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Anomaly Cancellations in the Type I D9-anti-D9 System and the USp(32)
String Theory: We check some consistency conditions for the D9-anti-D9 system in type I
string theory. The gravitational anomaly and gauge anomaly for SO(n) x SO(m)
gauge symmetry are shown to be cancelled when n-m=32. In addition, we find that
a string theory with USp(n) x USp(m) gauge symmetry also satisfies the anomaly
cancellation conditions. After tachyon condensation, the theory reduces to a
tachyon-free USp(32) string theory, though there is no spacetime supersymmetry. | hep-th |
Slowly rotating black holes in Quasi-topological gravity: While cubic Quasi-topological gravity is unique, there is a family of quartic
Quasi-topological gravities in five dimensions. These theories are defined by
leading to a first order equation on spherically symmetric spacetimes,
resembling the structure of the equations of Lovelock theories in
higher-dimensions, and are also ghost free around AdS. Here we construct slowly
rotating black holes in these theories, and show that the equations for the
off-diagonal components of the metric in the cubic theory are automatically of
second order, while imposing this as a restriction on the quartic theories
allows to partially remove the degeneracy of these theories, leading to a
three-parameter family of Lagrangians of order four in the Riemann tensor. This
shows that the parallel with Lovelock theory observed on spherical symmetry,
extends to the realm of slowly rotating solutions. In the quartic case, the
equations for the slowly rotating black hole are obtained from a consistent,
reduced action principle. These functions admit a simple integration in terms
of quadratures. Finally, in order to go beyond the slowly rotating regime, we
explore the consistency of the Kerr-Schild ansatz in cubic Quasi-topological
gravity. Requiring the spacetime to asymptotically match with the rotating
black hole in GR, for equal oblateness parameters, the Kerr-Schild deformation
of an AdS vacuum, does not lead to a solution for generic values of the
coupling. This result suggests that in order to have solutions with finite
rotation in Quasi-topological gravity, one must go beyond the Kerr-Schild
ansatz. | hep-th |
Surgical invariants of four-manifolds: A new topological invariant of closed connected orientable four-dimensional
manifolds is proposed. The invariant, constructed via surgery on a special
link, is a four-dimensional counterpart of the celebrated SU(2) three-manifold
invariant of Reshetikhin, Turaev and Witten. | hep-th |
Brane solutions in strings with broken supersymmetry and dilaton
tadpoles: The tachyon-free nonsupersymmetric string theories in ten dimensions have
dilaton tadpoles which forbid a Minkowski vacuum. We determine the maximally
symmetric backgrounds for the $USp(32)$ Type I string and the $SO(16)\times
SO(16)$ heterotic string. The static solutions exhibit nine dimensional
Poincar\'e symmetry and have finite 9D Planck and Yang-Mills constants. The low
energy geometry is given by a ten dimensional manifold with two boundaries
separated by a finite distance which suggests a spontaneous compactification of
the ten dimensional string theory. | hep-th |
Superconformal mechanics, black holes, and non-linear realizations: The OSp(2|2)-invariant planar dynamics of a D=4 superparticle near the
horizon of a large mass extreme black hole is described by an N=2
superconformal mechanics, with the SO(2) charge being the superparticle's
angular momentum. The {\it non-manifest} superconformal invariance of the
superpotential term is shown to lead to a shift in the SO(2) charge by the
value of its coefficient, which we identify as the orbital angular momentum.
The full SU(1,1|2)-invariant dynamics is found from an extension to N=4
superconformal mechanics. | hep-th |
The Standard Model, The Exceptional Jordan Algebra, and Triality: Jordan, Wigner and von Neumann classified the possible algebras of quantum
mechanical observables, and found they fell into 4 "ordinary" families, plus
one remarkable outlier: the exceptional Jordan algebra. We point out an
intriguing relationship between the complexification of this algebra and the
standard model of particle physics, its minimal left-right-symmetric
$SU(3)\times SU(2)_{L}\times SU(2)_{R}\times U(1)$ extension, and $Spin(10)$
unification. This suggests a geometric interpretation, where a single
generation of standard model fermions is described by the tangent space
$(\mathbb{C}\otimes\mathbb{O})^{2}$ of the complex octonionic projective plane,
and the existence of three generations is related to $SO(8)$ triality. | hep-th |
Closed Superstrings in a Uniform Magnetic Field and Regularization
Criterion: We summarize exact solutions of closed superstrings in a constant magnetic
field, from a view point of the regularization criterion. Some models will be
excluded according to this criterion. The spectrum-generating algebra is also
constructed in these interacting models. | hep-th |
Fluctuations of inflationary magnetogenesis: This analysis aims at exploring what can be said about the growth rate of
magnetized inhomogeneities under two concurrent hypotheses: a phase of quasi-de
Sitter dynamics driven by a single inflaton field and the simultaneous presence
of a spectator field coupled to gravity and to the gauge sector. Instead of
invoking ad hoc correlations between the various components, the system of
scalar inhomogeneities is diagonalized in terms of two gauge-invariant
quasi-normal modes whose weighted sum gives the curvature perturbations on
comoving orthogonal hypersurfaces. The predominance of the conventional
adiabatic scalar mode implies that the growth rate of magnetized
inhomogeneities must not exceed 2.2 in Hubble units if the conventional
inflationary phase is to last about 70 efolds and for a range of slow roll
parameters between 0.1 and 0.001. Longer and shorter durations of the quasi-de
Sitter stage lead, respectively, either to tighter or to looser bounds which
are anyway more constraining than the standard backreaction demands imposed on
the gauge sector. Since a critical growth rate of order 2 leads to a quasi-flat
magnetic energy spectrum, the upper bounds on the growth rate imply a lower
bound on the magnetic spectral index. The advantages of the uniform curvature
gauge are emphasized and specifically exploited throughout the treatment of the
multicomponent system characterizing this class of problems. | hep-th |
Explaining the Electroweak Scale and Stabilizing Moduli in M Theory: In a recent paper \cite{Acharya:2006ia} it was shown that in $M$ theory vacua
without fluxes, all moduli are stabilized by the effective potential and a
stable hierarchy is generated, consistent with standard gauge unification. This
paper explains the results of \cite{Acharya:2006ia} in more detail and
generalizes them, finding an essentially unique de Sitter (dS) vacuum under
reasonable conditions. One of the main phenomenological consequences is a
prediction which emerges from this entire class of vacua: namely gaugino masses
