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A new class of N=1 no-scale supergravity models: We introduce a new N=1 no-scale supergravity model with F- and D-term
breaking. It contains a single chiral supermultiplet T and a single U(1) vector
multiplet U, gauging an axionic shift symmetry. Both supersymmetry and the
gauge symmetry are spontaneously broken, with the spin-3/2, spin-1 and spin-1/2
masses sliding along a classical flat direction, with a single real massless
scalar in the spectrum. The other degrees of freedom are absorbed by the
massive gravitino and vector. We extend our model, under very mild conditions,
to general gauge groups and matter content. | Supersymmetry and gauge symmetry breaking with naturally vanishing
vacuum energy: We review the construction of $N=1$ supergravity models where the Higgs and
super-Higgs effects are simultaneously realized, with naturally vanishing
classical vacuum energy and goldstino components along gauge-non-singlet
directions: this situation is likely to occur in the effective theories of
realistic string models. (Invited talk presented at SUSY--95, Palaiseau,
France, 15--19 May 1995) |
Confinement at Weak Coupling: The free energy of U(N) and SU(N) gauge theory was recently found to be of
order N^0 to all orders of a perturbative expansion about a center-symmetric
orbit of vanishing curvature. Here I consider extended models for which this
expansion is perturbatively stable. The extreme case of an SU(2) gauge theory
whose configuration space is restricted to center-symmetric orbits has recently
been investigated on the lattice hep-lat/0509156. In extension of my talk, a
discussion and possible interpretation of the observed finite temperature phase
transition is given. The transfer matrix of constrained SU(N) lattice gauge
theory is constructed for any finite temperature. | Weak Hopf symmetry and tube algebra of the generalized multifusion
string-net model: We investigate the multifusion generalization of string-net ground states and
lattice Hamiltonians, delving into its associated weak Hopf symmetry. For the
multifusion string-net, the gauge symmetry manifests as a general weak Hopf
algebra, leading to a reducible vacuum string label; the charge symmetry,
serving as a quantum double of gauge symmetry, constitutes a connected weak
Hopf algebra. This implies that the associated topological phase retains its
characterization by a unitary modular tensor category (UMTC). The bulk charge
symmetry can also be captured by a weak Hopf tube algebra. We offer an explicit
construction of the weak Hopf tube algebra structure and thoroughly discuss its
properties. The gapped boundary and domain wall models are extensively
discussed, with these $1d$ phases characterized by unitary multifusion
categories (UMFCs). We delve into the gauge and charge symmetries of these $1d$
phases, as well as the construction of the boundary and domain wall tube
algebras. Additionally, we illustrate that the domain wall tube algebra can be
regarded as a cross product of two boundary tube algebras. We establish the
anyon condensation theory to elucidate the bulk-to-boundary and bulk-to-wall
condensation phenomena from UMTCs to a UMFCs. As an application of our model,
we elucidate how to interpret the defective string-net as a restricted
multifusion string-net. |
Moduli Space of Global Symmetry in N=1 Supersymmetric Theories and the
Quasi-Nambu-Goldstone Bosons: We derive the moduli space for the global symmetry in N=1 supersymmetric
theories. We show, at the generic points, it coincides with the space of
quasi-Nambu-Goldstone (QNG) bosons, which appear besides the ordinary
Nambu-Goldstone (NG) bosons when global symmetry G breaks down spontaneously to
its subgroup H with preserving N=1 supersymmetry. At the singular points, most
of the NG bosons change to the QNG bosons and the unbroken global symmetry is
enhanced. The G-orbits parametrized by the NG bosons are the fibre at the
moduli space and the singular points correspond to the point where H-orbit (in
G-orbit) shrinks. We also show the low-energy effective Lagrangian is the
arbitrary function of the orbit map. | Noncommutative Integrable Field Theories in 2d: We study the noncommutative generalization of (euclidean) integrable models
in two-dimensions, specifically the sine- and sinh-Gordon and the U(N)
principal chiral models. By looking at tree-level amplitudes for the
sinh-Gordon model we show that its na\"\i ve noncommutative generalization is
{\em not} integrable. On the other hand, the addition of extra constraints,
obtained through the generalization of the zero-curvature method, renders the
model integrable. We construct explicit non-local non-trivial conserved charges
for the U(N) principal chiral model using the Brezin-Itzykson-Zinn-Justin-Zuber
method. |
Dynamical Black Hole Entropy in Effective Field Theory: In recent work, Hollands, Kov\'acs and Reall have built on previous work of
Wall to provide a definition of dynamical black hole entropy for gravitational
effective field theories (EFTs). This entropy satisfies a second law of black
hole mechanics to quadratic order in perturbations around a stationary black
hole. We determine the explicit form of this entropy for the EFT of 4d vacuum
gravity including terms in the action with up to 6 derivatives. An open
question concerns the gauge invariance of this definition of black hole
entropy. We show that gauge invariance holds for the EFT of vacuum gravity with
up to 6 derivatives but demonstrate that it can fail when 8 derivative terms
are included. We determine an entropy for Einstein-Gauss-Bonnet theory by
treating it as an EFT with vanishing 6 derivative terms. | Trace anomalies for Weyl fermions: too odd to be true?: We review recent discussions regarding the parity-odd contribution to the
trace anomaly of a chiral fermion. We pay special attention to the perturbative
approach in terms of Feynman diagrams, comparing in detail the results obtained
using dimensional regularization and the Breitenlohner--Maison prescription
with other approaches. |
Rollercoaster Cosmology: (Abridged) Does inflation have to happen all in one go? The answer is a
resounding no! All cosmological problems can be solved by a sequence of short
bursts of cosmic acceleration, interrupted by short epochs of decelerated
expansion. The spectrum of perturbations will still match the CMB and LSS if
the earliest stage of the last ${\cal O}(50)-{\cal O}(60)$ efolds is at least
${\cal O}(15)$ efolds long. Other stages can be considerably shorter. But as
long as they add up to ${\cal O}(50)-{\cal O}(60)$ efolds and the stages of
decelerated expansion in between them are shorter and also overall last less,
the ensuing cosmology will pass muster. The presence of the interruptions
resets the efold clock of each accelerating stage, and changes its value at the
CMB pivot point. This change opens up the theory space, loosening the bounds.
In particular some models that seem excluded at ${\cal N}=60$ fit very well as
shorter stages with ${\cal N}=30$. Interesting predictions are that both the
scalar and tensor spectra of perturbations are rapidly modified at short
wavelengths. These features could be tested with future CMB spectroscopy
searches and with short wavelength primordial gravity probes. The spatial
curvature in these models can be larger than the largest wavelength scalar
perturbations, because $\Omega_{\tt k}$ evolves differently than the scalar
perturbations $\frac{\delta \rho}{\rho}|_{\tt S}$. Finally, with many short
stages of accelerated expansion, the abundance of reheating products from
previous accelerated stages does not get completely wiped out. This implies
that the universe may contain additional populations of particles, more rare
than the visible ones, or even primordial black holes, created during a late
decelerated epoch before last reheating, which may be dark matter. | The Geometry of Electric Charge: The Charge Characteristic Class: It is well known that magnetic monopoles are related to the first Chern
class. In this note electric charge is used to construct an analogous
characteristic class: the charge class. |
Lie algebra cohomology and group structure of gauge theories: We explicitly construct the adjoint operator of coboundary operator and
obtain the Hodge decomposition theorem and the Poincar\'e duality for the Lie
algebra cohomology of the infinite-dimensional gauge transformation group. We
show that the adjoint of the coboundary operator can be identified with the
BRST adjoint generator $Q^{\dagger}$ for the Lie algebra cohomology induced by
BRST generator $Q$. We also point out an interesting duality relation -
Poincar\'e duality - with respect to gauge anomalies and Wess-Zumino-Witten
topological terms. We consider the consistent embedding of the BRST adjoint
generator $Q^{\dagger}$ into the relativistic phase space and identify the
noncovariant symmetry recently discovered in QED with the BRST adjoint N\"other
charge $Q^{\dagger}$. | Hidden supersymmetry of domain walls and cosmologies: We show that all domain-wall solutions of gravity coupled to scalar fields
for which the worldvolume geometry is Minkowski or anti-de Sitter admit Killing
spinors, and satisfy corresponding first-order equations involving a
superpotential determined by the solution. By analytic continuation, all flat
or closed FLRW cosmologies are shown to satisfy similar first-order equations
arising from the existence of ``pseudo-Killing'' spinors. |
On the Classical $W_{4}^{(2)}$ Algebra: We consider the classical \w42 algebra from the integrable system viewpoint.
The integrable evolution equations associated with the \w42 algebra are
constructed and the Miura maps , consequently modifications, are presented.
Modifying the Miura maps, we give a free field realization the classical \w42
algebra. We also construct the Toda type integrable systems for it. | Factorization identities and algebraic Bethe ansatz for $D^{(2)}_{2}$
models: We express $D^{(2)}_{2}$ transfer matrices as products of $A^{(1)}_{1}$
transfer matrices, for both closed and open spin chains. We use these
relations, which we call factorization identities, to solve the models by
algebraic Bethe ansatz. We also formulate and solve a new integrable XXZ-like
open spin chain with an even number of sites that depends on a continuous
parameter, which we interpret as the rapidity of the boundary. |
Quantum $\mathcal{R}$-matrices as universal qubit gates: We study the Chern-Simons approach to the topological quantum computing. We
use quantum $\mathcal{R}$-matrices as universal quantum gates and study the
approximations of some one-qubit operations. We make some modifications to the
known Solovay-Kitaev algorithm suitable for our particular problem. | On the cusp anomalous dimension in the ladder limit of $\mathcal N=4$
SYM: We analyze the cusp anomalous dimension in the (leading) ladder limit of
$\mathcal N=4$ SYM and present new results for its higher-order perturbative
expansion. We study two different limits with respect to the cusp angle $\phi$.
The first is the light-like regime where $x = e^{i\,\phi}\to 0$. This limit is
characterised by a non-trivial expansion of the cusp anomaly as a sum of powers
of $\log x$, where the maximum exponent increases with the loop order. The
coefficients of this expansion have remarkable transcendentality features and
can be expressed by products of single zeta values. We show that the whole
logarithmic expansion is fully captured by a solvable Woods-Saxon like
one-dimensional potential. From the exact solution, we extract generating
functions for the cusp anomaly as well as for the various specific
transcendental structures appearing therein. The second limit that we discuss
is the regime of small cusp angle. In this somewhat simpler case, we show how
to organise the quantum mechanical perturbation theory in a novel efficient way
by means of a suitable all-order Ansatz for the ground state of the associated
Schr\"odinger problem. Our perturbative setup allows to systematically derive
higher-order perturbative corrections in powers of the cusp angle as explicit
non-perturbative functions of the effective coupling. This series approximation
is compared with the numerical solution of the Schr\"odinger equation to show
that we can achieve very good accuracy over the whole range of coupling and
cusp angle. Our results have been obtained by relatively simple techniques.
Nevertheless, they provide several non-trivial tests useful to check the
application of Quantum Spectral Curve methods to the ladder approximation at
non zero $\phi$, in the two limits we studied. |
Fixing All Moduli for M-Theory on K3xK3: We analyze M-theory compactified on K3xK3 with fluxes preserving half the
supersymmetry and its F-theory limit, which is dual to an orientifold of the
type IIB string on $K3\times T^2/Z_2$. The geometry of attractive K3 surfaces
plays a significant role in the analysis. We prove that the number of choices
for the K3 surfaces is finite and we show how they can be completely
classified. We list the possibilities in one case. We then study the instanton
effects and see that they will generically fix all of the moduli. We also
discuss situations where the instanton effects might not fix all the moduli. | Topological violation of global symmetries in quantum gravity: We discuss a topological reason why global symmetries are not conserved in
quantum gravity, at least when the symmetry comes from compactification of a
higher form symmetry. The mechanism is purely topological and does not require
any explicit breaking term in the UV Lagrangian. Local current conservation
does not imply global charge conservation in a sum over geometries in the path
integral. We explicitly consider the shift symmetry of an axion-like field
which originates from the compactification of a $p$-form gauge field. Our
topological construction is motivated by the brane/black-brane correspondence,
brane instantons, and an idea that virtual black branes of a simple kind may be
realized by surgery on spacetime manifolds. |
Sharp Boundaries for the Swampland: We reconsider the problem of bounding higher derivative couplings in
consistent weakly coupled gravitational theories, starting from general
assumptions about analyticity and Regge growth of the S-matrix. Higher
derivative couplings are expected to be of order one in the units of the UV
cutoff. Our approach justifies this expectation and allows to prove precise
bounds on the order one coefficients. Our main tool are dispersive sum rules
for the S-matrix. We overcome the difficulties presented by the graviton pole
by measuring couplings at small impact parameter, rather than in the forward
limit. We illustrate the method in theories containing a massless scalar
coupled to gravity, and in theories with maximal supersymmetry. | Random Matrix Theory for Complexity Growth and Black Hole Interiors: We study a precise and computationally tractable notion of operator
complexity in holographic quantum theories, including the ensemble dual of
Jackiw-Teitelboim gravity and two-dimensional holographic conformal field
theories. This is a refined, "microcanonical" version of K-complexity that
applies to theories with infinite or continuous spectra (including quantum
field theories), and in the holographic theories we study exhibits exponential
growth for a scrambling time, followed by linear growth until saturation at a
time exponential in the entropy $\unicode{x2014}$a behavior that is
characteristic of chaos. We show that the linear growth regime implies a
universal random matrix description of the operator dynamics after scrambling.
Our main tool for establishing this connection is a "complexity renormalization
group" framework we develop that allows us to study the effective operator
dynamics for different timescales by "integrating out" large K-complexities. In
the dual gravity setting, we comment on the empirical match between our version
of K-complexity and the maximal volume proposal, and speculate on a connection
between the universal random matrix theory dynamics of operator growth after
scrambling and the spatial translation symmetry of smooth black hole interiors. |
Entropy Linear Response Theory with Non-Markovian Bath: We developed a perturbative calculation for entropy dynamics considering a
sudden coupling between a system and a bath. The theory we developed can work
in general environment without Markovian approximation. A perturbative formula
is given for bosonic environment and fermionic environment, respectively. We
find the Renyi entropy response is only related to the spectral functions of
the system and the environment, together with a specific statistical kernel
distribution function. We find a t^2 growth/decay in the short time limit and a
t linear growth/decay in longer time scale for second Renyi entropy. A
non-monotonic behavior of Renyi entropy for fermionic systems is found to be
quite general when the environment's temperature is lower. A Fourier's law in
heat transport is obtained when two systems' temperature are close to each
other. A consistency check is made for Sachdev-Ye-Kitaev model coupling to free
fermions, a Page curve alike dynamics is found in a process dual to black hole
evaporation. An oscillation of entanglement entropy is found for a gapped
spectrum of environment. | Towards a Non-Supersymmetric String Phenomenology: Over the past three decades, considerable effort has been devoted to studying
the rich and diverse phenomenologies of heterotic strings exhibiting spacetime
supersymmetry. Unfortunately, during this same period, there has been
relatively little work studying the phenomenologies associated with their
non-supersymmetric counterparts. The primary reason for this relative lack of
attention is the fact that strings without spacetime supersymmetry are
generally unstable, exhibiting large one-loop dilaton tadpoles. In this paper,
we demonstrate that this hurdle can be overcome in a class of tachyon-free
four-dimensional string models realized through coordinate-dependent
compactifications. Moreover, as we shall see, it is possible to construct
models in this class whose low-lying states resemble the Standard Model (or
even potential unified extensions thereof) --- all without any light
superpartners, and indeed without supersymmetry at any energy scale. The
existence of such models thus opens the door to general studies of
non-supersymmetric string phenomenology, and in this paper we proceed to
discuss a variety of theoretical and phenomenological issues associated with
such non-supersymmetric strings. On the theoretical side, we discuss the
finiteness properties of such strings, the general characteristics of their
mass spectra, the magnitude and behavior of their one-loop cosmological
constants, and their interpolation properties. By contrast, on the
phenomenological side, the properties we discuss are more model-specific and
include their construction techniques, their natural energy scales, their
particle and charge assignments, and the magnitudes of their associated Yukawa
couplings and scalar masses. |
Yukawa couplings from magnetized D-brane models on non-factorisable tori: We compute Yukawa couplings in type IIB string theory compactified on a non
factorisable six-torus in the presence of D9 branes and fluxes. The setting
studied in detail, is obtained by T-dualising an intersecting brane
configuration of type IIA theory compactified on a torus generated by the
SO(12) root lattice. Particular deformations of such torus are taken into
account and provide moduli dependent couplings. Agreement with the type IIA
result is found in a non trivial way. The classical type IIB calculation gives
also information on a factor accessible only by quantum computations on the
type IIA side. | Cosmological equations and Thermodynamics on Apparent Horizon in Thick
Braneworld: We derive the generalized Friedmann equation governing the cosmological
evolution inside the thick brane model in the presence of two curvature
correction terms: a four-dimensional scalar curvature from induced gravity on
the brane, and a five-dimensional Gauss-Bonnet curvature term. We find two
effective four-dimensional reductions of the Friedmann equation in some limits
and demonstrate that they can be rewritten as the first law of thermodynamics
on the apparent horizon of thick braneworld. |
Recent developments in heterotic compactifications: In this short review, we outline three sets of developments in understanding
heterotic string compactifications. First, we outline recent progress in
heterotic analogues of quantum cohomology computations. Second, we discuss a
potential swampland issue in heterotic strings, and new heterotic string
constructions that can be used to fill in the naively missing theories. Third,
we discuss recent developments in string compactifications on stacks and their
applications, concluding with an outline of work-in-progress on heterotic
string compactifications on gerbes. | Spectral Curves for Super-Yang-Mills with Adjoint Hypermultiplet for
General Lie Algebras: The Seiberg-Witten curves and differentials for $\N=2$ supersymmetric
Yang-Mills theories with one hypermultiplet of mass $m$ in the adjoint
representation of the gauge algebra $\G$, are constructed for arbitrary
classical or exceptional $\G$ (except $G_2$). The curves are obtained from the
recently established Lax pairs with spectral parameter for the (twisted)
elliptic Calogero-Moser integrable systems associated with the algebra $\G$.
