifshitz models labelled by their integer Lifshitz exponent, whose parity
determines the properties of the entanglement entropies. The cumulants of the
local charge operator and the Schatten norms of the underlying kernels are also
explored.
|
A note on vortices from Lorentz-violating models: We consider two self-dual abelian Higgs systems obtained from Lorentz
breaking symmetry models by dimensional reduction. For the first model, we show
that the self-dual equations are identical to those of Nielsen-Olesen vortices.
Also, we show that our vortices have electric charge. In the second case we
show that self-dual Chern-Simons-Higgs vortices without electric charge are
possible.
|
Nonlinear Oscillatory Shear Tests in Viscoelastic Holography: We provide the first characterization of the nonlinear and time dependent
rheologic response of viscoelastic bottom-up holographic models. More
precisely, we perform oscillatory shear tests in holographic massive gravity
theories with finite elastic response, focusing on the large amplitude
oscillatory shear (LAOS) regime. The characterization of these systems is done
using several techniques: (I) the Lissajous figures, (II) the Fourier analysis
of the stress signal, (III) the Pipkin diagram and (IV) the dependence of the
storage and loss moduli on the amplitude of the applied strain. We find
substantial evidence for a strong strain stiffening mechanism, typical of
hyper-elastic materials such as rubbers and complex polymers. This indicates
that the holographic models considered are not a good description for rigid
metals, where strain stiffening is not commonly observed. Additionally, a
crossover between a viscoelastic liquid regime at small graviton mass (compared
to the temperature scale), and a viscoelastic solid regime at large values is
observed. Finally, we discuss the relevance of our results for soft matter and
for the understanding of the widely used homogeneous holographic models with
broken translations.
|
Entanglement Entropy of Magnetic Electron Stars: We study the behavior of the entanglement entropy in $(2+1)$--dimensional
strongly coupled theories via the AdS/CFT correspondence. We consider theories
at a finite charge density with a magnetic field, with their holographic dual
being Einstein-Maxwell-Dilaton theory in four dimensional anti--de Sitter
gravity. Restricting to black hole and electron star solutions at zero
temperature in the presence of a background magnetic field, we compute their
holographic entanglement entropy using the Ryu-Takayanagi prescription for both
strip and disk geometries. In the case of the electric or magnetic zero
temperature black holes, we are able to confirm that the entanglement entropy
is invariant under electric-magnetic duality. In the case of the electron star
with a finite magnetic field, for the strip geometry, we find a discontinuity
in the first derivative of the entanglement entropy as the strip width is
increased.
|
The Dirac field in Taub-NUT background: We investigate the SO(4,1) gauge-invariant theory of the Dirac fermions in
the external field of the Kaluza-Klein monopole, pointing out that the quantum
modes can be recovered from a Klein-Gordon equation analogous to the Schr\"
odinger equation in the Taub-NUT background. Moreover, we show that there is a
large collection of observables that can be directly derived from those of the
scalar theory. These offer many possibilities of choosing complete sets of
commuting operators which determine the quantum modes. In addition there are
some spin- like and Dirac-type operators involving the covariantly constant
Killing-Yano tensors of the hyper-K\" ahler Taub-NUT space. The energy
eigenspinors of the central modes in spherical coordinates are completely
evaluated in explicit, closed form.
|
A gauge theory for the 2+1 dimensional incompressible Euler equations: We show that in two dimensions the incompressible Euler equations can be
re-expressed in terms of an abelian gauge theory with a Chern-Simons term. The
magnetic field corresponds to fluid vorticity and the electric field is the
product of the vorticity and the gradient of the stream function. This picture
can be extended to active scalar models, including the surface
quasi-geostrophic equation. We examine the theory in the presence of a boundary
and show that the Noether charge algebra is a Kac-Moody algebra. We argue that
this symmetry is associated with the nodal lines of zero magnetic field.
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.