are significantly suppressed relative to the gravitino mass. We also present
evidence that, for those vacua in which the vacuum energy is small, the
gravitino mass, which sets all the superpartner masses, is automatically in the
TeV - 100 TeV range. | hep-th |
On the instability of 3d null singularities: String propagation on a three-dimensional Lorentzian string orbifold with a
null singularity has been studied by Horowitz and Steif, and more recently by
Liu, Moore and Seiberg. We analyze the target space as a classical
gravitational background. The singularity becomes spacelike when an arbitrarily
small amount of matter is thrown at the singularity. This can be seen directly
by studying the null singularity as a limit of the M=0, J=0 BTZ black hole
metric. | hep-th |
Decomposing the SU(N) Connection and the Wu-Yang Potential: Based on the decomposition of SU(2) gauge field, we derive a generalization
of the decomposition theory for the SU(N) gauge field. We thus obtain the
invariant electro-magnetic tensors of SU(N) groups and the extended Wu-Yang
potentials. The sourceless solutions are also discussed. | hep-th |
Aspects of the Holographic Study of Flavor Dynamics: This thesis is dedicated to the holographic study of flavor dynamics. The
technique employed is a D7-brane probing of various D3-brane backgrounds. The
first topic covered studies the influence of an external magnetic field on a
flavored large N Yang-Mills theory. The theory exhibits spontaneous chiral
symmetry breaking. The meson spectrum exhibits Zeeman splitting and
characteristic GMOR relation. The second topic examines thermal properties of
the dual gauge theory. The third topic studies the phase structure of the
finite temperature dual gauge theory in the presence of magnetic field. A phase
diagram of the theory is obtained and the meson spectrum is explored. The
fourth topic studies the addition of an external electric field. The observed
effect is dissociation of the bound quarks, favoring the meson melting, the
dissociation of mesons corresponds to an insulator/conductor phase transition.
The fifth topic studies the addition of an R-charge chemical potential via
brane probing of the spinning D3-brane geometry. The corresponding phase
diagram is obtained. The chemical potential favors the dissociation of mesons.
The last topic explores universal properties of gauge theories dual to the
Dp/Dq system. A universal discrete self-similar behavior associated to the
insulator/conductor phase transition is observed and the corresponding scaling
exponents are computed. | hep-th |
Moduli space volume of vortex and localization: Volume of moduli space of BPS vortices on a compact genus h Riemann surface
Sigma_h is evaluated by means of topological field theory and localization
technique. Vortex in Abelian gauge theory with a single charged scalar field
(ANO vortex) is studied first and is found that the volume of the moduli space
agrees with the previous results obtained more directly by integrating over the
moduli space metric. Next we extend the evaluation to non-Abelian gauge groups
and multi-flavors of scalar fields in the fundamental representation. We find
that the result of localization can be consistently understood in terms of
moduli matrix formalism wherever possible. More details are found in our paper
in Prog.Theor.Phys.126 (2011) 637. | hep-th |
Calculating Casimir Energies in Renormalizable Quantum Field Theory: Quantum vacuum energy has been known to have observable consequences since
1948 when Casimir calculated the force of attraction between parallel uncharged
plates, a phenomenon confirmed experimentally with ever increasing precision.
Casimir himself suggested that a similar attractive self-stress existed for a
conducting spherical shell, but Boyer obtained a repulsive stress. Other
geometries and higher dimensions have been considered over the years. Local
effects, and divergences associated with surfaces and edges have been studied
by several authors. Quite recently, Graham et al. have re-examined such
calculations, using conventional techniques of perturbative quantum field
theory to remove divergences, and have suggested that previous self-stress
results may be suspect. Here we show that the examples considered in their work
are misleading; in particular, it is well-known that in two dimensions a
circular boundary has a divergence in the Casimir energy for massless fields,
while for general dimension $D$ not equal to an even integer the corresponding
Casimir energy arising from massless fields interior and exterior to a
hyperspherical shell is finite. It has also long been recognized that the
Casimir energy for massive fields is divergent for $D\ne1$. These conclusions
are reinforced by a calculation of the relevant leading Feynman diagram in $D$
and three dimensions. There is therefore no doubt of the validity of the
conventional finite Casimir calculations. | hep-th |
Unification of twistors and Ramond vectors: We generalize the idea of supertwistors and introduce a new supersymmetric
object - the $\theta$-twistor which includes the composite Ramond vector [11]
well known from the spinning string dynamics. The symmetries of the chiral
$\theta$-twistor superspace are studied. It is shown that the chiral spin
structure introduced by the $\theta$-twistor breaks the superconformal boost
symmetry but preserves the scale symmetry and the super-Poincare symmetry. This
geometrical effect of breaking correlates with the Gross-Wess effect of the
conformal boost breaking for bosonic scattering amplitudes. | hep-th |
Preheating with Fractional Powers: We consider preheating in models in which the potential for the inflaton is
given by a fractional power, as is the case in axion monodromy inflation. We
assume a standard coupling between the inflaton field and a scalar matter
field. We find that in spite of the fact that the oscillation of the inflaton
about the field value which minimizes the potential is anharmonic, there is
nevertheless a parametric resonance instability, and we determine the Floquet
exponent which describes this instability as a function of the parameters of
the inflaton potential. | hep-th |
Metric and coupling reversal in string theory: Invariance under reversing the sign of the metric G_{MN}(x) and/or the sign
of the string coupling field H(x), where <H(x)> = g_s, leads to four possible
Universes denoted 1,I,J,K according as (G,H) goes to (G,H), (-G,H), (-G,-H),
(G,-H), respectively. Universe 1 is described by conventional string/M theory
and contains all M, D, F and NS branes. Universe I contains only D(-1), D3 and
D7. Universe J contains only D1, D5, D9 and Type I. Universe K contains only F1
and NS5 of IIB and Heterotic SO(32). | hep-th |
String versus Einstein frame in an AdS/CFT induced quantum dilatonic
brane-world universe: AdS/CFT induced quantum dilatonic brane-world where 4d boundary is flat or de
Sitter (inflationary) or Anti-de Sitter brane is considered. The classical
brane tension is fixed but boundary QFT produces the effective brane tension
via the account of corresponding conformal anomaly induced effective action.