Curves and differentials are shown to have the proper group theoretic and
complex analytic structure, and to behave as expected when $m$ tends either to
0 or to $\infty$. By way of example, the prepotential for $\G = D_n$, evaluated
with these techniques, is shown to agree with standard perturbative results. A
renormalization group type equation relating the prepotential to the
Calogero-Moser Hamiltonian is obtained for arbitrary $\G$, generalizing a
previous result for $\G = SU(N)$. Duality properties and decoupling to theories
with other representations are briefly discussed. |
Spectrum of Dyons and Black Holes in CHL orbifolds using Borcherds Lift: The degeneracies of supersymmetric quarter BPS dyons in four dimensions and
of spinning black holes in five dimensions in a CHL compactification are
computed exactly using Borcherds lift. The Hodge anomaly in the construction
has a physical interpretation as the contribution of a single M-theory
Kaluza-Klein 6-brane in the 4d-5d lift. Using factorization, it is shown that
the resulting formula has a natural interpretation as a two-loop partition
function of left-moving heterotic string, consistent with the heuristic picture
of dyons in the M-theory lift of string webs. | B-field in AdS(3)/CFT(2) Correspondence and Integrability: We construct topological Wess-Zumino term for supercoset sigma-models on
various AdS(3) backgrounds. For appropriately chosen set of parameters, the
sigma-model remains integrable when the Wess-Zumino term is added to the
action. Moreover, the conditions for integrability, kappa-symmetry and
conformal invariance are equivalent to each other. |
Quintessential Maldacena-Maoz Cosmologies: Maldacena and Maoz have proposed a new approach to holographic cosmology
based on Euclidean manifolds with disconnected boundaries. This approach
appears, however, to be in conflict with the known geometric results [the
Witten-Yau theorem and its extensions] on spaces with boundaries of
non-negative scalar curvature. We show precisely how the Maldacena-Maoz
approach evades these theorems. We also exhibit Maldacena-Maoz cosmologies with
[cosmologically] more natural matter content, namely quintessence instead of
Yang-Mills fields, thereby demonstrating that these cosmologies do not depend
on a special choice of matter to split the Euclidean boundary. We conclude that
if our Universe is fundamentally anti-de Sitter-like [with the current
acceleration being only temporary], then this may force us to confront the
holography of spaces with a connected bulk but a disconnected boundary. | Functional determinants and Casimir energy in higher dimensional
spherically symmetric background potentials: In this paper we analyze the spectral zeta function associated with a Laplace
operator acting on scalar functions on an N-dimensional Euclidean space in the
presence of a spherically symmetric background potential. The obtained analytic
continuation of the spectral zeta function is then used to derive very simple
results for the functional determinant of the operator and the Casimir energy
of the scalar field. |
Note on the deformation of chiral algebra: We introduce a new type of deformation of the chiral symmetry based on the
deformation of the Laurent expansion of the conformal energy momentum tensor.
Two kinds of solutions of the deformed equations of continuity are worked out.
Known results are recovered, others features are also discussed. | An Exact Solution to O(26) Sigma Model coupled to 2-D Gravity: By a mapping to the bosonic string theory, we present an exact solution to
the O(26) sigma model coupled to 2-D quantum gravity. In particular, we obtain
the exact gravitational dressing to the various matter operators classified by
the irreducible representations of O(26). We also derive the exact form of the
gravitationally modified beta function for the original coupling constant
$e^2$. The relation between our exact solution and the asymptotic solution
given in ref[3] is discussed in various aspects. |
Higher-spin gauge models with (1,1) supersymmetry in AdS${}_3$:
Reduction to (1,0) superspace: In three dimensions, there are two types of ${\cal N}=2$ anti-de Sitter (AdS)
supersymmetry, which are denoted (1,1) and (2,0). They are characterised by
different supercurrents and support different families of higher-spin gauge
models (massless and massive) which were constructed in arXiv:1807.09098 and
arXiv:1809.00802 for the (1,1) and (2,0) cases, respectively, using superspace
techniques. It turns out that the precise difference between the (1,1) and
(2,0) higher-spin supermultiplets can be pinned down by reducing these gauge
theories to (1,0) AdS superspace. The present paper is devoted to the $(1,1)
\to (1,0)$ AdS superspace reduction. In conjunction with the outcomes of the
$(2,0) \to (1,0)$ AdS superspace reduction carried out in arXiv:1905.05050, we
demonstrate that every known higher-spin theory with (1,1) or (2,0) AdS
supersymmetry decomposes into a sum of two off-shell (1,0) supermultiplets
which belong to four series of inequivalent higher-spin gauge models. The
latter are reduced to components. | Reply to "A note on the innocuous implications of a minimum length in
quantum gravity" by P.H. Frampton: We reply to the comment "A note on the innocuous implications of a minimum
length in quantum gravity" by P.H. Frampton [Class. Quantum Grav. 26 (2009)
018001, arXiv:arXiv:0808.0283] on our paper "Dangerous implications of a
minimum length in quantum gravity" [Class. Quantum Grav. 25 (2008) 195013,
arXiv:0803.0749]. |
Cones, Tri-Sasakian Structures and Superconformal Invariance: In this note we show that rigid N=2 superconformal hypermultiplets must have
target manifolds which are cones over tri-Sasakian metrics. We comment on the
relation of this work to cone-branes and the AdS/CFT correspondence. | Open-string integrals with multiple unintegrated punctures at genus one: We study integrals appearing in intermediate steps of one-loop open-string
amplitudes, with multiple unintegrated punctures on the $A$-cycle of a torus.
We construct a vector of such integrals which closes after taking a total
differential with respect to the $N$ unintegrated punctures and the modular
parameter $\tau$. These integrals are found to satisfy the elliptic
Knizhnik-Zamolodchikov-Bernard (KZB) equations, and can be written as a power
series in $\alpha$' -- the string length squared -- in terms of elliptic
multiple polylogarithms (eMPLs). In the $N$-puncture case, the KZB equation
reveals a representation of $B_{1,N}$, the braid group of $N$ strands on a
torus, acting on its solutions. We write the simplest of these braid group
elements -- the braiding one puncture around another -- and obtain generating
functions of analytic continuations of eMPLs. The KZB equations in the
so-called universal case is written in terms of the genus-one Drinfeld-Kohno
algebra $\mathfrak{t}_{1,N} \rtimes \mathfrak{d}$, a graded algebra. Our
construction determines matrix representations of various dimensions for
several generators of this algebra which respect its grading up to commuting
terms. |
Tunneling Without Bounce: The false vacua of some potentials do not decay via Euclidean bounces. This
typically happens for tunneling actions with a flat direction (in field
configuration space) that is lifted by a perturbation into a sloping valley,
pushing the bounce off to infinity. Using three different approaches we find a
consistent picture for such decays. In the Euclidean approach the bottom of the
action valley consists of a family of pseudo-bounces (field configurations with
some key good properties of bounces except extremizing the action). The
pseudo-bounce result is validated by minimizing a WKB action in Minkowski space
along appropriate paths in configuration space. Finally, the simplest approach
uses the tunneling action method proposed recently with a simple modification
of boundary conditions. | The TCFHs of D=11 AdS backgrounds and hidden symmetries: We present the TCFHs of all AdS backgrounds of 11-dimensional supergravity
and explore some of the properties of the associated connections. Therefore we
demonstrate that all Killing spinor bilinears satisfy a generalisation of the
conformal Killing-Yano equations with respect to the TCFH connection. In
addition we explore the hidden symmetries of spinning particle probes
propagating on these backgrounds. We give several examples of hidden symmetries
for probes on the maximal supersymmetric AdS backgrounds as well as on some AdS
backgrounds that arise as near horizon geometries of intersecting M-branes. |
On the noncommutative eikonal: We study the eikonal approximation to quantum mechanics on the Moyal plane.
Instead of using a star product, the analysis is carried out in terms of
operator-valued wavefunctions depending on noncommuting, operator-valued
coordinates. | Topological Entanglement of Polymers and Chern-Simons Field Theory: In recent times some interesting field theoretical descriptions of the
statistical mechanics of entangling polymers have been proposed by various
authors. In these approaches, a single test polymer fluctuating in a background
of static polymers or in a lattice of obstacles is considered. The extension to
the case in which the configurations of two or more polymers become non-static
is not straightforward unless their trajectories are severely constrained. In
this paper we present another approach, based on Chern--Simons field theory,
which is able to describe the topological entanglements of two fluctuating
polymers in terms of gauge fields and second quantized replica fields. |
Two gravitational shock waves on the AdS_3 brane: A gravitational shock wave is a solution to Einstein equations describing the
gravitational field of a massless particle. We obtain such a geometry for a
particle moving on a AdS_3 brane embedded in a AdS_4 bulk (the lower
dimensional version of the "locally localized gravity" model of Karch and
Randall). In order to do this, we use two different techniques. First, we solve
directly Einstein equations sourced by a massless particle. Then we boost to
the speed of light the AdS_3 brane black hole solution of Emparan et al while
sending its mass parameter to zero. Surprisingly, we obtain two different
results. We discuss the origin of these two different solutions both in the
bulk and in the CFT picture. As a by-product, we derive the expression for the
shock wave associated to a transversally accelerating particle in AdS_4. | On the Breaking of Conformal Symmetry in the AdS/CFT Correspondence: The renormalization of the boundary action in the AdS/CFT correspondence is
considered and the breaking of conformal symmetry is discussed. |
Flavored extended instanton in QCD: In this paper we discuss new flavored space-like defects in confined QCD
which can be considered as the Euclidean extended instantons carrying the
topologically quantized currents. We focus on the simplest 1d space-like defect
- the S-Skyrmion solution extended in one space coordinate and localized in
Euclidean time. It can be identified both in the holographic QCD and in the
Chiral Perturbation Theory(ChPT). The Skyrmion charges get transformed into the
corresponding currents for S-Skyrmion. The analogy with the Thouless pump and
the quantum phase slip phenomena is mentioned. | A Resummable beta-Function for Massless QED: Within the set of schemes defined by generalized, manifestly gauge invariant
exact renormalization groups for QED, it is argued that the beta-function in
the four dimensional massless theory cannot possess any nonperturbative power
corrections. Consequently, the perturbative expression for the beta-function
must be resummable. This argument cannot be extended to flows of the other
couplings or to the anomalous dimension of the fermions and so perturbation
theory does not define a unique trajectory in the critical surface of the
Gaussian fixed point. Thus, resummability of the beta-function is not
inconsistent with the expectation that a non-trivial fixed point does not
exist. |
BPS Skyrme neutron stars in generalized gravity: We study the coupling of nuclear matter described by the BPS Skyrme model to
generalized gravity. Concretely, we consider the Starobinsky model which
provides the leading-order correction to the Einstein-Hilbert action. Static
solutions describing neutron stars are found both for the full field theory and
for the mean-field approximation. We always consider the full Starobinsky model
in the nonperturbative approach, using appropriately generalized shooting
methods for the numerical neutron star calculations. Many of our results are
similar to previous investigations of neutron stars for the Starobinsky model
using other models of nuclear matter, but there are some surprizing
discrepancies. The "Newtonian mass" relevant for the surface redshift, e.g.,
results larger than the ADM mass in our model, in contrast to other
investigations. This difference is related to the particularly high stiffness
of nuclear matter described by the BPS Skyrme model and offers an interesting
possibility to distinguish different models of nuclear matter within
generalized gravity. | Some Algebraic Geometry Aspects of Gravitational Theories with Covariant
and Contravariant Connections and Metrics (GTCCCM) and Possible Applications
to Theories with Extra Dimensions: On the base of the distinction between covariant and contravariant metric
tensor components, an approach from algebraic geometry will be proposed, aimed
at finding new solutions of the Einstein's equations both in GTCCCM and in
standard gravity theory, if these equations are treated as algebraic equations.
As a partial case, some physical applications of the approach have been
considered in reference to theories with extra dimensions. The s.c. "length
function" l(x) has been introduced and has been found as a solution of
quasilinear differential equations in partial derivatives for two different
cases, corresponding to "compactification + rescaling" and "rescaling +
compactification" of the type I low-energy string theory action. New (although
complicated) relations between the parameters in the action have been found,
valid also for the standard approach in theories with extra dimensions. |
Black hole microstates from branes at angle: We derive the leading g_s perturbation of the SUGRA fields generated by a
supersymmetric configuration of respectively 1, 2 or 4 D3-branes intersecting
at an arbitrary angle via the computation of the string theory disk scattering
amplitude of one massless NSNS field interacting with open strings stretched
between the branes. The configuration with four branes is expected to be
relevant for black hole microstate counting in four dimensions. | Bimetric QED: We study, as a model of Lorentz symmetry breaking, the quantisation and
renormalisation of an extension of QED in a flat spacetime where the photons
and electrons propagate differently and do not share the same lightcone. We
will refer to this model as Bimetric QED (BIMQED). As a preliminary we discuss
the formulation of electrodynamics in a pre-metric formalism showing
nevertheless that there is, on the basis of a simple criteron, a preferred
metric. Arising from this choice of metric is a Weyl-like tensor (WLT). The
Petrov classification of the WLT gives rise to a corresponding classification
of Lorentz symmetry breaking. We do not impose any constraint on the strength
of the symmetry breaking and are able to obtain explicit dispersion relations
for photon propagation in each of the Petrov classes. The associated
birefringence appears in some cases as two distinct polarisation dependent
lightcones and in other cases as a a more complicated structure that cannot be
disentangled in a simple way.
We show how in BIMQED the renormalisation procedure can, in addition to its
effect on standard parameters such as charge and mass, force the
renormalisation of the metrics and the WLT. Two particularly tractable cases
are studied in detail for which we can obtain renormalisation group flows for
the parameters of the model together with an analysis of fixed point structure.
Of course these results are consistent with previous studies but we are not
constrained to treat Lorentz symmetry breaking as necessarily weak. As we found
in a previous study of a scalar field theory model an acceptable causal
structure for the model imposes constraints on relationship between the various
lightcones in BIMQED. |
Exact, E=0, Solutions for General Power-Law Potentials. I. Classical
Orbits: For zero energy, $E=0$, we derive exact, classical solutions for {\em all}
power-law potentials, $V(r)=-\gamma/r^\nu$, with $\gamma>0$ and $-\infty
<\nu<\infty$. When the angular momentum is non-zero, these solutions lead to
the orbits $\r(t)= [\cos \mu (\th(t)-\th_0(t))]^{1/\mu}$, for all $\mu \equiv
\nu/2-1 \ne 0$. When $\nu>2$, the orbits are bound and go through the origin.
This leads to discrete discontinuities in the functional dependence of $\th(t)$
and $\th_0(t)$, as functions of $t$, as the orbits pass through the origin. We
describe a procedure to connect different analytic solutions for successive
orbits at the origin. We calculate the periods and precessions of these bound
orbits, and graph a number of specific examples. Also, we explain why they all
must violate the virial theorem. The unbound orbits are also discussed in
detail. This includes the unusual orbits which have finite travel times to
infinity and also the special $\nu = 2$ case. | Nonextremal black holes in gauged supergravity and the real formulation
of special geometry: We give a rather general recipe for constructing nonextremal black hole
solutions to N=2, D=4 gauged supergravity coupled to abelian vector multiplets.