This results in inducing of brane-worlds in accordance with AdS/CFT set-up as
warped compactification. The explicit, independent construction of quantum
induced dilatonic brane-worlds in two frames: string and Einstein one is done.
It is demonstrated their complete equivalency for all quantum cosmological
brane-worlds under discussion, including several examples of classical
brane-world black holes. This is different from quantum corrected 4d dilatonic
gravity where de Sitter solution exists in Einstein but not in Jordan (string)
frame. The role of quantum corrections on massive graviton perturbations around
Anti-de Sitter brane is briefly discussed. | hep-th |
The Casimir effect with quantized charged spinor matter in background
magnetic field: We study the influence of a background uniform magnetic field and boundary
conditions on the vacuum of a quantized charged spinor matter field confined
between two parallel neutral plates; the magnetic field is directed
orthogonally to the plates. The admissible set of boundary conditions at the
plates is determined by the requirement that the Dirac Hamiltonian operator be
self-adjoint. It is shown that, in the case of a sufficiently strong magnetic
field and a sufficiently large separation of the plates, the generalized
Casimir force is repulsive, being independent of the choice of a boundary
condition, as well as of the distance between the plates. The detection of this
effect seems to be feasible in the foreseeable future. | hep-th |
Brackets, Sigma Models and Integrability of Generalized Complex
Structures: It is shown how derived brackets naturally arise in sigma-models via Poisson-
or antibracket, generalizing a recent observation by Alekseev and Strobl. On
the way to a precise formulation of this relation, an explicit coordinate
expression for the derived bracket is obtained. The generalized Nijenhuis
tensor of generalized complex geometry is shown to coincide up to a de-Rham
closed term with the derived bracket of the structure with itself, and a new
coordinate expression for this tensor is presented. The insight is applied to
two known two-dimensional sigma models in a background with generalized complex
structure. Introductions to geometric brackets on the one hand and to
generalized complex geometry on the other hand are given in the appendix. | hep-th |
Thermodynamics of accelerating AdS$_4$ black holes from the covariant
phase space: We study the charges and first law of thermodynamics for accelerating,
non-rotating black holes with dyonic charges in AdS$_4$ using the covariant
phase space formalism. In order to apply the formalism to these solutions
(which are asymptotically locally AdS and admit a non-smooth conformal boundary
$\mathscr{I}$) we make two key improvements: 1) We relax the requirement to
impose Dirichlet boundary conditions and demand merely a well-posed variational
problem. 2) We keep careful track of the codimension-2 corner term induced by
the holographic counterterms, a necessary requirement due to the presence of
"cosmic strings" piercing $\mathscr{I}$. Using these improvements we are able
to match the holographic Noether charges to the Wald Hamiltonians of the
covariant phase space and derive the first law of black hole thermodynamics
with the correct "thermodynamic length" terms arising from the strings. We
investigate the relationship between the charges imposed by supersymmetry and
show that our first law can be consistently applied to various classes of
non-supersymmetric solutions for which the cross-sections of the horizon are
spindles. | hep-th |
A note about a new class of two-kinks: We present a model of two-kinks resulting from an explicit composition of two
standards kinks of the $\phi^4$ model based on the procedure of Ref.
\cite{uchiyama}. The two-kinks have an additional parameter accounting for the
separation of the standard kinks of $\phi^4$ model. We have shown that the
two-kinks have two discrete internal modes besides the zeroth mode and the
continuous spectrum. This new feature signalizes that the head-on collision a
two-kinks/two-antikinks pair exhibits a rich and complex behavior due to the
additional channel from which the energy of the system can be stored. We have
exhibited the fractal structure associated with the main configurations after
the collision. We have inferred the fractality as the imprint of the nonlinear
exchange of energy into the two discrete internal modes. | hep-th |
Schwinger Pair Production in dS_2 and AdS_2: We study Schwinger pair production in scalar QED from a uniform electric
field in dS_2 with scalar curvature R_{dS} = 2 H^2 and in AdS_2 with R_{AdS} =
- 2 K^2. With suitable boundary conditions, we find that the pair-production
rate is the same analytic function of the scalar curvature in both cases. | hep-th |
Multiple Membranes in M-theory: We review developments in the theory of multiple, parallel membranes in
M-theory. After discussing the inherent difficulties pertaining to a maximally
supersymmetric lagrangian formulation with the appropriate field content and
symmetries, we discuss how introducing the concept of 3-algebras allows for
such a description. Different choices of 3-algebras lead to distinct classes of
2+1 dimensional theories with varying degrees of supersymmetry. We then
describe how these are equivalent to a type of conventional superconformal
Chern-Simons gauge theories at level k, coupled to bifundamental matter.
Analysing the physical properties of these theories leads to the identification
of a certain subclass of models with configurations of M2-branes in Z_k
orbifolds of M-theory. In addition these models give rise to a whole new sector
of the gauge/gravity duality in the form of an AdS_4/CFT_3 correspondence. We
also discuss mass deformations, higher derivative corrections as well as the
possibility of extracting information about M5-brane physics. | hep-th |
The Hydrohedron: Bootstrapping Relativistic Hydrodynamics: As an effective theory, relativistic hydrodynamics is fixed by symmetries up
to a set of transport coefficients. A lot of effort has been devoted to
explicit calculations of these coefficients. Here we propose a shift in
perspective: we deploy bootstrap techniques to rule out theories that are
inconsistent with microscopic causality. What remains is a universal convex
geometry in the space of transport coefficients, which we call the hydrohedron.
The landscape of all consistent theories necessarily lie inside or on the edges
of the hydrohedron. We analytically construct cross-sections of the hydrohedron
corresponding to bounds on transport coefficients that appear in sound and
diffusion modes for theories without stochastic fluctuations. | hep-th |
Standard Models and Split Supersymmetry from Intersecting Brane
Orbifolds: We construct four dimensional three generation non-supersymmetric $SU(3)_c
\times SU(2)_L \times U(1)_Y$ intersecting D6-brane models with $\nu_R$\rq{s}.
At three stacks we find exactly the MSSM chiral fermion matter spectrum. At 4-,
5-stacks we find models with the massless fermion spectrum of the N=1 Standard
Model and massive exotic non-chiral matter; these models flow also to only the
SM. At 8-stacks we find MSSM-like models, with minimal massless exotics, made
from two different N=1 sectors. Exotic triplet masses put a lower bound on the
string scale of $2.79/2.89 \times 10^6$ GeV for a Higgs 124/126 GeV. It\rq{}s
the first appearance of N=0 stringy quivers with the MSSM and matter in
antisymmetric representations and perturbatively missing Yukawa couplings. The
present models are based on orientifolds of ${\bf T^6/(Z_3 \times Z_3)}$
compactifications of IIA theory based on the torus lattice AAA; all complex
moduli are fixed by the orbifold symmetry. We also present the spectrum rules +
GS anomaly cancellation for the ABB lattice. Moreover, we point out the
relevance of intersecting/and present D6-brane constructions on ideas related
to existence of split supersymmetry in nature. In this context we present
non-susy models with only the SM-matter and also MSSM-matter dominated models,
with massive gauginos and light higgsinos, that achieve the correct
supersymmetric GUT value for the Weinberg angle $sin^2 \theta = \frac{3}{8}$ at
a string scale $5 \cdot 10^{13} \ GeV < M_{S} < 1.4 \cdot 10^{17}$ GeV. It
appears that if only the SM survives at low energy the unification scale is
preserved at $5.03 \times 10^{13}$ GeV when n$_H$ =1, 3, 6. These models
support the existence of split supersymmetry scenario in string theory. | hep-th |
Reggeized gluon states in Quantum Chromodynamics: The reggeized gluon states, which are also called Reggeons, appear in the
scattering amplitude of hadrons in Regge limit. The wave-function of Reggeons
satisfy the BKP equation, which in multi-colour limit of Quantum Chromodynamics
is equivalent to the Schrodinger equation of the XXX Heisenberg SL(2,C) spin
chain model. In this work we solve the BKP equation, show the spectrum of the
energy and other integrals of motion for a number of Reggeons N=2,...,8.
Moreover, we consider deep inelastic scattering where due to the reggeized
gluons states we are able to calculate anomalous dimensions and corresponding
to their twists. | hep-th |
Kac-Moody Algebras in M-theory: In this thesis, we consider several aspects of over-extended and
very-extended Kac-Moody algebras in relation with theories of gravity coupled
to matter. In the first part, we focus on the occurrence of KM algebras in the
cosmological billiards. We analyse the billiards in the simplified situation of
spatially homogeneous cosmologies. The most generic cases lead to the same
algebras as those met in the general inhomogeneous case, but also sub-algebras
of the "generic" ones appear. Next, we consider particular gravitational
theories which, upon toroidal compactification to D=3 space-time dimensions,
reduce to a theory of gravity coupled to a symmetric space non-linear
sigma-model. We show that the billiard analysis gives direct information on
possible dimensional oxidations (or on their obstructions) and field content of
the oxidation endpoint. We also consider all hyperbolic Kac-Moody algebras and
completely answer the question of whether or not a specific theory exists
admitting a billiard characterised by the given hyperbolic algebra. In the
second part, we turn to the set up of such gravity-matter theories through the
building of an action explicitly invariant under a Kac-Moody group. As a first
step to include fermions, we check the compatibility of the presence of a Dirac
fermion with the (hidden duality) symmetries appearing in the toroidal
compactification down to 3 space-time dimensions. Next, we investigate how the
fermions (with spin 1/2 or 3/2) fit in the conjecture for hidden over-extended
symmetry G++. Finally, in the context of G+++ invariant actions, we derive all
the possible signatures for all the GB++ theories that can be obtained from the
conventional one (1,D-1) by "dualities" generated by Weyl reflections. This
generalizes the results obtained for E8++. | hep-th |
Coulomb interaction from the interplay between Confinement and Screening: It has been noticed that confinement effects can be described by the addition
of a $ \sqrt {- F_{\mu \nu}^a F^{a\mu \nu}} $ term in the Lagrangian density.