This problem simplifies considerably if one uses the formalism developed in
arXiv:1112.2876, based on dimensional reduction and the real formulation of
special geometry. We use this to find new nonextremal black holes for several
choices of the prepotential, that generalize the BPS solutions found in
arXiv:0911.4926. Some physical properties of these black holes are also
discussed. |
Towards M2-brane Theories for Generic Toric Singularities: We construct several examples of (2+1) dimensional N=2 supersymmetric
Chern-Simons theories, whose moduli space is given by non-compact toric
Calabi-Yau four-folds, which are not derivable from any (3+1) dimensional CFT.
One such example is the gauge theory associated with the cone over Q^{111}. For
several examples, we explicitly confirm the matter content, superpotential
interactions and RG flows suggested by crystal models. Our results provide
additional support to the idea that crystal models are relevant for describing
the structure of these CFTs. | Phase Transition of charged Rotational Black Hole and Quintessence: In this paper, we calculate thermodynamical quantity of Kerr-Newman-AdS black
hole solution in quintessence matter. Then, we show that how the rotation and
cosmological parameters effect to the thermodynamics properties of black hole.
Also, we investigate both types of phase transition for different values of
$\omega$ parameter in extended phase space. We notice that type one of phase
transition occurs for $P<0.42$ and $a<0.5$. And also we see that the phase
transition point shifts to higher entropy when pressure $P$, rotation parameter
$a$ and $\alpha$ increase. Also, we find that by changing parameter $\omega$
from -1 to $-\frac{1}{3}$, the critical point shifts to higher entropy. Then we
study type two of phase transition and show critical points increase by
increasing parameter $\alpha$. Also, we show that the critical point shifts to
higher entropy when $\alpha$, $\omega$ and rotation parameter $a$ decrease.
Finally, we find that by decreasing pressure the first critical point shifts to
lower entropy and second critical point shifts to higher entropy. |
Cosmic Decoherence: Massive Fields: We study the decoherence of massive fields during inflation based on the
Zurek's density matrix approach. With the cubic interaction between inflaton
and massive fields, the reduced density matrix for the massive fields can be
calculated in the Schr\"odinger picture which is related to the variance of the
non-Gaussian exponent in the wave functional. The decoherence rate is computed
in the one-loop form from functional integration. For heavy fields with
$m\gtrsim \mathcal{O}(H)$, quantum fluctuations will easily stay in the quantum
state and decoherence is unlikely. While for light fields with mass smaller
than $\mathcal{O}(H)$, quantum fluctuations are easily decohered within
$5\sim10$ e-folds after Hubble crossing. Thus heavy fields can play a key role
in studying problems involving inflationary quantum information. | Geodesic Flow on the n-Dimensional Ellipsoid as a Liouville Integrable
System: We show that the motion on the n-dimensional ellipsoid is complete integrable
by exhibiting n integrals in involution. The system is separable at classical
and quantum level, the separation of classical variables being realized by the
inverse of the momentum map. This system is a generic one in a new class of
n-dimensional complete integrable Hamiltonians defined by an arbitrary function
f(q,p) invertible with respect to momentum p and rational in the coordinate q. |
Induced Chern-Simons term by dimensional reduction: We derive an induced Abelian Chern-Simons (CS) term in 2+1 dimensions, by
dimensional reduction from the finite-temperature theory of a Dirac field with
both vector and axial-vector couplings to two Abelian gauge fields, in 3+1
dimensions. In our construction, the CS term emerges for the lowest Matsubara
mode of the vector Abelian field, by integrating the fermionic field, under the
assumption that the axial vector field is in a "vacuum" configuration. This
configuration is characterized by a single number, which in turn determines the
coefficient of the induced CS term for the Abelian vector field. | Supersymmetric dyonic black holes of IIA string on Six Torus: A class of four-dimensional static supersymmetric black hole solutions of
effective supergravity Lagrangian of IIA superstring compactified on $T^6$ is
constructed by explicitly solving Killing spinor equations (KSEs). These
solutions are dyonic black holes parametrized by four charges, with dilaton and
diagonal internal metric components as the only non-zero scalar fields, and
preserve $1 \over 8$ of $N=8$ supersymmetry. The KSEs with only
Neveu-Schwarz-Neveu-Schwarz charges relate spinors with opposite chirality from
ten-dimensional view point, and have identical structures with KSEs of
toroidally compactified heterotic string. We also find a solution with four
Ramond-Ramond charges which is U-dual to the solution with four
Neveu-Schwarz-Neveu-Schwarz charges, and corresponds to the intersecting
D-brane configuration with two 2-branes and two 4-branes. A configuration with
both Neveu-Schwarz-Neveu-Schwarz charges and Ramond-Ramond charges is also
found. We show that the configurations T-dual to the above solutions are also
solutions of the KSEs. The patterns of supersymmetry breaking are studied in
detail. |
Exact solution of the Dirac equation for a Coulomb and a scalar
Potential in the presence of of an Aharonov-Bohm and magnetic monopole fields: In the present article we analyze the problem of a relativistic Dirac
electron in the presence of a combination of a Coulomb field, a $1/r$ scalar
potential as well as a Dirac magnetic monopole and an Aharonov-Bohm potential.
Using the algebraic method of separation of variables, the Dirac equation
expressed in the local rotating diagonal gauge is completely separated in
spherical coordinates, and exact solutions are obtained. We compute the energy
spectrum and analyze how it depends on the intensity of the Aharonov-Bohm and
the magnetic monopole strengths. | Large angular momentum closed strings colliding with D-branes: We investigate colliding processes of closed strings with large angular
momenta with D-branes. We give explicit CFT calculations for closed string
states with an arbitrary number of bosonic excitations and no or one fermion
excitation. The results reproduce the correspondence between closed string
states and single trace operators in the boundary gauge theory recently
suggested by Berenstein, Maldacena and Nastase. |
Primordial Black Holes and Gravitational Waves in
Multi-Axion-Chern-Simons Inflation: We study aspects of inflation and the possibility of enhanced production of
primordial black holes (PBHs) and gravitational waves (GWs) in a
string-inspired model of two axion fields coupled to Chern-Simons gravity,
which results in a running-vacuum-model inflation. Fluctuations of the scale
invariant spectrum, consistent with the cosmological data, are provided in this
model by world-sheet (non-perturbative) instanton terms of the axion field
arising from string compactification. As a result of such modulations, there is
an enhanced production of PBHs and GWs in such cosmologies, which may lead to
observable in principle patterns in the profile of GWs during the radiation
era. Moreover, we demonstrate that the PBHs may provide a significant amount of
Dark Matter in this Universe. For comparison, we also discuss a two-stage
inflation cosmological model of conventional string-inspired axion monodromy,
involving again two axion fields. The resulting modifications imprinted on the
GWs spectra between these two classes of models are distinct, and can, in
principle, be distinguished by future interferometers. We consider models with
more or less instantaneous reheating. We also make some remarks on the effects
of a prolonged reheating period in leading to further enhancement of the power
spectrum and thus fractions of PBHs that play the role of Dark matter. | D0 Matrix Mechanics: New Fuzzy Solutions at Large N: We wish to consider in this report the large N limit of a particular matrix
model introduced by Myers describing D-brane physics in the presence of an RR
flux background. At finite N, fuzzy spheres appear naturally as non-trivial
solutions to this matrix model and have been extensively studied. In this
report, we wish to demonstrate several new classes of solutions which appear in
the large N limit, corresponding to the fuzzy cylinder,the fuzzy plane and a
warped fuzzy plane. The latter two solutions arise from a possible "central
extension" to our model that arises after we account for non-trivial issues
involved in the large N limit. As is the case for finite N, these new solutions
are to be interpreted as constituent D0-branes forming D2 bound states
describing new fuzzy geometries. |
Scaling of variables and the relation between noncommutative parameters
in Noncommutative Quantum Mechanics: We consider Noncommutative Quantum Mechanics with phase space
noncommutativity. In particular, we show that a scaling of variables leaves the
noncommutative algebra invariant, so that only the self-consistent effective
parameters of the model are physically relevant. We also discuss the recently
proposed relation of direct proportionality between the noncommutative
parameters, showing that it has a limited applicability. | Whitham-Toda hierarchy and N = 2 supersymmetric Yang-Mills theory: The exact solution of $N=2$ supersymmetric $SU(N)$ Yang-Mills theory is
studied in the framework of the Whitham hierarchies. The solution is identified
with a homogeneous solution of a Whitham hierarchy. This integrable hierarchy
(Whitham-Toda hierarchy) describes modulation of a quasi-periodic solution of
the (generalized) Toda lattice hierarchy associated with the hyperelliptic
curves over the quantum moduli space. The relation between the holomorphic
pre-potential of the low energy effective action and the $\tau$ function of the
(generalized) Toda lattice hierarchy is also clarified. |
The Ring Structure of Chiral Operators for Minimal Models Coupled to 2D
Gravity: (Talk presented at the 1992 ICTP summer workshop in high energy physics and
cosmology) The BRST cohomology ring for $(p,q)$ models coupled to gravity is
discussed. In addition to the generators of the ghost number zero ring, the
existence of a generator of ghost number $-1$ and its inverse is proven and
used to construct the entire ring. Some comments are made regarding the algebra
of the vector fields on the ring and the supersymmetric extension. | Finite-Volume Spectra of the Lee-Yang Model: We consider the non-unitary Lee-Yang minimal model ${\cal M}(2,5)$ in three
different finite geometries: (i) on the interval with integrable boundary
conditions labelled by the Kac labels $(r,s)=(1,1),(1,2)$, (ii) on the circle
with periodic boundary conditions and (iii) on the periodic circle including an
integrable purely transmitting defect. We apply $\varphi_{1,3}$ integrable
perturbations on the boundary and on the defect and describe the flow of the
spectrum. Adding a $\Phi_{1,3}$ integrable perturbation to move off-criticality
in the bulk, we determine the finite size spectrum of the massive scattering
theory in the three geometries via Thermodynamic Bethe Ansatz (TBA) equations.
We derive these integral equations for all excitations by solving, in the
continuum scaling limit, the TBA functional equations satisfied by the transfer
matrices of the associated $A_{4}$ RSOS lattice model of Forrester and Baxter
in Regime III. The excitations are classified in terms of $(m,n)$ systems. The
excited state TBA equations agree with the previously conjectured equations in
the boundary and periodic cases. In the defect case, new TBA equations confirm
previously conjectured transmission factors. |
A Novel Formula for Bulk Viscosity from the Null Horizon Focusing
Equation: The null horizon focusing equation is equivalent via the fluid/gravity
correspondence to the entropy balance law of the fluid. Using this equation we
derive a simple novel formula for the bulk viscosity of the fluid. The formula
is expressed in terms of the dependence of scalar fields at the horizon on
thermodynamic variables such as the entropy and charge densities. We apply the
formula to three classes of gauge theory plasmas: non-conformal branes,
perturbations of the N=4 supersymmetric Yang-Mills theory and holographic
models of QCD, and discuss its range of applicability. | Decagon at Two Loops: We have computed the simplest five point function in $\mathcal{N} = 4$ SYM at
two loops using the hexagonalization approach to correlation functions. Along
the way we have determined all two-particle mirror contributions at two loops
and we have computed all the integrals involved in the final result. As a test
of our results we computed a few four-point functions and they agree with the
perturbative results computed previously. We have also obtained $l$ loop
results for some parts of the two-particle contributions with $l$ arbitrary. We
also derive differential equations for a class of integrals that should appear
at higher loops in the five point function. |
Geometry of AdS black hole thermodynamics in extended phase space: We consider the geometry of anti-de-Sitter (AdS) black hole thermodynamics in
four dimensions, where the equation of state in the extended phase space
formalism allows explicit comparison with normal fluid systems. We show that
for the two-dimensional parameter manifolds considered here, the scalar
curvature is proportional to the thermodynamic volume. This allows us to
critically examine the applicability of geometric methods in black hole
thermodynamics in extended phase space. We show how several standard features
that are expected to hold in normal fluid systems impose severe restrictions on
the black hole parameters, leading to the fact that several results in the
current literature on the geometry of thermodynamics in extended phase space
may be physically invalid. These are true for both charged and rotating AdS
black holes. As a by-product of our analysis, we examine a conjecture regarding
the equality of the correlation lengths of co-existing phases near criticality,
in charged AdS black hole backgrounds, and find reasonable validity. | Low-scale SUSY breaking and the (s)goldstino physics: For a 4D N=1 supersymmetric model with a low SUSY breaking scale (f) and
general Kahler potential K(Phi^i,Phi_j^*) and superpotential W(Phi^i) we study,
in an effective theory approach, the relation of the goldstino superfield to
the (Ferrara-Zumino) superconformal symmetry breaking chiral superfield X. In
the presence of more sources of supersymmetry breaking, we verify the
conjecture that the goldstino superfield is the (infrared) limit of X for
zero-momentum and Lambda->\infty. (Lambda is the effective cut-off scale). We
then study the constraint X^2=0, which in the one-field case is known to
decouple a massive sgoldstino and thus provide an effective superfield
description of the Akulov-Volkov action for the goldstino. In the presence of
additional fields that contribute to SUSY breaking we identify conditions for
which X^2=0 remains valid, in the effective theory below a large but finite
sgoldstino mass. The conditions ensure that the effective expansion (in
1/Lambda) of the initial Lagrangian is not in conflict with the decoupling
limit of the sgoldstino (1/m_sgoldstino\sim Lambda/f, f<Lambda^2). |
Any compact group is a gauge group: The assignment of local observables in the vacuum sector, fulfilling the
standard axioms of local quantum theory, is known to determine uniquely a
compact group G of gauge transformations of the first kind together with a
central involutive element k of G, and a complete normal algebra of fields
carrying the localizable charges, on which k defines the Bose/Fermi grading.
We show here that any such pair {G,k}, where G is compact metrizable, does
actually appear. The corresponding model can be chosen to fulfill also the
split property.
This is not a dynamical phenomenon: a given {G,k} arises as the gauge group
of a model where the local algebras of observables are a suitable subnet of
local algebras of a possibly infinite product of free field theories. | An easy way to solve two-loop vertex integrals: Negative dimensional integration is a step further dimensional regularization
ideas. In this approach, based on the principle of analytic continuation,
Feynman integrals are polynomial ones and for this reason very simple to
handle, contrary to the usual parametric ones. The result of the integral
worked out in $D<0$ must be analytically continued again --- of course --- to
real physical world, $D>0$, and this step presents no difficulties. We consider
four two-loop three-point vertex diagrams with arbitrary exponents of
propagators and dimension. These original results give the correct well-known
particular cases where the exponents of propagators are equal to unity. |
On the Uniqueness of Black Hole Attractors: We examine the attractor mechanism for extremal black holes in the context of
five dimensional N = 2 supergravity and show that attractor points are unique
in the extended vector multiplet moduli space. Implications for black hole
entropy are discussed. | Classification of Simple Current Invariants: We summarize recent work on the classification of modular invariant partition
functions that can be obtained with simple currents in theories with a center
(Z_p)^k with p prime. New empirical results for other centers are also
presented. Our observation that the total number of invariants is
monodromy-independent for (Z_p)^k appears to be true in general as well. (Talk
presented in the parallel session on string theory of the Lepton-Photon/EPS
Conference, Geneva, 1991.) |
A unified representation-theoretic approach to special functions: A representation-theoretic approach to special functions was developed in the
40-s and 50-s in the works of I.M.Gelfand, M.A.Naimark, N.Ya.Vilenkin, and
their collaborators. The essence of this approach is the fact that most
classical special functions can be obtained as suitable specializations of
matrix elements or characters of representations of groups. Another rich source
of special functions is the theory of Clebsch-Gordan coefficients which
describes the geometric juxtaposition of irreducible components inside the
tensor product of two representations. Finally, in recent works on
representations of (quantum) affine Lie algebras it was shown that matrix
elements of intertwining operators between certain representations of these
algebras are interesting special functions -- (q-)hypergeometric functions and
their generalizations.