We now study the combined effect of such "confinement term" and that of a mass
term. The surprising result is that the interplay between these two terms gives
rise to a Coulomb interaction. Our picture has a certain correspondence with
the quasiconfinement picture described by Giles, Jaffe and de Rujula for QCD
with symmetry breaking. | hep-th |
Emergent Gravity from Noncommutative Spacetime: We showed before that self-dual electromagnetism in noncommutative (NC)
spacetime is equivalent to self-dual Einstein gravity. This result implies a
striking picture about gravity: Gravity can emerge from electromagnetism in NC
spacetime. Gravity is then a collective phenomenon emerging from gauge fields
living in fuzzy spacetime. We elucidate in some detail why electromagnetism in
NC spacetime should be a theory of gravity. In particular, we show that NC
electromagnetism is realized through the Darboux theorem as a diffeomorphism
symmetry G which is spontaneously broken to symplectomorphism H due to a
background symplectic two-form $B_{\mu\nu}=(1/\theta)_{\mu\nu}$, giving rise to
NC spacetime. This leads to a natural speculation that the emergent gravity
from NC electromagnetism corresponds to a nonlinear realization G/H of the
diffeomorphism group, more generally its NC deformation. We also find some
evidences that the emergent gravity contains the structure of generalized
complex geometry and NC gravity. To illuminate the emergent gravity, we
illustrate how self-dual NC electromagnetism nicely fits with the twistor space
describing curved self-dual spacetime. We also discuss derivative corrections
of Seiberg-Witten map which give rise to higher order gravity. | hep-th |
Optical Properties of a θ-Vacuum: Chern-Simons (CS) forms generalize the minimal coupling between gauge
potentials and point charges, to sources represented by charged extended
objects (branes). The simplest example of such a CS-brane coupling is a domain
wall coupled to the electromagnetic CS three-form. This describes a
topologically charged interface where the CS form AdA is supported, separating
two three-dimensional spatial regions in 3+1 spacetime. Electrodynamics at
either side of the brane is described by the same Maxwell's equations, but
those two regions have different vacua, characterized by a different value of
the \theta-parameter multiplying the Pontryagin form F ^ F. The \theta-term is
the abelian version of the concept introduced by 't Hooft for the resolution of
the U(1) problem in QCD. We point out that CS-generalized classical
electrodynamics shows new phenomena when two neighboring regions with different
\theta-vacua are present. These topological effects result from surface effects
induced by the boundary and we explore the consequences of such boundary
effects for the propagation of the electromagnetic field in Maxwell theory.
Several features, including optical and electrostatic/magnetostatic responses,
which may be observable in condensed matter systems, like topological
insulators, are discussed. | hep-th |
String creation in D6-brane background: The production of string charge during a crossing of certain oriented
D-branes is studied. We compute the string charge in the system of a probe
D2-brane and a background D6-brane by use of the equations of motion in the
ten-dimensions. We confirm the creation of string charge as inflow from the
background D6-brane. | hep-th |
Hamiltonian Dynamics of Cosmological Quintessence Models: The time-evolution dynamics of two nonlinear cosmological real gas models has
been reexamined in detail with methods from the theory of Hamiltonian dynamical
systems. These examples are FRWL cosmologies, one based on a gas, satisfying
the van der Waals equation and another one based on the virial expansion gas
equation. The cosmological variables used are the expansion rate, given by the
Hubble parameter, and the energy density. The analysis is aided by the
existence of global first integral as well as several special (second)
integrals in each case. In addition, the global first integral can serve as a
Hamiltonian for a canonical Hamiltonian formulation of the evolution equations.
The conserved quantities lead to the existence of stable periodic solutions
(closed orbits) which are models of a cyclic Universe. The second integrals
allow for explicit solutions as functions of time on some special trajectories
and thus for a deeper understanding of the underlying physics. In particular,
it is shown that any possible static equilibrium is reachable only for infinite
time. | hep-th |
Magnetic monopoles and symmetries in noncommutative space: In this paper, we review the progress in the analysis of magnetic monopoles
as generalized states in quantum mechanics. We show that the considered model
contains rich algebraic structure that generates symmetries which have been
utilized in different physical contexts. Even though are we focused on quantum
mechanics in noncommutative space $\textbf{R}_\lambda^3$, the results can be
reconstructed in ordinary quantum mechanics in $\textbf{R}^3$ as well. | hep-th |
BPS Equations and the Stress Tensor: We exploit the relationship between the space components of the
energy-momentum tensor and the supercurrent to discuss the connection between
the BPS equations and the vanishing of the components of the stress tensor in
various supersymmetric theories with solitons.
Using the fact that certain combination of supercharges annihilate BPS
states, we show that $T_{ij}=0$ for kinks, vortices and dyons, displaying the
connection between supersymmetry and non-interacting BPS solitons. | hep-th |
Nonsupersymmetric Brane/Antibrane Configurations in Type IIA and M
Theory: We study metastable nonsupersymmetric configurations in type IIA string
theory, obtained by suspending D4-branes and anti-D4-branes between
holomorphically curved NS5's, which are related to those of hep-th/0610249 by
T-duality. When the numbers of branes and antibranes are the same, we are able
to obtain an exact M theory lift which can be used to reliably describe the
vacuum configuration as a curved NS5 with dissolved RR flux for g_s<<1 and as a
curved M5 for g_s>>1. When our weakly coupled description is reliable, it is
related by T-duality to the deformed IIB geometry with flux of hep-th/0610249
with moduli exactly minimizing the potential derived therein using special
geometry. Moreover, we can use a direct analysis of the action to argue that
this agreement must also hold for the more general brane/antibrane
configurations of hep-th/0610249. On the other hand, when our strongly coupled
description is reliable, the M5 wraps a nonholomorphic minimal area curve that
can exhibit quite different properties, suggesting that the residual structure
remaining after spontaneous breaking of supersymmetry at tree level can be