In this paper we suggest a general method of getting special functions from
representation theory which unifies the three methods mentioned above and
allows one to define and study many new special functions. We illustrate this
method by a number of examples -- Macdonald's polynomials, eigenfunctions of
the Sutherland operator, Lame functions. | Classifying and constraining local four photon and four graviton
S-matrices: We study the space of all kinematically allowed four photon and four graviton
S-matrices, polynomial in scattering momenta. We demonstrate that this space is
the permutation invariant sector of a module over the ring of polynomials of
the Mandelstam invariants $s$, $t$ and $u$. We construct these modules for
every value of the spacetime dimension $D$, and so explicitly count and
parameterize the most general four photon and four graviton S-matrix at any
given derivative order. We also explicitly list the local Lagrangians that give
rise to these S-matrices. We then conjecture that the Regge growth of
S-matrices in all physically acceptable classical theories is bounded by $s^2$
at fixed $t$. A four parameter subset of the polynomial photon S-matrices
constructed above satisfies this Regge criterion. For gravitons, on the other
hand, no polynomial addition to the Einstein S-matrix obeys this bound for $D
\leq 6$. For $D \geq 7$ there is a single six derivative polynomial Lagrangian
consistent with our conjectured Regge growth bound. Our conjecture thus implies
that the Einstein four graviton S-matrix does not admit any physically
acceptable polynomial modifications for $D\leq 6$. A preliminary analysis also
suggests that every finite sum of pole exchange contributions to four graviton
scattering also such violates our conjectured Regge growth bound, at least when
$D\leq 6$, even when the exchanged particles have low spin. |
Supersymmetric Localization in AdS$_5$ and the Protected Chiral Algebra: ${\cal N} =4$ super Yang-Mills theory admits \cite{Beem:2013sza} a protected
subsector isomorphic to a two-dimensional chiral algebra, obtained by passing
to the cohomology of a certain supercharge. In the large $N$ limit, we expect
this chiral algebra to have a dual description as a subsector of IIB
supergravity on $AdS_5 \times S^5$. This subsector can be carved out by a
version of supersymmetric localization, using the bulk analog of the boundary
supercharge. We illustrate this procedure in a simple model, the theory of an
${\cal N}=4$ vector multiplet in $AdS_5$, for which a convenient off-shell
description is available. This model can be viewed as the simplest truncation
of the full $AdS_5 \times S^5$ supergravity, in which case the vector multiplet
should be taken in the adjoint representation of ${\mathfrak g}_F = \mathfrak
{su}(2)_F$. Localization yields Chern-Simons theory on $AdS_3$ with gauge
algebra ${\mathfrak g}_F$, whose boundary dual is the affine Lie algebra
$\widehat {\mathfrak g}_F$. We comment on the generalization to the full bulk
theory. We propose that the large $N$ limit of the chiral algebra of ${\cal
N}=4$ SYM is again dual to Chern-Simons theory, with gauge algebra a suitable
higher-spin superalgebra. | Causal faster than light travel from travel-localized second time
coordinate: I present a {\em general relativistic} model with a compactified second time
coordinate that {\em a priori} allows for causal, yet faster than light travel
in the background of a FLRW geometry, by local modification of a higher
dimensional background geometry, specifically with respect to the radius of the
compactified time coordinate. The modification can be induced via the fields of
the model.
I show that one cannot convert (as possible in special relativistic models,
or simple general relativistic models) the super-luminality into closed
time-like loops violating causality, due to a novel combination of factors, at
least for $v_{\rm max}\leq \sqrt{2}$. The physics of the second time is
constrained by postulates derived from reasonable physical assumptions.
I comment on the possibility of experimental implications of the model. |
The Universe from a Single Particle: We explore the emergence of many-body physics from quantum mechanics via
spontaneous symmetry breaking. To this end, we study potentials which are
functionals on the space of Hamiltonians enjoying an unstable critical point
corresponding to a random quantum mechanical system (the Gaussian unitary
ensemble), but also less symmetrical local minima corresponding to interacting
systems at the level of operators. | d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories: We study three dimensional O(N)_k and U(N)_k Chern-Simons theories coupled to
a scalar field in the fundamental representation, in the large N limit. For
infinite k this is just the singlet sector of the O(N) (U(N)) vector model,
which is conjectured to be dual to Vasiliev's higher spin gravity theory on
AdS_4. For large k and N we obtain a parity-breaking deformation of this
theory, controlled by the 't Hooft coupling lambda = 4 \pi N / k. For infinite
N we argue (and show explicitly at two-loop order) that the theories with
finite lambda are conformally invariant, and also have an exactly marginal
(\phi^2)^3 deformation.
For large but finite N and small 't Hooft coupling lambda, we show that there
is still a line of fixed points parameterized by the 't Hooft coupling lambda.
We show that, at infinite N, the interacting non-parity-invariant theory with
finite lambda has the same spectrum of primary operators as the free theory,
consisting of an infinite tower of conserved higher-spin currents and a scalar
operator with scaling dimension \Delta=1; however, the correlation functions of
these operators do depend on lambda. Our results suggest that there should
exist a family of higher spin gravity theories, parameterized by lambda, and
continuously connected to Vasiliev's theory. For finite N the higher spin
currents are not conserved. |
Light cone formalism in AdS spacetime: Light cone form of field dynamics in anti-de Sitter spacetime is described.
We also present light cone reformulation of the boundary conformal field theory
representations. AdS/CFT correspondence between the bulk fields and the
boundary operators is discussed. | Einstein-Proca theory from the Einstein-Cartan formulation: We construct a theory of gravity in which a propagating massive vector field
arises from a quadratic curvature invariant. The Einstein-Cartan formulation
and a partial suppression of torsion ensure the absence of ghost and
strong-coupling problems, as we prove with nonlinear Lagrangian and Hamiltonian
analysis. Augmenting General Relativity with a propagating torsion vector, our
theory provides a purely gravitational origin of Einstein-Proca models and
constrains their parameter space. As an outlook to phenomenology, we discuss
the gravitational production of fermionic dark matter. |
Fundamental String and D1-brane in I-brane Background: This paper is devoted to the study of dynamics of fundamental string and
D1-brane in I-brane background. We consider configurations where string and
D1-brane uniformly wrap transverse spheres. We explicitly determine
corresponding conserved charges and find relations between them. | Spiraling String in Gauss-Bonnet Geometry: In this paper, we consider a spiraling string falling in the bulk with
Gauss$-$Bonnet geometry that is holographically dual to a heavy particle
rotating through a hot plasma at finite coupling. One finds such interesting
simple problem provides a novel perspective on different channels of the energy
loss in the corresponding strongly coupled theory. Depends on the sign of the
coupling, one observes that the influence of finite coupling on total energy
loss and contribution of drag force and radiation channels appears as a shift
on curves with respect to the plasma with infinite coupling. Also we found that
crossover between regime in which drag force contribution is predominant to
regime in which energy loss is due to radiation, does not depend on the
Gauss$-$Bonnet coupling. |
Symmetry breaking boundaries II. More structures; examples: Various structural properties of the space of symmetry breaking boundary
conditions that preserve an orbifold subalgebra are established. To each such
boundary condition we associate its automorphism type. It is shown that
correlation functions in the presence of such boundary conditions are
expressible in terms of twisted boundary blocks which obey twisted Ward
identities. The subset of boundary conditions that share the same automorphism
type is controlled by a classifying algebra, whose structure constants are
shown to be traces on spaces of chiral blocks. T-duality on boundary conditions
is not a one-to-one map in general. These structures are illustrated in a
number of examples. Several applications, including the construction of non-BPS
boundary conditions in string theory, are exhibited. | Vassiliev invariants for pretzel knots: We compute Vassiliev invariants up to order six for arbitrary pretzel knots,
which depend on $g+1$ parameters $n_1,\ldots,n_{g+1}$. These invariants are
symmetric polynomials in $n_1,\ldots,n_{g+1}$ whose degree coincide with their
order. We also discuss their topological and integer-valued properties. |
Statistical sum in the CFT driven cosmology: The path integration technique recently developed for the statistical sum of
the microcanonical ensemble in cosmology is applied to the calculation of the
one-loop preexponential factor in the cosmological model generated by a
conformal field theory with a large number of quantum species -- the model of
initial conditions possibly related to the resolution of the cosmological
constant and landscape problems. The result is obtained for the family of
background cosmological instantons with one oscillation of the FRW scale
factor. The magnitude of the prefactor is analytically and numerically
estimated for fields of various spins conformally coupled to gravity, which
justifies the validity of semiclassical expansion for this family of
cosmological instantons. | Fermionic Casimir densities in toroidally compactified spacetimes with
applications to nanotubes: Fermionic condensate and the vacuum expectation values of the energy-momentum
tensor are investigated for a massive spinor fields in higher-dimensional
spacetimes with an arbitrary number of toroidally compactified spatial
dimensions. By using the Abel-Plana summation formula and the zeta function
technique we present the vacuum expectation values in two different forms.
Applications of the general formulae to cylindrical and toroidal carbon
nanotubes are given. We show that the topological Casimir energy is positive
for metallic cylindrical nanotubes and is negative for semiconducting ones. The
toroidal compactification of a cylindrical nanotube along its axis increases
the Casimir energy for metallic-type (periodic) boundary conditions along its
axis and decreases the Casimir energy for the semiconducting-type
compactifications. |
Compactified D=11 Supermembranes and Symplectic Non-Commutative Gauge
Theories: It is shown that a double compactified D=11 supermembrane with non trivial
wrapping may be formulated as a symplectic non-commutative gauge theory on the
world volume. The symplectic non commutative structure is intrinsically
obtained from the symplectic 2-form on the world volume defined by the minimal
configuration of its hamiltonian. The gauge transformations on the symplectic
fibration are generated by the area preserving diffeomorphisms on the world
volume. Geometrically, this gauge theory corresponds to a symplectic fibration
over a compact Riemman surface with a symplectic connection. | Nilpotent (Anti-)BRST and (Anti-)co-BRST Symmetries in 2D non-Abelian
Gauge Theory: Some Novel Observations: We discuss the nilpotent Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and
(anti-)co-BRST symmetry transformations and derive their corresponding
conserved charges in the case of a two (1+1)-dimensional (2D) self-interacting
non-Abelian gauge theory (without any interaction with matter fields). We point
out a set of novel features that emerge out in the BRST and co-BRST analysis of
the above 2D gauge theory. The algebraic structures of the symmetry operators
(and corresponding conserved charges) and their relationship with the
cohomological operators of differential geometry are established, too. To be
more precise, we demonstrate the existence of a single Lagrangian density that
respects the continuous symmetries which obey proper algebraic structure of the
cohomological operators of differential geometry. In literature, such
observations have been made for the coupled (but equivalent) Lagrangian
densities of the 4D non-Abelian gauge theory. We lay emphasis on the existence
and properties of the Curci-Ferrari (CF) type restrictions in the context of
(anti-)BRST and (anti-)co-BRST symmetry transformations and pinpoint their key
differences and similarities. All the observations, connected with the
(anti-)co-BRST symmetries, are completely novel. |
Separation of Variables in the Classical Integrable SL(3) Magnetic Chain: There are two fundamental problems studied by the theory of hamiltonian
integrable systems: integration of equations of motion, and construction of
action-angle variables. The third problem, however, should be added to the
list: separation of variables. Though much simpler than two others, it has
important relations to the quantum integrability. Separation of variables is
constructed for the $SL(3)$ magnetic chain --- an example of integrable model
associated to a nonhyperelliptic algebraic curve. | Transport in holographic superfluids: We construct a slowly varying space-time dependent holographic superfluid and
compute its transport coefficients. Our solution is presented as a series
expansion in inverse powers of the charge of the order parameter. We find that
the shear viscosity associated with the motion of the condensate vanishes. The
diffusion coefficient of the superfluid is continuous across the phase
transition while its third bulk viscosity is found to diverge at the critical
temperature. As was previously shown, the ratio of the shear viscosity of the
normal component to the entropy density is 1/(4 pi). As a consequence of our
analysis we obtain an analytic expression for the backreacted metric near the
phase transition for a particular type of holographic superfluid. |
M theory and the Coulomb phase of higher rank DT invariants: In this paper, we advance an M theory model corresponding to the Coulomb
phase of higher rank Donaldson-Thomas(DT) invariants. | Supersymmetric Wilson loops in N=4 super Chern-Simons-matter theory: We investigate the supersymmetric Wilson loops in $d=3$ $\mathcal{N}=4$ super
Chern-Simons-matter theory obtained from non-chiral orbifold of ABJM theory. We
work in both Minkowski spacetime and Euclidean space, and we construct 1/4 and
1/2 BPS Wilson loops. We also provide a complete proof that the difference
between 1/4 and 1/2 Wilson loops is $Q$-exact with $Q$ being some supercharge
that is preserved by both the 1/4 and 1/2 Wilson loops. This plays an important
role in applying the localization techniques to compute the vacuum expectation
values of Wilson loops. We also study the M-theory dual of the 1/2 BPS circular
Wilson loop. |
Charging Up the Functional Bootstrap: We revisit the problem of bootstrapping CFT correlators of charged fields.
After discussing in detail how bounds for uncharged fields can be recycled to
the charged case, we introduce two sets of analytic functional bases for
correlators on the line. The first, which we call "simple", is essentially a
direct sum of analytic functionals for the uncharged case. We use it to
establish very general bounds on the OPE density appearing in charged
correlators. The second basis is dual to generalized free fields and we explain
how it is related to a charged version of the Polyakov bootstrap. We apply
these functionals to map out the space of correlators and obtain new improved
bounds on the 3d Ising twist defect. | Effective models of inflation from a non-local framework: The dilaton is a possible inflaton candidate following recent CMB data
allowing a non-minimal coupling to the Ricci curvature scalar in the early
Universe. In this paper, we introduce an approach that has seldom been used in
the literature, namely dilaton inflation with non-local features. More
concretely, employing non-local features expressed in J. High Energy Phys. 04
(2007) 029, we study quadratic variations around a de Sitter geometry of an
effective action with a non-local dilaton. The non-locality refers to an
infinite derivative kinetic term involving the operator
$\mathcal{F}\left(\Box\right)$. Algebraic roots of the characteristic equation
$\mathcal{F}(z)=0$ play a crucial role in determining the properties of the
theory. We subsequently study the cases when $\mathcal{F}\left(\Box\right)$ has
one real root and one complex root, from which we retrieve two concrete
effective models of inflation. In the first case we retrieve a class of single
field inflations with universal prediction of $n_{s}\sim0.967$ with any value
of the tensor to scalar ratio $r<0.1$ intrinsically controlled by the root of
the characteristic equation. The second case involves a new class of two field
conformally invariant models with a peculiar quadratic cross-product of scalar
fields. In this latter case, we obtain Starobinsky like inflation through a
spontaneously broken conformal invariance. Furthermore, an uplifted minimum of
the potential, which accounts for the vacuum energy after inflation is produced
naturally through this mechanism intrinsically within our approach. |
Unification of Non-Abelian SU(N) Gauge Theory and Gravitational Gauge
Theory: In this paper, a general theory on unification of non-Abelian SU(N) gauge
interactions and gravitational gauge interactions is discussed. SU(N) gauge
interactions and gravitational gauge interactions are formulated on the similar
basis and are unified in a semi-direct product group GSU(N). Based on this
model, we can discuss unification of fundamental interactions of Nature. | Geometric Engineering of Quantum Field Theories: Using the recent advances in our understanding of non-perturbative aspects of
type II strings we show how non-trivial exact results for $N=2$ quantum field
theories can be reduced to T-dualities of string theory. This is done by
constructing a local geometric realization of quantum field theories together
with a local application of mirror symmetry. This construction is not based on
any duality conjecture and thus reduces non-trivial quantum field theory
results to much better understood T-dualities of type II strings. Moreover it
can be used in principle to construct in a systematic way the vacuum structure
for arbitrary $N=2$ gauge theories with matter representations. |
MHV Lagrangian for N=4 Super Yang-Mills: Here we formulate two field redefinitions for N=4 Super Yang-Mills in light
cone superspace that generates only MHV vertices in the new Lagrangian. After
careful consideration of the S-matrix equivalence theorem, we see that only the
canonical transformation gives the MHV Lagrangian that would correspond to the
CSW expansion. Being in superspace, it is easier to analyse the equivalence
theorem at loop level. We calculate the on shell amplitude for 4pt
$(\bar{\Lambda}\bar{{\rm A}}\Lambda {\rm A})$ MHV in the new lagrangian and
show that it reproduces the previously known form. We also briefly discuss the
relationship with the off-shell continuation prescription of CSW. | Majorana mass, time reversal symmetry, and the dimension of space: The Weyl fermions with a well defined chirality are known to demand that the
dimension of space which they inhabit must be odd. It is shown here, however,
that not all odd dimensional spaces are equally good hosts: in particular, an
arbitrary number of chiral Weyl fermions can acquire a Majorana mass only in
three (modulo eight) dimensions. The argument utilizes a) the precise analogy
that exists between the Majorana mass term and the Cooper pairing of
time-reversed Weyl fermions, and b) the conditions on the requisite
time-reversal operator, which are implied by the Clifford algebra. The theorem
connects the observed odd number of neutrino flavors, the time reversal
symmetry, and the dimension of our space, and strengthens the argument for the
possible violation of the lepton number conservation law. |
Generalised proofs of the first law of entanglement entropy: In this paper we develop generalised proofs of the holographic first law of
entanglement entropy using holographic renormalisation. These proofs establish
the holographic first law for non-normalizable variations of the bulk metric,
hence relaxing the boundary conditions imposed on variations in earlier works.