further broken by the effects of string interactions. Finally, we discuss the
boundary condition issues raised in hep-th/0608157 for nonsupersymmetric IIA
configurations, their implications for our setup, and their realization on the
type IIB side. | hep-th |
On orbifolds and free fermion constructions: This work develops the correspondence between orbifolds and free fermion
models. A complete classification is obtained for orbifolds X/G with X the
product of three elliptic curves and G an abelian extension of a group (Z_2)^2
of twists acting on X. Each such quotient X/G is shown to give a geometric
interpretation to an appropriate free fermion model, including the geometric
NAHE+ model. However, the semi-realistic NAHE free fermion model is proved to
be non-geometric: its Hodge numbers are not reproduced by any orbifold X/G. In
particular cases it is shown that X/G can agree with some Borcea-Voisin
threefolds, an orbifold limit of the Schoen threefold, and several further
orbifolds thereof. This yields free fermion models with geometric
interpretations on such special threefolds. | hep-th |
Baxter operators for arbitrary spin II: This paper presents the second part of our study devoted to the construction
of Baxter operators for the homogeneous closed XXX spin chain with the quantum
space carrying infinite or finite-dimensional $s\ell_2$ representations. We
consider the Baxter operators used in \cite{BLZ,Shortcut}, formulate their
construction uniformly with the construction of our previous paper. The
building blocks of all global chain operators are derived from the general
Yang-Baxter operators and all operator relations are derived from general
Yang-Baxter relations. This leads naturally to the comparison of both
constructions and allows to connect closely the treatment of the cases of
infinite-dimensional representation of generic spin and finite-dimensional
representations of integer or half-integer spin. We proof not only the
relations between the operators but present also their explicit forms and
expressions for their action on polynomials representing the quantum states. | hep-th |
Multiboson Expansions for the q-Oscillator and $SU(1,1)_q$: All the hermitian representations of the ``symmetric" $q$-oscillator are
obtained by means of expansions. The same technique is applied to characterize
in a systematic way the $k$-order boson realizations of the $q$-oscillator and
$su(1,1)_q$. The special role played by the quadratic realizations of
$su(1,1)_q$ in terms of boson and $q$-boson operators is analysed and
clarified. | hep-th |
Some inequalities bridging stringy parameters and cosmological
observables: By demanding the validity of an effective field theory description during
inflation, in this note we derive some peculiar inequalities among the three
interesting stringy and cosmological parameters, namely the tensor-to-scalar
ratio ($r$), the string coupling ($g_s$) and the compactification volume
(${\cal V}$). In deriving these inequalities, we explicitly demand that the
inflationary scale and the Hubble parameter during inflation are well below the
Kaluza-Klein (KK) mass scale, string scale, and the four dimensional Planck
mass. For the inflationary models developed within the framework of type IIB
orientifold comapctification, we investigate the regions of parameters space
spanned by the three parameters $(r, g_s, {\cal V})$ by satisfying our
inequalities, and we find that the same can reduce the size of available
parameter space quite significantly. Moreover, we comment on obtaining further
constraints on the parameters by comparing gravitino mass ($m_{3/2}$) with the
Hubble scale ($H$), which also provides a lower bound on tensor-to-scalar ratio
($r$), for the cases when $m_{3/2} <H$. We also illustrate the outcome of our
bounds in some specific class of string(-inspired) models. | hep-th |
String Theory on AdS_3: It was shown by Brown and Henneaux that the classical theory of gravity on
AdS_3 has an infinite-dimensional symmetry group forming a Virasoro algebra.
More recently, Giveon, Kutasov and Seiberg (GKS) constructed the corresponding
Virasoro generators in the first-quantized string theory on AdS_3. In this
paper, we explore various aspects of string theory on AdS_3 and study the
relation between these two works. We show how semi-classical properties of the
string theory reproduce many features of the AdS/CFT duality. Furthermore, we
examine how the Virasoro symmetry of Brown and Henneaux is realized in string
theory, and show how it leads to the Virasoro Ward identities of the boundary
CFT. The Virasoro generators of GKS emerge naturally in this analysis. Our work
clarifies several aspects of the GKS construction: why the Brown-Henneaux
Virasoro algebra can be realized on the first-quantized Hilbert space, to what
extent the free-field approximation is valid, and why the Virasoro generators
act on the string worldsheet localized near the boundary of AdS_3. On the other
hand, we find that the way the central charge of the Virasoro algebra is
generated is different from the mechanism proposed by GKS. | hep-th |
Edge States and Entanglement Entropy: It is known that gauge fields defined on manifolds with spatial boundaries
support states localized at the boundaries. In this paper, we demonstrate how
coarse-graining over these states can lead to an entanglement entropy. In
particular, we show that the entanglement entropy of the ground state for the
quantum Hall effect on a disk exhibits an approximate ``area " law. | hep-th |
Manifestly Supersymmetric Lax Integrable Hierarchies: A systematic method of constructing manifestly supersymmetric
$1+1$-dimensional KP Lax hierarchies is presented. Closed expressions for the
Lax operators in terms of superfield eigenfunctions are obtained. All hierarchy
equations being eigenfunction equations are shown to be automatically invariant
under the (extended) supersymmetry. The supersymmetric Lax models existing in
the literature are found to be contained (up to a gauge equivalence) in our
formalism. | hep-th |
Exact O(d,d) Transformations in WZW Models: Using the algebraic Hamiltonian approach, we derive the exact to all orders
O(d,d) transformations of the metric and the dilaton field in WZW and WZW coset
models for both compact and non-compact groups. It is shown that under the
exact $O(d)\times O(d)$ transformation only the leading order of the inverse
metric $G^{-1}$ is transformed. The quantity $\sqrt{G}\exp(\Phi)$ is the same
in all the dual models and in particular is independent of k. We also show that
the exact metric and dilaton field that correspond to G/U(1)^d WZW can be
obtained by applying the exact O(d,d) transformations on the (ungauged) WZW, a
result that was known to one loop order only. As an example we give the O(2,2)
transformations in the $SL(2,R)$ WZW that transform to its dual exact models.