Boundary and counterterm contributions to conserved charges computed via
covariant phase space analysis have been explored previously. Here we discuss
in detail how counterterm contributions are treated in the covariant phase
approach to proving the first law. Our methodology would be applicable to
generalizing other holographic information analyses to wider classes of
gravitational backgrounds. | Refined topological vertex for a 5D $Sp(N)$ gauge theory with
antisymmetric matter: We consider Type IIB 5-brane web diagrams for a 5D $Sp(N)$ gauge theory with
an antisymmetric hypermultiplet and $N_f$ fundamental hypermultiplets. The
corresponding 5-branes can be obtained by Higgsing a 5-brane web for quiver
gauge theory. We use the refined topological vertex formalism to compute
Nekrasov partition functions of 5D $Sp(2)$ theories with one antisymmetric
hypermultiplet and flavors. Our results agree with the known results obtained
from the ADHM method. We also discuss a particular tuning of K\"ahler
parameters associated with this Higgsing. |
Towards a world-sheet description of doubled geometry in string theory: Starting from a sigma-model for a doubled target-space geometry, we show that
the number of target-space dimensions can be reduced by half through a gauging
procedure. We apply this formalism to a class of backgrounds relevant for
double field theory, and illustrate how choosing different gaugings leads to
string-theory configurations T-dual to each other. We furthermore discuss that
given a conformal doubled theory, the reduced theories are conformal as well.
As an example we consider the three-dimensional SU(2) WZW model and show that
the only possible reduced backgrounds are the cigar and trumpet CFTs in two
dimensions, which are indeed T-dual to each other. | Matter matters in Einstein-Cartan gravity: We study scalar, fermionic and gauge fields coupled nonminimally to gravity
in the Einstein-Cartan formulation. We construct a wide class of models with
nondynamical torsion whose gravitational spectra comprise only the massless
graviton. Eliminating non-propagating degrees of freedom, we derive an
equivalent theory in the metric formulation of gravity. It features contact
interactions of a certain form between and among the matter and gauge currents.
We also discuss briefly the inclusion of curvature-squared terms. |
Novel Extension of MSSM and ``TeV Scale'' Coupling Unification: Motivated by the coupling unification problem, we propose a novel extension
of the Minimal Supersymmetric Standard Model. One of the predictions of this
extension is existence of new states neutral under SU(3)_c X SU(2)_w but
charged under U(1)_Y. The mass scale for these new states can be around the
mass scale of the electroweak Higgs doublets. This suggests a possibility of
their detection in the present or near future collider experiments. Unification
of gauge couplings in this extension is as precise (at one loop) as in the
MSSM, and can occur in the TeV range. | Magnetic catalysis of parity breaking in a massive Gross-Neveu model and
high-temperature superconductivity: In the framework of a (2+1)-dimensional P-even massive Gross-Neveu model, an
external magnetic field is shown to induce a parity breaking first order phase
transition. Possibility of applying the results obtained to description of
magnetic phase transitions in high-temperature superconductors is discussed. |
Supergravity and "New" Six-Dimensional Gauge Theories: In the first part of this letter, we analyse the supergravity dual
descriptions of six-dimensional field theories realized on the worldvolume of
(p,q) five-branes (OD5 theory). We show that in order for the low-energy gauge
theory description to be valid the theta parameter must be rational. Irrational
values of theta require a strongly coupled string description of the system at
low-energy. We discuss the phase structure and deduce some properties of these
theories. In the second part we construct and study the supergravity
description of NS5-branes with two electric RR field, which provides a dual
description of six-dimensional theories with several light open D-brane
excitations. | Generalised Permutation Branes on a product of cosets $G_{k_1}/H\times
G_{k_2}/H$: We study the modifications of the generalized permutation branes defined in
hep-th/0509153, which are required to give rise to the non-factorizable branes
on a product of cosets $G_{k_1}/H\times G_{k_2}/H$. We find that for $k_1\neq
k_2$ there exists big variety of branes, which reduce to the usual permutation
branes, when $k_1=k_2$ and the permutation symmetry is restored. |
Accelerating Universes in String Theory via Field Redefinition: We study cosmological solutions in the effective heterotic string theory with
$\alpha'$-correction terms in string frame. It is pointed out that the
effective theory has an ambiguity via field redefinition and we analyze
generalized effective theories due to this ambiguity. We restrict our analysis
to the effective theories which give equations of motion of second order in the
derivatives, just as "Galileon" field theory. This class of effective actions
contains two free coupling constants. We find de Sitter solutions as well as
the power-law expanding universes in our four-dimensional Einstein frame. The
accelerated expanding universes are always the attractors in the present
dynamical system. | Non-BPS D-branes on a Calabi-Yau Orbifold: A system containing a pair of non-BPS D-strings of type IIA string theory on
an orbifold, representing a single D2-brane wrapped on a nonsupersymmetric
2-cycle of a Calabi-Yau 3-fold with $(h^{(1,1)},h^{(1,2)})$ = (11,11), is
analyzed. In certain region of the moduli space the configuration is stable. We
show that beyond the region of stability the system can decay into a pair of
non-BPS D3-branes. At one point on the boundary of the region of stability,
there exists a marginal deformation which connects the system of non-BPS
D-strings to the system of non-BPS D3-branes. Across any other point on the
boundary of the region of stability, the transition from the system of non-BPS
D-strings to the system of non-BPS D3-branes is first order. We discuss the
phase diagram in the moduli space for these configurations. |
Notes on a SQCD-like plasma dual and holographic renormalization: We study the thermodynamics and the jet quenching parameter of a black hole
solution dual to a SQCD-like plasma which includes the backreaction of
fundamental flavors. The free energy is calculated in several ways, including
some recently proposed holographic renormalization prescriptions. The validity
of the latter is confirmed by the consistency with the other methods. The
resulting thermodynamic properties are similar to the Little String Theory
ones: the temperature is fixed at the Hagedorn value and the free energy is
vanishing. Finally, an accurate analysis of the relevant string configurations
shows that the jet quenching parameter is zero in this model, in agreement with
previous findings. | Heat kernel, effective action and anomalies in noncommutative theories: Being motivated by physical applications (as the phi^4 model) we calculate
the heat kernel coefficients for generalised Laplacians on the Moyal plane
containing both left and right multiplications. We found both star-local and
star-nonlocal terms. By using these results we calculate the large mass and
strong noncommutativity expansion of the effective action and of the vacuum
energy. We also study the axial anomaly in the models with gauge fields acting
on fermions from the left and from the right. |
U(1) symmetric $α$-attractors: We present a class of supergravity $\alpha$-attractors with an approximate
global U(1) symmetry corresponding to the axion direction. We also develop a
multi-field generalization of these models and show that the $\alpha$-attractor
models with U(1) symmetries have a dual description in terms of a two-form
superfield coupled to a three-form superfield. | The Black Hole Interior and a Curious Sum Rule: We analyze the Euclidean geometry near non-extremal NS5-branes in string
theory, including regions beyond the horizon and beyond the singularity of the
black brane. The various regions have an exact description in string theory, in
terms of cigar, trumpet and negative level minimal model conformal field
theories. We study the worldsheet elliptic genera of these three superconformal
theories, and show that their sum vanishes. We speculate on the significance of
this curious sum rule for black hole physics. |
Equivariant Cohomology and Gauged Bosonic sigma-Models: We re-examine the problem of gauging the Wess-Zumino term of a d-dimensional
bosonic sigma-model. We phrase this problem in terms of the equivariant
cohomology of the target space and this allows for the homological analysis of
the obstruction. As a check, we recover the obstructions of Hull and Spence and
also a generalization of the topological terms found by Hull, Rocek and de Wit.
When the symmetry group is compact, we use topological tools to derive
vanishing theorems which guarantee the absence of obstructions for low
dimension (d<=4) but for a variety of target manifolds. For example, any
compact semisimple Lie group can be gauged in a three-dimensional sigma-model
with simply connected target space. When the symmetry group is semisimple but
not necessarily compact, we argue in favor of the persistence of these
vanishing theorems by making use of (conjectural) equivariant minimal models
(in the sense of Sullivan). By way of persuasion, we construct by hand a few
such equivariant minimal models, which may be of independent interest. We
illustrate our results with two examples: d=1 with a symplectic target space,
and d=2 with target space a Lie group admitting a bi-invariant metric. An
alternative homological interpretation of the obstruction is obtained by a
closer study of the Noether method. This method displays the obstruction as a
class in BRST cohomology at ghost number 1. We comment on the relationship with
consistent anomalies. | Canonical Analysis of Scalar Fields in Two Dimensional Curved Space: Scalar fields on a two dimensional curved surface are considered and the
canonical structure of this theory analyzed. Both the first and second order
forms of the Einstein-Hilbert (EH) action for the metric are used (these being
inequivalent in two dimensions). The Dirac constraint formalism is used to find
the generator of the gauge transformation, using the formalisms of Henneaux,
Teitelboim and Zanelli (HTZ) and of Castellani (C). The HTZ formalism is
slightly modified in the case of the first order EH action to accommodate the
gauge transformation of the metric; this gauge transformation is unusual as it
mixes the affine connection with the scalar field. |
The Casimir effect for parallel plates involving massless Majorana
fermions at finite temperature: We study the Casimir effect for parallel plates with massless Majorana
fermions obeying the bag boundary conditions at finite temperature. The thermal
influence will modify the effect. It is found that the sign of the Casimir
energy keeps negative if the product of plate distance and the temperature is
larger than a special value or the energy will change to be positive. The
Casimir energy rises with the stronger thermal influence. We show that the
attractive Casimir force between two parallel plates becomes greater with the
increasing temperature. In the case of piston system involving the same
Majorana fermions with the same boundary conditions, the attractive force on
the piston will weaker in the hotter surrounding. | Refined geometric transition and $qq$-characters: We show the refinement of the prescription for the geometric transition in
the refined topological string theory and, as its application, discuss a
possibility to describe $qq$-characters from the string theory point of view.
Though the suggested way to operate the refined geometric transition has passed
through several checks, it is additionally found in this paper that the
presence of the preferred direction brings a nontrivial effect. We provide the
modified formula involving this point. We then apply our prescription of the
refined geometric transition to proposing the stringy description of doubly
quantized Seiberg--Witten curves called $qq$-characters in certain cases. |
Scalar Fields Nonminimally Coupled to pp Waves: Here, we report pp waves configurations of three-dimensional gravity for
which a scalar field nonminimally coupled to them acts as a source. In absence
of self-interaction the solutions are gravitational plane waves with a profile
fixed in terms of the scalar wave. In the self-interacting case, only power-law
potentials parameterized by the nonminimal coupling constant are allowed by the
field equations. In contrast with the free case the self-interacting scalar
field does not behave like a wave since it depends only on the wave-front
coordinate. We address the same problem when gravitation is governed by
topologically massive gravity and the source is a free scalar field. From the
pp waves derived in this case, we obtain at the zero topological mass limit,
new pp wave solutions of conformal gravity for any arbitrary value of the
nonminimal coupling parameter. Finally, we extend these solutions to the
self-interacting case of conformal gravity. | Large N, Z_N Strings and Bag Models: We study Z_N strings in nonabelian gauge theories, when they can be
considered as domain walls compactified on a cylinder and stabilized by the
flux inside. To make the wall vortex approximation reliable, we must take the
't Hooft large N limit. Our construction has many points in common with the
phenomenological bag models of hadrons. |
A Canonical Approach to Self-Duality of Dirichlet $3$-Brane: The self-duality of Dirichlet $3$-brane action under the $SL(2,R)$ duality
transformation of type IIB superstring theory is shown in the Hamiltonian form
of the path integral for the partition function by performing the direct
integration with respect to the boundary gauge field. Through the integration
in the phase space the canonical momentum conjugate to the boundary gauge field
can be effectively replaced by the dual gauge field. | Deformations of surface defect moduli spaces: Given a 4d ${\mathcal N}=2$ supersymmetric theory with an ${\mathcal
N}=(2,2)$ supersymmetric surface defect, a marginal perturbation of the bulk
theory induces a complex structure deformation of the defect moduli space. We
describe a concrete way of computing this deformation using the bulk-defect
OPE. |
Quantum Electrodynamics Mediated by a Photon with Generalized
(Continuous) Spin: We present rules for computing scattering amplitudes of charged scalar matter
and photons, where the photon has non-zero spin Casimir $\rho$, and is
therefore a continuous spin particle (CSP). The amplitudes reduce to familiar
scalar QED when $\rho\rightarrow 0$. As a concrete example, we compute the pair
annihilation and Compton scattering amplitudes in this theory and comment on
their physical properties, including unitarity and scaling behavior at small
and large $\rho$. | Writing CFT correlation functions as AdS scattering amplitudes: We explore the Mellin representation of conformal correlation functions
recently proposed by Mack. Examples in the AdS/CFT context reinforce the
analogy between Mellin amplitudes and scattering amplitudes. We conjecture a
simple formula relating the bulk scattering amplitudes to the asymptotic
behavior of Mellin amplitudes and show that previous results on the flat space
limit of AdS follow from our new formula. We find that the Mellin amplitudes
are particularly useful in the case of conformal gauge theories in the planar
limit. In this case, the four point Mellin amplitudes are meromorphic functions
whose poles and their residues are entirely determined by two and three point
functions of single-trace operators. This makes the Mellin amplitudes the ideal
objects to attempt the conformal bootstrap program in higher dimensions. |
Haunted Kaluza Universe with Four-dimensional Lorentzian Flat, Kerr, and
Taub-NUT Slices: The duality between the original Kaluza's theory and Klein's subsequent
modification is duality between slicing and threading decomposition of the
five-dimensional spacetime. The field equations of the original Kaluza's theory
lead to the interpretation of the four-dimensional Lorentzian Kerr and
Taub--NUT solutions as resulting from static electric and magnetic charges and
dipoles in the presence of ghost matter and constant dilaton, which models
Newton's constant. | Classification of p-branes, NUTs, Waves and Intersections: We give a full classification of the multi-charge supersymmetric $p$-brane
solutions in the massless and massive maximal supergravities in dimensions
$D\ge2$ obtained from the toroidal reduction of eleven-dimensional
supergravity. We derive simple universal rules for determining the fractions of
supersymmetry that they preserve. By reversing the steps of dimensional
reduction, the $p$-brane solutions become intersections of $p$-branes, NUTs and
waves in D=10 or D=11. Having classified the lower-dimensional $p$-branes, this
provides a classification of all the intersections in D=10 and D=11 where the
harmonic functions depend on the space transverse to all the individual
objects. We also discuss the structure of U-duality multiplets of $p$-brane
solutions, and show how these translate into multiplets of harmonic and
non-harmonic intersections. |
Finite temperature Casimir interaction between spheres in
$(D+1)$-dimensional spacetime: Exact computations and asymptotic expansions: We consider the finite temperature Casimir interaction between two Dirichlet
spheres in $(D+1)$-dimensional Minkowski spacetime. The Casimir interaction
free energy is derived from the zero temperature Casimir interaction energy via
the Matsubara formalism. In the high temperature region, the Casimir
interaction is dominated by the term with zero Matsubara frequency, and it is
known as the classical term since this term is independent of the Planck
constant $\hbar$. Explicit expression of the classical term is derived and it
is computed exactly using appropriate similarity transforms of matrices. We
then compute the small separation asymptotic expansion of this classical term
up to the next-to-leading order term. For the remaining part of the finite
temperature Casimir interaction with nonzero Matsubara frequencies, we obtain
its small separation asymptotic behavior by applying certain prescriptions to
the corresponding asymptotic expansion at zero temperature. This gives us a
leading term that is shown to agree precisely with the proximity force
approximation at any temperature. The next-to-leading order term at any
temperature is also derived and it is expressed as an infinite sum over
integrals. To obtain the asymptotic expansion at the low and medium temperature
regions, we apply the inverse Mellin transform techniques. In the low
temperature region, we obtain results that agree with our previous work on the
zero temperature Casimir interaction. | Kinky D-Strings: We study two-dimensional SQED viewed as the world-volume theory of a D-string
in the presence of D5-branes with non-zero background fields that induce
attractive forces between the branes. In various approximations, the low-energy
dynamics is given by a hyperKahler, or hyperKahler with torsion, massive
sigma-model. We demonstrate the existence of kink solutions corresponding to
the string interpolating between different D5-branes. Bound states of the
D-string with fundamental strings are identified with Q-kinks which, in turn,
are identified with dyonic instanton strings on the D5-brane world-volume. |
Unquenched Flavors in the Klebanov-Witten Model: Using AdS/CFT, we study the addition of an arbitrary number of backreacting
flavors to the Klebanov-Witten theory, making many checks of consistency
between our new Type IIB plus branes solution and expectations from field
theory. We study generalizations of our method for adding flavors to all N=1
SCFTs that can be realized on D3-branes at the tip of a Calabi-Yau cone. Also,
general guidelines suitable for the addition of massive flavor branes are
developed. | Softly Broken N=1 Supersymmetric QCD: We study softly broken N=1 supersymmetric QCD with the gauge group $SU(N_c)$
and $N_f$ flavours of quarks for $N_f > N_c+1$. We investigate the phase
structure of its dual theory adding generic soft supersymmetry breking terms,
i.e. soft scalar masses, trilinear coupling terms of scalar fields and gaugino
masses. It is found that the trilinear coupling terms play an improtant role in
determining the potential minima. Also we compare softly broken original and
dual theories in the broken phase. |
A finite temperature generalization of Zamolodchikov's C-theorem: We prove a C-theorem within the framework of two dimensional quantum field
theories at finite temperature. There exists a function C(g) of coupling
constants which is non-increasing along renormalization group trajectories and
non-decreasing along temperature trajectory and stationary only at the fixed
points. The connection between the C-theorem at zero temperature and the
C-theorem at finite temperature is discussed. We also consider the
thermodynamical aspects of the C-theorem. If we define the C-function in an
arbitrary number of dimensions in anology to the two dimensional case, we can
show that its behavior is not universal. The phase transitions destroy the
monotonic properties of the C-function. The proof of the C-theorem is also
presented within the framework of the Kallen-Lehmann spectral representation at
finite temperature. | Some exact infrared properties of gluon and ghost propagators and
long-range force in QCD: We derive some exact relations in Landau gauge that follow from a cut-off at
the Gribov horizon which is then implemented by a local, renormalizable action
involving auxiliary bose and fermi ghosts. The fermi ghost propagator is more
singular than $1/k^2$ at $k = 0$, and the relation $\alpha_D + 2 \alpha_G = (D
- 4)/2$ holds between the infrared critical exponents of the gluon and ghost
propagators $D(k)$ and $G(k)$ in $D$ Euclidean dimensions. Finally, in $D$
Euclidean dimensions, there is a long-range force, transmitted by the
propagator of the auxiliary bose ghost that corresponds to a linearly rising
potential with tensor coupling to colored quarks that is proportional to the
renormalization-group invariant $g^2 D(k) G^2(k)$. A comparison with numerical
results is discussed. |
Characters of the Positive Energy UIRs of D=4 Conformal Supersymmetry: We give character formulae for the positive energy unitary irreducible
representations of the N-extended D=4 conformal superalgebras su(2,2/N). Using
these we also derive decompositions of long superfields as they descend to the
unitarity threshold. These results are also applicable to irreps of the complex
Lie superalgebras sl(4/N). Our derivations use results from the representation
theory of su(2,2/N) developed already in the 80s. | Charged Black Holes in a Five-dimensional Kaluza-Klein Universe: We examine an exact solution which represents a charged black hole in a
Kaluza-Klein universe in the five-dimensional Einstein-Maxwell theory. The
spacetime approaches to the five-dimensional Kasner solution that describes
expanding three dimensions and shrinking an extra dimension in the far region.