These include also the exact 3D black string and the exact 2D black hole with
an extra $U(1)$ free field. | hep-th |
Local quenches and quantum chaos from higher spin perturbations: We study local quenches in 1+1 dimensional conformal field theories at
large-c by operators carrying higher spin charge. Viewing such states as
solutions in Chern-Simons theory, representing infalling massive particles with
spin-three charge in the BTZ background, we use the Wilson line prescription to
compute the single-interval entanglement entropy (EE) and scrambling time
following the quench. We find that the change in EE is finite (and real) only
if the spin-three charge q is bounded by the energy of the perturbation E, as
|q|/c < E^2/c^2. We show that the Wilson line/EE correlator deep in the
quenched regime and its expansion for small quench widths overlaps with the
Regge limit for chaos of the out-of-time-ordered correlator. We further find
that the scrambling time for the two-sided mutual information between two
intervals in the thermofield double state increases with increasing spin-three
charge, diverging when the bound is saturated. For larger values of the charge,
the scrambling time is shorter than for pure gravity and controlled by the
spin-three Lyapunov exponent 4\pi/\beta. In a CFT with higher spin chemical
potential, dual to a higher spin black hole, we find that the chemical
potential must be bounded to ensure that the mutual information is a concave
function of time and entanglement speed is less than the speed of light. In
this case, a quench with zero higher spin charge yields the same Lyapunov
exponent as pure Einstein gravity. | hep-th |
Spontaneous fragmentation of topological black holes: We study the metastability of Anti-de Sitter topological black holes with
compact hyperbolic horizons. We focus on the five-dimensional case, an AdS/CFT
dual to thermal states in the maximally supersymmetric large-N Yang-Mills
theory, quantized on a three-dimensional compact hyperboloid. We estimate the
various rates for quantum-statistical D3-brane emission, using WKB methods in
the probe-brane approximation, including thermal tunneling and Schwinger pair
production. The topological black holes are found to be metastable at high
temperature. At low temperatures, D-branes are emitted without exponential
suppression in superradiant modes, producing an instability in qualitative
agreement with expectations from weakly-coupled gauge dynamics. | hep-th |
Noncommutative gravity in three dimensions coupled to point-like sources: Noncommutative gravity in three dimensions with no cosmological constant is
reviewed. We find a solution which describes the presence of a torsional
source. | hep-th |
Oxidation = group theory: Dimensional reduction of theories involving (super-)gravity gives rise to
sigma models on coset spaces of the form G/H, with G a non-compact group, and H
its maximal compact subgroup. The reverse process, called oxidation, is the
reconstruction of the possible higher dimensional theories, given the lower
dimensional theory. In 3 dimensions, all degrees of freedom can be dualized to
scalars. Given the group G for a 3 dimensional sigma model on the coset G/H, we
demonstrate an efficient method for recovering the higher dimensional theories,
essentially by decomposition into subgroups. The equations of motion, Bianchi
identities, Kaluza-Klein modifications and Chern-Simons terms are easily
extracted from the root lattice of the group G. We briefly discuss some aspects
of oxidation from the E_{8(8)}/SO(16) coset, and demonstrate that our formalism
reproduces the Chern-Simons term of 11-d supergravity, knows about the
T-duality of IIA and IIB theory, and easily deals with self-dual tensors, like
the 5-tensor of IIB supergravity. | hep-th |
Observing braneworld black holes: Spacetime in the vicinity of an event horizon can be probed using
observations which explore the dynamics of the accretion disc. Many high energy
theories of gravity lead to modifications of the near horizon regime,
potentially providing a testing ground for these theories. In this paper, we
explore the impact of braneworld gravity on this region by formulating a method
of deriving the general behaviour of the as yet unknown braneworld black hole
solution. We use simple bounds to constrain the solution close to the horizon. | hep-th |
Eleven dimensional supergravity as a constrained topological field
theory: We describe a new first-order formulation of D=11 supergravity which shows
that that theory can be understood to arise from a certain topological field
theory by the imposition of a set of local constraints on the fields, plus a
lagrange multiplier term. The topological field theory is of interest as the
algebra of its constraints realizes the D=11 supersymmetry algebra with central
charges. | hep-th |
Evaluation of Periods via Fibrations in Seiberg-Witten Theories and in
Type-II String: We show how to evaluate the periods in Seiberg-Witten theories and in
K3-fibered Calabi-Yau manifolds by using fibrations of the theories. In the
Seiberg-Witten theories, it is shown that the dual pair of fields can be
constructed from the classical fields in a simple form. As for Calabi-Yau
manifolds which are fibrations of K3 surface, we obtain the solutions of the
Picard-Fuchs equations from the periods of K3 surface. By utilizing the
expression of periods for two-parameter models of type-II string, we derive the
solutions of the Picard-Fuchs equations around the points of enhanced gauge
symmetry and show a simple connection to the SU(2) Seiberg-Witten theory. | hep-th |
Weyl-Invariant Higher Curvature Gravity Theories in n Dimensions: We study the particle spectrum and the unitarity of the generic n-dimensional
Weyl-invariant quadratic curvature gravity theories around their (anti-)de
Sitter [(A)dS] and flat vacua. Weyl symmetry is spontaneously broken in (A)dS
and radiatively broken at the loop level in flat space. Save the three
dimensional theory (which is the Weyl-invariant extension of the new massive
gravity), the graviton remains massless and the unitarity requires that the
only viable Weyl-invariant quadratic theory is the Weyl-invariant extension of
the Einstein-Gauss-Bonnet theory. The Weyl gauge field on the other hand
becomes massive. Symmetry breaking scale fixes all the dimensionful parameters
in the theory. | hep-th |
A note on conformal symmetry in projective superspace: We describe a sufficient condition for actions constructed in projective
superspace to possess an SU(2) R-symmetry. We check directly that this
condition implies that the corresponding hyperkahler varieties, constructed by
means of the generalized Legendre transform, have a Swann bundle structure. | hep-th |
A Note on Multi-trace Deformations and AdS/CFT: We derive the general formula, at a finite cutoff, for the change in the
boundary condition of a scalar field in AdS under a Multiple-trace deformation
of the dual CFT. Our analysis suggests that fluctuations around the classical
solution in AdS should not be constrained by boundary conditions. | hep-th |
Superluminality in dilatationally invariant generalized Galileon
theories: We consider small perturbations about homogeneous backgrounds in
dilatationally-invariant Galileon models. The issues we address are stability
(absence of ghosts and gradient instabilities) and superluminality. We show
that in Minkowski background, it is possible to construct the Lagrangian in
such a way that any homogeneous Galileon background solution is stable and
small perturbations about it are subluminal. On the other hand, in the case of
FLRW backgrounds, for any Lagrangian functions there exist homogeneous
background solutions to the Galileon equation of motion and time-dependence of
the scale factor, such that the stability conditions are satisfied, but the
Galileon perturbations propagate with superluminal speed. Thus, a popular class
of the generalized Galileon models is plagued by superluminality. | hep-th |
Topologically Massive Gravity from the Heterotic String: Topologically massive gravity (TMG) in three dimensions provides an
interesting toy model for constructing a quantum theory of gravity. Although it
can be thought of as standing as a theory in its own right, it is also of
interest to see whether it can be described within the larger framework of
string theory or M-theory. In this paper, we show that it can be embedded
within the heterotic string, via a compactification on $S^3\times T^4$. Since
all solutions of TMG can now be lifted to ten dimensions, this allows us to
give a string and brane interpretation to quantities such as the central
charges in the conformal field theory on the boundary of TMG, and the entropy
of the BTZ black hole solution. | hep-th |
Einstein gravity 3-point functions from conformal field theory: We study stress tensor correlation functions in four-dimensional conformal
field theories with large $N$ and a sparse spectrum. Theories in this class are
expected to have local holographic duals, so effective field theory in anti-de
Sitter suggests that the stress tensor sector should exhibit universal,
gravity-like behavior. At the linearized level, the hallmark of locality in the
emergent geometry is that stress tensor three-point functions $\langle
TTT\rangle$, normally specified by three constants, should approach a universal
structure controlled by a single parameter as the gap to higher spin operators
is increased. We demonstrate this phenomenon by a direct CFT calculation.