The metric is continuous but not smooth at the black hole horizon. There
appears a mild curvature singularity that a free-fall observer can traverse the
horizon. The horizon is a squashed three-sphere with a constant size, and the
metric is approximately static near the horizon. |
Formula for Fixed Point Resolution Matrix of Permutation Orbifolds: We find a formula for the resolution of fixed points in extensions of
permutation orbifold conformal field theories by its (half-)integer spin simple
currents. We show that the formula gives a unitary and modular invariant S
matrix. | Witten indices of abelian M5 brane on $\mathbb{R}\times S^5$: Witten indices and partition functions are computed for abelian 6d tensor and
hypermultiplets on $\mathbb{R}\times S^5$ in Lorentzian signature in an R gauge
field background which preserves some supersymmetry. We consider a generic
supersymmetric squashing that also admits squashing of the Hopf fiber. Wick
rotation to Euclidean M5 brane amounts to Wick rotation of squashing parameters
and the hypermultiplet mass parameter. We compute Casimir energies for tensor
and hypermultiplets separately for general squashing, and match these with the
corresponding gravitational anomaly polynomials. We extract Witten indices on
$\mathbb{R}\times \mathbb{CP}^2$ and find that this is zero, again matching
with the vanishing anomaly polynomial on an odd dimensional space. |
Background Independence and the Open Topological String Wavefunction: The open topological string partition function in the background of a D-brane
on a Calabi-Yau threefold specifies a state in the Hilbert space associated
with the quantization of the underlying special geometry. This statement is a
consequence of the extended holomorphic anomaly equation after an appropriate
shift of the closed string variables, and can be viewed as the expression of
background independence for the open-closed topological string. We also clarify
various other aspects of the structure of the extended holomorphic anomaly
equation. We conjecture that the collection of all D-branes furnishes a basis
of the Hilbert space, and revisit the BPS interpretation of the open
topological string wavefunction in this light. | On new exact conformal blocks and Nekrasov functions: Recently, an intriguing family of the one-point toric conformal blocks AGT
related to the $\mathcal{N}=2^*\,\, SU(2)$ Nekrasov functions was discovered by
M. Beccaria and G. Macorini. Members of the family are distinguished by having
only finite amount of poles as functions of the intermediate dimension/v.e.v.
in gauge theory. Another remarkable property is that these conformal
blocks/Nekrasov functions can be found in closed form to all orders in the
coupling expansion. In the present paper we use Zamolodchikov's recurrence
equation to systematically account for these exceptional conformal blocks. We
conjecture that the family is infinite-dimensional and describe the
corresponding parameter set. We further apply the developed technique to
demonstrate that the four-point spheric conformal blocks feature analogous
exact expressions. We also study the modular transformations of the finite-pole
blocks. |
Branes and Black holes in Collision: We study the collision of a brane with a black hole. Our aim is to explore
the topology changing process of perforation of a brane. The brane is described
as a field theoretical domain wall in the context of an axion-like model
consisting of a complex scalar effective field theory with approximate U(1)
symmetry. We simulate numerically the dynamics of the collision and illustrate
the transition from the configuration without a hole to the pierced one with
the aid of a phase diagram. The process of perforation is found to depend on
the collisional velocity, and, contrary to our expectation, we observe that
above a critical value of the velocity, the black hole has no chance to
perforate the wall. That is: high energy collisions do not assist piercing. We
also show that, only when the model parameters are fine-tuned so that the
energy scale of the string is very close to that of the domain wall, the
collision of the wall with the black hole has a possibility to provide a
mechanism to erase domain walls, if the hole expands. However, in such cases,
domain walls will form with many holes edged by a string and therefore
disappear eventually. Therefore this mechanism is unlikely to be a solution to
the cosmological domain wall problem, although it may cause some minor effects
on the evolution of a domain wall network. | A Note on Noncommutative and False Noncommutative spaces: We show that the algebra of functions on noncommutative space allows two
different representations. One is describing the genuine noncommutative space,
while another one can be rewritten in commutative form by a redefinition of
generators. |
World-volume Effective Action of Exotic Five-brane in M-theory: We study the world-volume effective action of an exotic five-brane, known as
the M-theory 5${}^3$-brane (M5${}^3$-brane) in eleven dimensions. The
supermultiplet of the world-volume theory is the $\mathcal{N} = (2, 0)$ tensor
multiplet in six dimensions. The world-volume action contains three Killing
vectors $\hat{k}_{\hat{I}} {}^M \ (\hat{I} =1,2,3)$ associated with the
$U(1)^3$ isometry. We find the effective T-duality rule for the
eleven-dimensional backgrounds that transforms the M5-brane effective action to
that of the M5${}^3$-brane. We also show that our action provides the source
term for the M5${}^3$-brane geometry in eleven-dimensional supergravity | Casimir effect in axion electrodynamics with lattice regularizations: The Casimir effect is induced by the interplay between photon fields and
boundary conditions, and in particular, photon fields modified in axion
electrodynamics may lead to the sign-flipping of the Casimir energy. We propose
a theoretical approach to derive the Casimir effect in axion electrodynamics.
This approach is based on a lattice regularization and enables us to discuss
the dependence on the lattice spacing for the Casimir energy. With this
approach, the sign-flipping behavior of the Casimir energy is correctly
reproduced. By taking the continuum limit of physical quantity calculated on
the lattice, we can obtain the results consistent with the continuum theory.
This approach can also be applied to the Casimir effect at nonzero temperature. |
Hamiltonian Truncation with Larger Dimensions: Hamiltonian Truncation (HT) is a numerical approach for calculating
observables in a Quantum Field Theory non-perturbatively. This approach can be
applied to theories constructed by deforming a conformal field theory with a
relevant operator of scaling dimension $\Delta$. UV divergences arise when
$\Delta$ is larger than half of the spacetime dimension $d$. These divergences
can be regulated by HT or by using a more conventional local regulator. In this
work we show that extra UV divergences appear when using HT rather than a local
regulator for $\Delta \geq d/2+1/4$, revealing a striking breakdown of
locality. Our claim is based on the analysis of conformal perturbation theory
up to fourth order. As an example we compute the Casimir energy of $d=2$
Minimal Models perturbed by operators whose dimensions take values on either
side of the threshold $d/2+1/4$. | Leading and Subleading UV Divergences in Scattering Amplitudes for D=8
N=1 SYM Theory in All Loops: We consider the leading and subleading UV divergences for the four-point
on-shell scattering amplitudes in D=8 N=1 sypersymmetric Yang-Mills theory
within the spinor-helicity and superfield formalism. This theory belongs to the
class of maximally supersymmetric gauge theories and presumably possesses
distinguished properties beyond perturbation theory. We obtain the recursive
relations that allow one to get the leading and subleading divergences in all
loops in a pure algebraic way staring from the one loop (for the leading poles)
and two loop (for the subleading ones) diagrams. As a particular example where
the recursive relations have a simple form we consider the ladder type
diagrams. The all loop summation of the leading and subleading divergences is
performed with the help of the differential equations which are the
generalization of the RG equations for non-renormalizable theories. They have
explicit solutions for the ladder type diagrams. We discuss the properties of
the obtained solutions and interpretation of the results. |
Stable non-BPS D-branes and their classical description: We review how to describe the stable non-BPS D-branes of type II string
theory from a classical perspective, and discuss the properties of the
space-time geometry associated to these configurations. This is relevant in
order to see whether and how the gauge/gravity correspondence can be formulated
in non-conformal and non-supersymmetric settings. | Low-temperature behavior of the Abelian Higgs model in anti-de Sitter
space: We explore the low-temperature behavior of the Abelian Higgs model in AdS_4,
away from the probe limit in which back-reaction of matter fields on the metric
can be neglected. Over a significant range of charges for the complex scalar,
we observe a second order phase transition at finite temperature. The
symmetry-breaking states are superconducting black holes. At least when the
charge of the scalar is not too small, we observe at low temperatures the
emergence of a domain wall structure characterized by a definite index of
refraction. We also compute the conductivity as a function of frequency. |
Decay of Vacuum Energy: This paper studies interacting massive particles on the de Sitter background.
It is found that the vacuum acts as an inversely populated medium which is able
to generate stimulated radiation. Without back reaction (not considered in this
paper) this effect leads to the explosion. It is expected that the proposed
"cosmic laser" mechanism depletes the curvature and may help to solve the
cosmological constant problem. | Non-abelian $Z$-theory: Berends-Giele recursion for the
$α'$-expansion of disk integrals: We present a recursive method to calculate the $\alpha'$-expansion of disk
integrals arising in tree-level scattering of open strings which resembles the
approach of Berends and Giele to gluon amplitudes. Following an earlier
interpretation of disk integrals as doubly partial amplitudes of an effective
theory of scalars dubbed as $Z$-theory, we pinpoint the equation of motion of
$Z$-theory from the Berends-Giele recursion for its tree amplitudes. A computer
implementation of this method including explicit results for the recursion up
to order $\alpha'^7$ is made available on the website
http://repo.or.cz/BGap.git |
The Dynamical Yang-Baxter Relation and the Minimal Representation of the
Elliptic Quantum Group: In this paper, we give the general forms of the minimal $L$ matrix (the
elements of the $L$-matrix are $c$ numbers) associated with the Boltzmann
weights of the $A_{n-1}^1$ interaction-round-a-face (IRF) model and the minimal
representation of the $A_{n-1}$ series elliptic quantum group given by Felder
and Varchenko. The explicit dependence of elements of $L$-matrices on spectral
parameter $z$ are given. They are of five different forms (A(1-4) and B). The
algebra for the coefficients (which do not depend on $z$) are given. The
algebra of form A is proved to be trivial, while that of form B obey
Yang-Baxter equation (YBE). We also give the PBW base and the centers for the
algebra of form B. | Generalized Deformed su(2) Algebras, Deformed Parafermionic Oscillators
and Finite W Algebras: Several physical systems (two identical particles in two dimensions,
isotropic oscillator and Kepler system in a 2-dim curved space) and
mathematical structures (quadratic algebra QH(3), finite W algebra $\bar {\rm
W}_0$) are shown to posses the structure of a generalized deformed su(2)
algebra, the representation theory of which is known. Furthermore, the
generalized deformed parafermionic oscillator is identified with the algebra of
several physical systems (isotropic oscillator and Kepler system in 2-dim
curved space, Fokas--Lagerstrom, Smorodinsky--Winternitz and Holt potentials)
and mathematical constructions (generalized deformed su(2) algebra, finite W
algebras $\bar {\rm W}_0$ and W$_3^{(2)}$). The fact that the Holt potential is
characterized by the W$_3^{(2)}$ symmetry is obtained as a by-product. |
F-theory and All Things Rational: Surveying U(1) Symmetries with
Rational Sections: We study elliptic fibrations for F-theory compactifications realizing 4d and
6d supersymmetric gauge theories with abelian gauge factors. In the fibration
these U(1) symmetries are realized in terms of additional rational sections. We
obtain a universal characterization of all the possible U(1) charges of matter
fields by determining the corresponding codimension two fibers with rational
sections. In view of modelling supersymmetric Grand Unified Theories, one of
the main examples that we analyze are U(1) symmetries for SU(5) gauge theories
with \bar{5} and 10 matter. We use a combination of constraints on the normal
bundle of rational curves in Calabi-Yau three- and four-folds, as well as the
splitting of rational curves in the fibers in codimension two, to determine the
possible configurations of smooth rational sections. This analysis
straightforwardly generalizes to multiple U(1)s. We study the flops of such
fibers, as well as some of the Yukawa couplings in codimension three.
Furthermore, we carry out a universal study of the U(1)-charged GUT singlets,
including their KK-charges, and determine all realizations of singlet fibers.
By giving vacuum expectation values to these singlets, we propose a systematic
way to analyze the Higgsing of U(1)s to discrete gauge symmetries in F-theory. | On three dimensions as the preferred dimensionality of space via the
Brandenberger-Vafa mechanism: In previous work it was shown that, in accord with the Brandenberger-Vafa
mechanism, three is the maximum number of spatial dimensions that can grow
large cosmologically from an initial thermal fluctuation. Here we complement
that work by considering the possibility of successive fluctuations. Suppose an
initial fluctuation causes at least one dimension to grow, and suppose
successive fluctuations occur on timescales of order alpha'^{1/2}. If the
string coupling is sufficiently large, we show that such fluctuations are
likely to push a three-dimensional subspace to large volume where winding modes
annihilate. In this setting three is the preferred number of large dimensions.
Although encouraging, a more careful study of the dynamics and statistics of
fluctuations is needed to assess the likelihood of our assumptions. |
Five-dimensional Super-Yang-Mills and its Kaluza-Klein tower: We compactify the abelian 6d (1,0) tensor multiplet on a circle bundle, thus
reducing the theory down to 5d SYM while keeping all the KK modes. This abelian
classical field theory, when interpreted suitably, has a nonlocal
superconformal symmetry. Furthermore, a nonabelian generalization, where all
the KK modes are kept, is possible for the nonlocal superconformal symmetry,
whereas for the local superconformal symmetry we can only realize a subgroup. | Local momentum space: Scalar field and gravity: We use the local momentum space technique to obtain an expansion of the
Feynman propagators for scalar field and graviton up to first order in the
background curvature. The expressions for the propagators are cross-checked
with the past literature as well as with the expressions for the traced heat
kernel coefficients. The propagators so obtained are used to compute one-loop
divergences in the Vilkovisky-Dewitt's effective action for a scalar field
non-minimally coupled with gravity for an arbitrary spacetime metric
background. The Vilkovisky-DeWitt effective action is then compared with the
standard effective action in the limit $\kappa =0$, where $\kappa = 2/M_P$ in
terms of the Planck mass. The comparison yields the important result that
taking the limit $\kappa=0$ after computing the Vikovisky-DeWitt effective
action is not equivalent to computing the Vikovisky-DeWitt effective action for
the same theory in the absence of gravity. |
Heterotic free fermionic and symmetric toroidal orbifold models: Free fermionic models and symmetric heterotic toroidal orbifolds both
constitute exact backgrounds that can be used effectively for phenomenological
explorations within string theory. Even though it is widely believed that for
Z2xZ2 orbifolds the two descriptions should be equivalent, a detailed
dictionary between both formulations is still lacking. This paper aims to fill
this gap: We give a detailed account of how the input data of both descriptions
can be related to each other. In particular, we show that the generalized GSO
phases of the free fermionic model correspond to generalized torsion phases
used in orbifold model building. We illustrate our translation methods by
providing free fermionic realizations for all Z2xZ2 orbifold geometries in six
dimensions. | Semiclassical calculation of an induced decay of false vacuum: We consider a model where a scalar field develops a metastable vacuum state
and weakly interacts with another scalar field. In this situation we find the
probability of decay of the false vacuum stimulated by the presence and
collisions of particles of the second field. The discussed calculation is an
illustration of the recently suggested thermal approach to treatment of induced
semiclassical processes. |
Constrained Dynamics of an Anomalous $(g/neq 2)$ Relativistic Spinning
Particle in Electromagnetic Background: In this paper we have considered the dynamics of an anomalous ($g\neq 2$)
charged relativistic spinning particle in the presence of an external
electromagnetic field. The constraint analysis is done and the complete set of
Dirac brackets are provided that generate the canonical Lorentz algebra and
dynamics through Hamiltonian equations of motion. The spin-induced effective
curvature of spacetime and its possible connection with Analogue Gravity models
are commented upon. | A model for gauge theories with Higgs fields: We discuss in details a simple, purely bosonic, quantum field theory
belonging to larger class of models with the following properties: a) They are
asymptotically free, with a dynamically generated mass scale. b) They have a
space of parameters which gets quantum corrections drastically modifying the
classical singularity structure. The quantum theory can have massless solitons,
Argyres-Douglas-like CFTs, exhibit confinement, etc... c) The physics can, to a
large extent, be worked out in models with a large number of supersymmetries as
well as in purely bosonic ones. In the former case, exact BPS mass formulas can
be derived, brane constructions and embedding in M theory do exist. d) The
models have an interesting 1/N expansion, and it is possible to define a double
scaling limit in the sense of the ``old'' matrix models when approaching the
singularities in parameter space. These properties make these theories very
good toy models for four dimensional gauge theories with Higgs fields, and
provide a framework where the effects of breaking supersymmetry can be
explicitly studied. In our model, we work out in details the quantum space of
parameters. We obtain the non-local lagrangian description of the
Argyres-Douglas-like CFT, and show that it admits a strongly coupled fixed
point. We also explicitly demonstrate property d). The possibility of defining
such double scaling limits was not anticipated on the gauge theory side, and
could be of interest to understand the gauge theory/string theory
correspondence. |
Dessins d'Enfants, Seiberg-Witten Curves and Conformal Blocks: We show how to map Grothendieck's dessins d'enfants to algebraic curves as
Seiberg-Witten curves, then use the mirror map and the AGT map to obtain the
corresponding 4d $\mathcal{N}=2$ supersymmetric instanton partition functions
and 2d Virasoro conformal blocks. We explicitly demonstrate the 6 trivalent
dessins with 4 punctures on the sphere. We find that the parametrizations
obtained from a dessin should be related by certain duality for gauge theories.
Then we will discuss that some dessins could correspond to conformal blocks
satisfying certain rules in different minimal models. | Non-local Geometry inside Lifshitz Horizon: Based on the quantum renormalization group, we derive the bulk geometry that
emerges in the holographic dual of the fermionic U(N) vector model at a nonzero
charge density. The obstruction that prohibits the metallic state from being
smoothly deformable to the direct product state under the renormalization group
flow gives rise to a horizon at a finite radial coordinate in the bulk. The
region outside the horizon is described by the Lifshitz geometry with a
higher-spin hair determined by microscopic details of the boundary theory. On
the other hand, the interior of the horizon is not described by any Riemannian
manifold, as it exhibits an algebraic non-locality. The non-local structure
inside the horizon carries the information on the shape of the filled Fermi
sea. |
The Generalised Born Oscillator and the Berry-Keating Hamiltonian: In this study, we introduce and investigate a family of quantum mechanical
models in 0+1 dimensions, known as generalized Born quantum oscillators. These
models represent a one-parameter deformation of a specific system obtained by
reducing the Nambu-Goto theory to 0+1 dimensions. Despite these systems showing
significant similarities with $\mathrm{T}\overline{\mathrm{T}}$-type
perturbations of two-dimensional relativistic models, our analysis reveals
their potential as interesting regularizations of the Berry-Keating theory. We
quantize these models using the Weyl quantization scheme up to very high orders
in $\hbar$. By examining a specific scaling limit, we observe an intriguing
connection between the generalized Born quantum oscillators and the
Riemann-Siegel $\theta$ function. | Collective Excitations of Holographic Quantum Liquids in a Magnetic
Field: We use holography to study N=4 supersymmetric SU(Nc) Yang-Mills theory in the
large-Nc and large-coupling limits coupled to a number Nf << Nc of
(n+1)-dimensional massless supersymmetric hypermultiplets in the Nc
representation of SU(Nc), with n=2,3. We introduce a temperature T, a baryon
number chemical potential mu, and a baryon number magnetic field B, and work in
a regime with mu >> T,\sqrt{B}. We study the collective excitations of these
holographic quantum liquids by computing the poles in the retarded Green's
function of the baryon number charge density operator and the associated peaks
in the spectral function. We focus on the evolution of the collective
excitations as we increase the frequency relative to T, i.e. the
hydrodynamic/collisionless crossover. We find that for all B, at low
frequencies the tallest peak in the spectral function is associated with
hydrodynamic charge diffusion. At high frequencies the tallest peak is
associated with a sound mode similar to the zero sound mode in the
collisionless regime of a Landau Fermi liquid. The sound mode has a gap
proportional to B, and as a result for intermediate frequencies and for B
sufficiently large compared to T the spectral function is strongly suppressed.
We find that the hydrodynamic/collisionless crossover occurs at a frequency
that is approximately B-independent. |
On the Inconsistency of Fayet-Iliopoulos Terms in Supergravity Theories: Motivated by recent discussions, we revisit the issue of whether globally
supersymmetric theories with non-zero Fayet-Iliopoulos terms may be
consistently coupled to supergravity. In particular, we examine claims that a
fundamental inconsistency arises due to the conflicting requirements which are
imposed on the $R$-symmetry properties of the theory by the supergravity
framework. We also prove that certain kinds of Fayet-Iliopoulos contributions
to the supercurrent supermultiplets of theories with non-zero Fayet-Iliopoulos
terms fail to exist. A key feature of our discussion is an explicit comparison
between results from the chiral (or ``old minimal'') and linear (or ``new
minimal'') formulations of supergravity, and the effects within each of these
formalisms that are induced by the presence of non-zero Fayet-Iliopoulos terms. | Supersymmetric N=1 Spin(10) Gauge Theory with Two Spinors via
a-Maximization: We give a detailed analysis of the superconformal fixed points of
four-dimensional N=1 supersymmetric Spin(10) gauge theory with two spinors and
vectors by using a-maximization procedure. |
Matrix Model Description of Laughlin Hall States: We analyze Susskind's proposal of applying the non-commutative Chern-Simons
theory to the quantum Hall effect. We study the corresponding regularized
matrix Chern-Simons theory introduced by Polychronakos. We use holomorphic
quantization and perform a change of matrix variables that solves the Gauss law
constraint. The remaining physical degrees of freedom are the complex
eigenvalues that can be interpreted as the coordinates of electrons in the
lowest Landau level with Laughlin's wave function. At the same time, a
statistical interaction is generated among the electrons that is necessary to
stabilize the ground state. The stability conditions can be expressed as the
highest-weight conditions for the representations of the W-infinity algebra in
the matrix theory. This symmetry provides a coordinate-independent
characterization of the incompressible quantum Hall states. | On Gauge Couplings in String Theory: We investigate the field dependence of the gauge couplings of $N=1$ string
vacua from the point of view of the low energy effective quantum field theory.
We find that field-theoretical considerations severely constrain the form of
the string loop corrections; in particular, the dilaton dependence of the gauge
couplings is completely universal at the one-loop level. The moduli dependence
of the string threshold corrections is also constrained, and we illustrate the
power of such constraints with a detailed discussion of the orbifold vacua and
the $(2,2)$ (Calabi-Yau) vacua of the heterotic string. |
On the vacuum energy of a spherical plasma shell: We consider the vacuum energy of the electromagnetic field interacting with a
spherical plasma shell together with a model for the classical motion of the
shell. We calculate the heat kernel coefficients, especially that for the TM
mode, and carry out the renormalization by redefining the parameters of the
classical model. It turns out that this is possible and results in a model,
which in the limit of the plasma shell becoming an ideal conductor reproduces
the vacuum energy found by Boyer in 1968. | An Asymptotic Method for Selection of Inflationary Modes: We present some features of early universe cosmology in terms of Hankel
functions index ($\nu$). Actually, the recent data from observational cosmology
indicate that our universe was nearly de Sitter space-time in the early times
which results in an approximate scale-invariant spectrum. This imposes some
constrains on index $\nu$ [1]. These constrains stimulate us to use general
solution of inflaton field equation for $\nu\neq{\frac{3}{2}}$. To obtain the
general solution for the inflationary background, we use asymptotic expansion
of Hankel functions up to non-linear order of $\frac{1}{k\eta}$. We consider
the non-linear modes as the fundamental modes for early universe during the
inflation. In this paper, we obtain the general form of the inflationary modes,
scale factor expansion, equation of state and some non-linear corrections of
power spectrum in terms of index \nu. These results are general and in the
quasi-de Sitter and de Sitter limit confirm the conventional results. |
Asymptotic States in Two Black Hole Moduli Space: We discuss the quantum states in the moduli space, which constructed with
maximally charged dilaton black holes. Considering the quantum mechanics in the
moduli space, we obtain the asymptotic states for the near-coincident black
holes and the widely separated black holes. We study the scattering process of
the dilaton black holes with the asymptotic states. In the scattering process,
the quantum effects in the black hole moduli space are investigated. | Gravitating monopole and black holes at intermediate Higgs masses: Self-gravitating SU(2) Higgs magnetic monopoles exist up to a critical value
of the ratio of the vector meson mass to the Planck mass, which depends on the
Higgs boson mass. At the critical value a critical solution with a degenerate
horizon is reached. As pointed out by Lue and Weinberg, there are two types of
critical solutions, with a transition at an intermediate Higgs boson mass. Here
we investigate this transition for black holes, and reconsider it for the case
of gravitating monopoles. |
Fivebrane Gravitational Anomalies: Freed, Harvey, Minasian and Moore have proposed a mechanism to cancel the
gravitational anomaly of the M-theory fivebrane coming from diffeomorphisms
acting on the normal bundle. This procedure is based on a modification of the
conventional M-theory Chern-Simons term. We compactify this space-time
interaction to the ten-dimensional type IIA theory. We then analyze the
relation to the anomaly cancellation mechanism for the type IIA fivebrane
proposed by Witten. | Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar
model: We construct and analyze the phase diagram of a self-interacting matrix field
in two dimensions coupled to the curvature of the non-commutative truncated
Heisenberg space. In the infinite size limit, the model reduces to the
renormalizable Grosse-Wulkenhaar's. The curvature term proves crucial for the
diagram's structure: when turned off, the triple point collapses into the
origin as matrices grow larger; when turned on, the triple point recedes from
the origin proportionally to the coupling strength and the matrix size. The
coupling attenuation that turns the Grosse-Wulkenhaar model into a
renormalizable version of the $\phi^4_\star$-model cannot stop the triple point
recession. As a result, the stripe phase escapes to infinity, removing the
problems with UV/IR mixing. |
Pressure corrections in decoupling SU(2) Yang-Mills Theory: The case of
dihedral diagrams involving both massive and massless modes: In this work we show the step by step calculations needed to quantify the
contribution of a three-loop order diagram with dihedral symmetry to the
radiative corrections of the pressure in SU(2) thermal Yang-Mills theory in
deconfining phase. We surveyed past developments, and performed computations
for separate channel combinations, defined by Mandelstam variables which are
constrained by two 4-vertices. An analytically integrable approximation for
high-temperature conditions was found, to verify the relevance of the
corrections for this diagram. A numerical analysis with Monte Carlo methods was
carried out to check the validity of such approximation, to compare it with the
full integral. A Dyson-Schwinger resummation had to be performed to all
dihedral loop orders in order to control the temperature dependency found. | Symplectic, Multisymplectic Structures and Euler-Lagrange Cohomology: We study the Euler-Lagrange cohomology and explore the symplectic or
multisymplectic geometry and their preserving properties in classical mechanism
and classical field theory in Lagrangian and Hamiltonian formalism in each case
respectively. By virtue of the Euler-Lagrange cohomology that is nontrivial in
the configuration space, we show that the symplectic or multisymplectic
geometry and related preserving property can be established not only in the
solution space but also in the function space if and only if the relevant
closed Euler-Lagrange cohomological condition is satisfied in each case. We
also apply the cohomological approach directly to Hamiltonian-like ODEs and
Hamiltonian-like PDEs no matter whether there exist known Lagrangian and/or
Hamiltonian associated with them. |
Massive Nambu-Goldstone Bosons: Nicolis and Piazza have recently pointed out the existence of
Nambu-Goldstone-like excitations in relativistic systems at finite density,
whose gap is exactly determined by the chemical potential and the symmetry
algebra. We show that the phenomenon is much more general than anticipated and
demonstrate the presence of such modes in a number of systems from
(anti)ferromagnets in magnetic field to superfluid phases of quantum
chromodynamics. Furthermore, we prove a counting rule for these massive
Nambu-Goldstone bosons and construct a low-energy effective Lagrangian that
captures their dynamics. | Interactions of strings on a T-fold: We consider the interactions of strings on T-folds from the world-sheet point
of view which are exact in $\alpha'$. As a concrete example, we take a model
where the internal torus at the so(8) enhancement point is twisted by T-duality
(T-folded), and compute the scattering amplitudes of a class of massless
strings. The four-point amplitudes involving both twisted and untwisted strings
are obtained in a closed form in terms of the hypergeometric function. By their
factorization, the three-point coupling of the twisted and untwisted strings is
found to be suppressed by the chiral momenta along the internal torus, and
quantized in integer powers of 1/4. The asymptotic forms of the four-point
amplitudes in high-energy limits are also obtained. Our results rely only on
general properties of the asymmetric orbifold by the T-duality twist and of the
Lie algebra lattice from the symmetry enhancement, and thus may be extended
qualitatively to more general T-folds. |
Fermions Coupled to a Conformal Boundary: A Generalization of the
Monopole-Fermion System: We study a class of models in which $N$ flavors of massless fermions on the
half line are coupled by an arbitrary orthogonal matrix to $N$ rotors living on
the boundary. Integrating out the rotors, we find the exact partition function
and Green's functions. We demonstrate that the coupling matrix must satisfy a
certain rationality constraint, so there is an infinite, discrete set of
possible coupling matrices. For one particular choice of the coupling matrix,
this model reproduces the low-energy dynamics of fermions scattering from a
magnetic monopole. A quick survey of the Green's functions shows that the
S-matrix is nonunitary. This nonunitarity is present in previous results for
the monopole-fermion system, although it appears not to have been noted. We
indicate how unitarity may be restored by expanding the Fock space to include
new states that are unavoidably introduced by the boundary interaction. | Gravitational anomalies, entanglement entropy, and flat-space holography: We introduce a prescription to compute the entanglement entropy of Galilean
conformal field theories by combining gravitational anomalies and an
\.{I}n\"{o}n\"{u}-Wigner contraction. We find that our expression for the
entanglement entropy in the thermal limit reproduces the Cardy formula for
Galilean conformal field theories. Using this proposal, we calculate the
entanglement entropy for a class of Galilean conformal field theories, which
are believed to be dual to three-dimensional flat-space cosmological solutions.
These geometries describe expanding (contracting) universes and can be viewed
as the flat-space limit of rotating Ba\~nados-Teitelboim-Zanelli black holes.
We show that our finding reduces, in the appropriate limits, to the results
discussed in the literature and provide interpretations for the previously
unexplored regimes, such as flat-space chiral gravity. |
Kaluza-Klein Pistons with non-Commutative Extra Dimensions: We calculate the scalar Casimir energy and Casimir force for a $R^3\times N$
Kaluza-Klein piston setup in which the extra dimensional space $N$ contains a
non-commutative 2-sphere, $S_{FZ}$. The cases to be studied are $T^d\times
S_{FZ}$ and $S_{FZ}$ respectively as extra dimensional spaces, with $T^d$ the
$d$ dimensional commutative torus. The validity of the results and the
regularization that the piston setup offers are examined in both cases. Finally
we examine the 1-loop corrected Casimir energy for one piston chamber, due to
the self interacting scalar field in the non-commutative geometry. The
computation is done within some approximations. We compare this case for the
same calculation done in Minkowski spacetime $M^D$. A discussion on the
stabilization of the extra dimensional space within the piston setup follows at
the end of the article. | Compactification in the Lightlike Limit: We study field theories in the limit that a compactified dimension becomes
lightlike. In almost all cases the amplitudes at each order of perturbation
theory diverge in the limit, due to strong interactions among the longitudinal
zero modes. The lightlike limit generally exists nonperturbatively, but is more
complicated than might have been assumed. Some implications for the matrix
theory conjecture are discussed. |
Chaos by Magic: There is a property of a quantum state called magic. It measures how
difficult for a classical computer to simulate the state. In this paper, we
study magic of states in the integrable and chaotic regimes of the higher-spin
generalization of the Ising model through two quantities called "Mana" and
"Robustness of Magic" (RoM). We find that in the chaotic regime, Mana increases
monotonically in time in the early-time region, and at late times these
quantities oscillate around some non-zero value that increases linearly with
respect to the system size. Our result also suggests that under chaotic
dynamics, any state evolves to a state whose Mana almost saturates the optimal
upper bound, i.e., the state becomes "maximally magical." We find that RoM also
shows similar behaviors. On the other hand, in the integrable regime, Mana and
RoM behave periodically in time in contrast to the chaotic case. In the anti-de
Sitter/conformal field theory correspondence (AdS/CFT correspondence),
classical spacetime emerges from the chaotic nature of the dual quantum system.
Our result suggests that magic of quantum states is strongly involved behind
the emergence of spacetime geometry. | Complexity and Time: For any quantum algorithm given by a path in the space of unitary operators
we define the computational complexity as the typical computational time
associated with the path. This time is defined using a quantum time estimator
associated with the path. This quantum time estimator is fully characterized by
the Lyapunov generator of the path and the corresponding quantum Fisher
information. The computational metric associated with this definition of
computational complexity leads to a natural characterization of cost factors on
the Lie algebra generators. Operator complexity growth in time is analyzed from
this perspective leading to a simple characterization of Lyapunov exponent in
case of chaotic Hamiltonians. The connection between complexity and entropy is
expressed using the relation between quantum Fisher information about quantum
time estimation and von Neumann entropy. This relation suggest a natural bound
on computational complexity that generalizes the standard time energy quantum
uncertainty. The connection between Lyapunov and modular Hamiltonian is briefly
discussed. In the case of theories with holographic duals and for those reduced
density matrix defined by tracing over a bounded region of the bulk, quantum
estimation theory is crucial to estimate quantum mechanically the geometry of
the tracing region. It is suggested that the corresponding quantum Fisher
information associated with this estimation problem is at the root of the
holographic bulk geometry. |
M-Theory Dynamics On A Manifold Of G_2 Holonomy: We analyze the dynamics of M-theory on a manifold of G_2 holonomy that is
developing a conical singularity. The known cases involve a cone on CP^3, where
we argue that the dynamics involves restoration of a global symmetry,
SU(3)/U(1)^2, where we argue that there are phase transitions among three
possible branches corresponding to three classical spacetimes, and S^3 x S^3
and its quotients, where we recover and extend previous results about smooth
continuations between different spacetimes and relations to four-dimensional
gauge theory. | Maximal $U(1)_Y$-violating $n$-point correlators in $\mathcal{N}=4$
super-Yang-Mills theory: This paper concerns a special class of $n$-point correlation functions of
operators in the stress tensor supermultiplet of $\mathcal{N}=4$ supersymmetric
$SU(N)$ Yang-Mills theory. These are "maximal $U(1)_Y$-violating" correlators
that violate the bonus $U(1)_Y$ charge by a maximum of $2(n-4)$ units. We will
demonstrate that such correlators satisfy $SL(2,\mathbb{Z})$-covariant
recursion relations that relate $n$-point correlators to $(n-1)$-point
correlators in a manner analogous to the soft dilaton relations that relate the
corresponding amplitudes in flat-space type IIB superstring theory. These
recursion relations are used to determine terms in the large-$N$ expansion of
$n$-point maximal $U(1)_Y$-violating correlators in the chiral sector,
including correlators with four superconformal stress tensor primaries and
$(n-4)$ chiral Lagrangian operators, starting from known properties of the
$n=4$ case. We concentrate on the first three orders in $1/N$ beyond the
supergravity limit. The Mellin representations of the correlators are
polynomials in Mellin variables, which correspond to higher derivative contact
terms in the low-energy expansion of type IIB superstring theory in $AdS_5
\times S^5$ at the same orders as $R^4, d^4R^4$ and $d^6R^4$. The coupling
constant dependence of these terms is found to be described by non-holomorphic
modular forms with holomorphic and anti-holomorphic weights $(n-4,4-n)$ that
are $SL(2, \mathbb{Z})$-covariant derivatives of Eisenstein series and certain
generalisations. This determines a number of non-leading contributions to
$U(1)_Y$-violating $n$-particle interactions ($n>4$) in the low-energy
expansion of type IIB superstring amplitudes in $AdS_5\times S^5$. |
Holographic Entanglement Negativity for Adjacent Subsystems in
$\mathrm{AdS_{d+1}/CFT_d}$: We establish our recently proposed holographic entanglement negativity
conjecture for mixed states of adjacent subsystems in conformal field theories
with concrete higher dimensional examples. In this context we compute the
holographic entanglement negativity for mixed states of adjacent subsystems in
$d$-dimensional conformal field theories dual to bulk $AdS_{d+1}$ vacuum and
$AdS_{d+1}$-Schwarzschild black holes. These representative examples provide
strong indication for the universality of our conjecture which affirms
significant implications for diverse applications. | Topological nodal line semimetals in holography: We show a holographic model of a strongly coupled topological nodal line
semimetal (NLSM) and find that the NLSM phase could go through a quantum phase
transition to a topologically trivial state. The dual fermion spectral function
shows that there are multiple Fermi surfaces each of which is a closed nodal
loop in the NLSM phase. The topological structure in the bulk is induced by the
IR interplay between the dual mass operator and the operator that deforms the
topology of the Fermi surface. We propose a practical framework for building
various strongly coupled topological semimetals in holography, which indicates
that at strong coupling topologically nontrivial semimetal states generally
exist. |
Shadows of the Planck Scale: The Changing Face of Compactification
Geometry: By studying the effects of the shape moduli associated with toroidal
compactifications, we demonstrate that Planck-sized extra dimensions can cast
significant ``shadows'' over low-energy physics. These shadows can greatly
distort our perceptions of the compactification geometry associated with large
extra dimensions, and place a fundamental limit on our ability to probe the
geometry of compactification simply by measuring Kaluza-Klein states. We also
discuss the interpretation of compactification radii and hierarchies in the
context of geometries with non-trivial shape moduli. One of the main results of
this paper is that compactification geometry is effectively renormalized as a
function of energy scale, with ``renormalization group equations'' describing
the ``flow'' of geometric parameters such as compactification radii and shape
angles as functions of energy. | Two-Dimensional Chiral Matrix Models and String Theories: We formulate and solve a class of two-dimensional matrix gauge models
describing ensembles of non-folding surfaces covering an oriented, discretized,
two-dimensional manifold. We interpret the models as string theories
characterized by a set of coupling constants associated to worldsheet
ramification points of various orders. Our approach is closely related to, but
simpler than, the string theory describing two-dimensional Yang-Mills theory.
Using recently developed character expansion methods we exactly solve the
models for target space lattices of arbitrary internal connectivity and
topology. |
T-Duality and Mixed Branes: In this article the action of T-duality on a mixed brane is studied in the
boundary state formalism. We also obtain a two dimensional mixed brane with
non-zero electric and magnetic fields, from a D$_1$-brane. | Effects of Dirac's Negative Energy Sea on Quantum Numbers: One route towards understanding both fractional charges and chiral anomalies
delves into Dirac's negative energy sea. Usually we think of Dirac's negative
energy sea as an unphysical construct, invented to render quantum field theory
physically acceptable by hiding the negative energy solutions. I suggest that
in fact physical consequences can be drawn from Dirac's construction. |
Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion: We use the inverse-dimensional expansion to compute analytically the
frequencies of a set of quasinormal modes of static black holes of
Einstein-(Anti-)de Sitter gravity, including the cases of spherical, planar or
hyperbolic horizons. The modes we study are decoupled modes localized in the
near-horizon region, which are the ones that capture physics peculiar to each
black hole (such as their instabilities), and which in large black holes
contain hydrodynamic behavior. Our results also give the unstable
Gregory-Laflamme frequencies of Ricci-flat black branes to two orders higher in
1/D than previous calculations. We discuss the limits on the accuracy of these
results due to the asymptotic but not convergent character of the 1/D
expansion, which is due to the violation of the decoupling condition at finite
D. Finally, we compare the frequencies for AdS black branes to calculations in
the hydrodynamic expansion in powers of the momentum k. Our results extend up
to k^9 for the sound mode and to k^8 for the shear mode. | Central Configurations in Three Dimensions: We consider the equilibria of point particles under the action of two body
central forces in which there are both repulsive and attractive interactions,
often known as central configurations, with diverse applications in physics, in
particular as homothetic time-dependent solutions to Newton's equations of
motion and as stationary states in the One Component Plasma model.
Concentrating mainly on the case of an inverse square law balanced by a linear
force, we compute numerically equilibria and their statistical properties. When
all the masses (or charges) of the particles are equal, for small numbers of
points they are regular convex deltahedra, which on increasing the number of
points give way to a multi-shell structure. In the limit of a large number of
points we argue using an analytic model that they form a homogeneous spherical
distribution of points, whose spatial distribution appears, from our
preliminary investigation, to be similar to that of a Bernal hard-sphere
liquid. |
Sigma-model for Generalized Composite p-branes: A multidimensional gravitational model containing several dilatonic scalar
fields and antisymmetric forms is considered. The manifold is chosen in the
form M = M_0 x M_1 x ... x M_n, where M_i are Einstein spaces (i > 0). The
block-diagonal metric is chosen and all fields and scale factors of the metric
are functions on M_0. For the forms composite (electro-magnetic) p-brane ansatz
is adopted. The model is reduced to gravitating self-interacting sigma-model
with certain constraints. In pure electric and magnetic cases the number of
these constraints is m(m - 1)/2 where m is number of 1-dimensional manifolds
among M_i. In the "electro-magnetic" case for dim M_0 = 1, 3 additional m
constraints appear. A family of "Majumdar-Papapetrou type" solutions governed
by a set of harmonic functions is obtained, when all factor-spaces M_k are
Ricci-flat. These solutions are generalized to the case of non-Ricci-flat M_0
when also some additional "internal" Einstein spaces of non-zero curvature are
added to M. As an example exact solutions for D = 11 supergravity and related
12-dimensional theory are presented. | Born-Infeld Corrections to the Entropy Function of Heterotic Black Holes: We use the black hole entropy function to study the effect of Born-Infeld
terms on the entropy of extremal black holes in heterotic string theory in four
dimensions. We find that after adding a set of higher curvature terms to the
effective action, attractor mechanism works and Born-Infeld terms contribute to
the stretching of near horizon geometry. In the alpha'--> 0 limit, the
solutions of attractor equations for moduli fields and the resulting entropy,
are in conformity with the ones for standard two charge black holes. |
Axion Monodromy and the Weak Gravity Conjecture: Axions with broken discrete shift symmetry (axion monodromy) have recently
played a central role both in the discussion of inflation and the `relaxion'
approach to the hierarchy problem. We suggest a very minimalist way to
constrain such models by the weak gravity conjecture for domain walls: While
the electric side of the conjecture is always satisfied if the
cosine-oscillations of the axion potential are sufficiently small, the magnetic
side imposes a cutoff, $\Lambda^3 \sim m f M_{pl}$, independent of the height
of these `wiggles'. We compare our approach with the recent related proposal by
Ibanez, Montero, Uranga and Valenzuela. We also discuss the non-trivial
question which version, if any, of the weak gravity conjecture for domain walls
should hold. In particular, we show that string compactifications with branes
of different dimensions wrapped on different cycles lead to a `geometric weak
gravity conjecture' relating volumes of cycles, norms of corresponding forms
and the volume of the compact space. Imposing this `geometric conjecture',
e.g.~on the basis of the more widely accepted weak gravity conjecture for
particles, provides at least some support for the (electric and magnetic)
conjecture for domain walls. | Sphaleron in the dilatonic electroweak theory: A numerical study of static, spherically symmetric sphaleron solutions in the
standard model coupled to the dilaton field is presented. We show that
sphaleron is surrounded by strong dilaton cloud which vanishes inside the
sphaleron. |
New Identities among Gauge Theory Amplitudes: Color-ordered amplitudes in gauge theories satisfy non-linear identities
involving amplitude products of different helicity configurations. We consider
the origin of such identities and connect them to the Kawai-Lewellen-Tye (KLT)
relations between gravity and gauge theory amplitudes. Extensions are made to
one-loop order of the full N=4 super Yang-Mills multiplet. | Modified spontaneous symmetry breaking pattern by brane-bulk interaction
terms: We show how translational invariance can be broken by the vacuum that drives
the spontaneous symmetry breaking of extra-dimensional extensions of the
Standard Model, when delta-like interactions between brane and bulk scalar
fields are present. We explicitly build some examples of vacuum configurations,
which induce the spontaneous symmetry breaking, and have non trivial profile in
the extra coordinate. |
Renormalization of the cyclic Wilson loop: In finite-temperature field theory, the cyclic Wilson loop is defined as a
rectangular Wilson loop spanning the whole compactified time direction. In a
generic non-abelian gauge theory, we calculate the perturbative expansion of
the cyclic Wilson loop up to order g^4. At this order and after charge
renormalization, the cyclic Wilson loop is known to be ultraviolet divergent.
We show that the divergence is not associated with cusps in the contour but is
instead due to the contour intersecting itself because of the periodic boundary
conditions. One consequence of this is that the cyclic Wilson loop mixes under
renormalization with the correlator of two Polyakov loops. The resulting
renormalization equation is tested up to order g^6 and used to resum the
leading logarithms associated with the intersection divergence. Implications
for lattice studies of this operator, which may be relevant for the
phenomenology of quarkonium at finite temperature, are discussed. | On Metastable Branes and a New Type of Magnetic Monopole: String compactifications with D-branes may exhibit regular magnetic monopole
solutions, whose presence does not rely on broken non-abelian gauge symmetry.
These stringy monopoles exist on interesting metastable brane configurations,
such as anti-D3 branes inside a flux compactification or D5-branes wrapping
2-cycles that are locally stable but globally trivial. In brane realizations of
SM-like gauge theories, the monopoles carry one unit of magnetic hypercharge.
Their mass can range from the string scale down to the multi-TeV regime. |
BPS coherent states and localization: We introduce coherent states averaged over a gauge group action to study
correlators of half BPS states in ${\cal N}=4 $ SYM theory. The overlaps of
these averaged coherent states are a generating function of correlators and can
be written in terms of the Harish-Chandra-Itzykzon-Zuber (HCIZ) integral. We
show that this formula immediately leads to a computation of the normalization
of two point functions in terms of characters obtained originally in the work
of Corley, Jevicki and Ramgoolam. We also find various generalizations for
$A_{n-1}$ quivers that follow directly from other solvable integrals over
unitary groups. All of these can be computed using localization methods. When
we promote the parameters of the generating function to collective coordinates,
there is a dominant saddle that controls the effective action of these coherent
states in the regime where they describe single AdS giant gravitons. We also
discuss how to add open strings to this formulation. These will produce
calculations that rely on correlators of matrix components of unitaries in the
ensemble that is determined by the HCIZ integral to determine anomalous
dimensions. We also discuss how sphere giants arise from Grassman integrals,
how one gets a dominant saddle and how open strings are added in that case. The
fact that there is a dominant saddle helps to understand how a $1/N$ expansion
arises for open strings. We generalize the coherent state idea to study $1/4$
and $1/8$ BPS states as more general integrals over unitary groups. | Confining Phase of Three Dimensional Supersymmetric Quantum
Electrodynamics: Abelian theories in three dimensions can have linearly confining phases as a
result of monopole-instantons, as shown, for SU(2) Yang-Mills theory broken to
its abelian subgroup, by Polyakov. In this article the generalization of this
phase for N=2 supersymmetric abelian theories is identified, using a dual
description. Topologically stable BPS-saturated and unsaturated particle and
string solitons play essential roles. A plasma of chiral monopoles of charge 1
and -1 (along with their antichiral conjugates) are required for a stable
confining vacuum. N=2 SU(2) Yang-Mills theory broken to U(1) lacks this phase
because its chiral monopoles all have the same charge, leading to a runaway
instability. The possibility of analogous confining phases of string theory,
and a dual field theoretic model thereof, are briefly discussed. |
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