Stress tensor exchange, by itself, violates causality and unitarity unless the
three-point functions are carefully tuned, and the unique consistent choice
exactly matches the prediction of Einstein gravity. Under some assumptions
about the other potential contributions, we conclude that this structure is
universal, and in particular, that the anomaly coefficients satisfy $a\approx
c$ as conjectured by Camanho et al. The argument is based on causality of a
four-point function, with kinematics designed to probe bulk locality, and
invokes the chaos bound of Maldacena, Shenker, and Stanford. | hep-th |
Comments on gluon scattering amplitudes via AdS/CFT: In this article we consider n gluon color ordered, planar amplitudes in N=4
super Yang Mills at strong 't Hooft coupling. These amplitudes are approximated
by classical surfaces in AdS_5 space. We compute the value of the amplitude for
a particular kinematic configuration for a large number of gluons and find that
the result disagrees with a recent guess for the exact value of the amplitude.
Our results are still compatible with a possible relation between amplitudes
and Wilson loops.
In addition, we also give a prescription for computing processes involving
local operators and asymptotic states with a fixed number of gluons. As a
byproduct, we also obtain a string theory prescription for computing the dual
of the ordinary Wilson loop, Tr P exp[ i\oint A ], with no couplings to the
scalars. We also evaluate the quark-antiquark potential at two loops. | hep-th |
Excited Hexagon Wilson Loops for Strongly Coupled N=4 SYM: This work is devoted to the six-gluon scattering amplitude in strongly
coupled N=4 supersymmetric Yang-Mills theory. At weak coupling, an appropriate
high energy limit of the so-called remainder function, i.e. of the deviation
from the BDS formula, may be understood in terms of the lowest eigenvalue of
the BFKL hamiltonian. According to Alday et al., amplitudes in the strongly
coupled theory can be constructed through an auxiliary 1-dimensional quantum
system. We argue that certain excitations of this quantum system determine the
Regge limit of the remainder function at strong coupling and we compute its
precise value. | hep-th |
Numerical Solution of the Ekpyrotic Scenario in the Moduli Space
Approximation: A numerical solution to the equations of motion for the ekpyrotic bulk brane
scenario in the moduli space approximation is presented. The visible universe
brane has positive tension, and we use a potential that goes to zero
exponentially at large distance, and also goes to zero at small distance. In
the case considered, no bulk brane, visible brane collision occurs in the
solution. This property and the general behavior of the solution is
qualitatively the same when the visible brane tension is negative, and for many
different parameter choices. | hep-th |
Old and new vacua of 5D maximal supergravity: We look for critical points with U(2) residual symmetry in 5-dimensional
maximally supersymmetric gauged supergravity, by varying the embedding tensor,
rather than directly minimizing the scalar potential. We recover all previously
known vacua and we find four new vacua, with different gauge groups and
cosmological constants. We provide the first example of a maximal supergravity
model in $D \geq 4$ having critical points with both positive and vanishing
cosmological constant. For each vacuum we also compute the full mass spectrum.
All results are analytic. | hep-th |
Closed time like curve and the energy condition in 2+1 dimensional
gravity: We consider gravity in 2+1 dimensions in presence of extended stationary
sources with rotational symmetry. We prove by direct use of Einstein's
equations that if i) the energy momentum tensor satisfies the weak energy
condition, ii) the universe is open (conical at space infinity), iii) there are
no CTC at space infinity, then there are no CTC at all. | hep-th |
Classical Solutions in Two-Dimensional String Theory and Gravitational
Collapse: A general solution to the $D=2$ 1-loop beta functions equations including
tachyonic back reaction on the metric is presented. Dynamical black hole
(classical) solutions representing gravitational collapse of tachyons are
constructed. A discussion on the correspondence with the matrix-model approach
is given. | hep-th |
Grassmannian sigma model on a finite interval: We discuss the two-dimensional Grassmannian sigma model $\mathbb{G}_{N, M}$
on a finite interval $L$. The different boundary conditions which allow to
obtain analytical solutions by the saddle-point method in the large $N$ limit
are considered. The nontrivial phase structure of the model on the interval
similar to $\mathbb{C}P(N)$ model is found. | hep-th |
Area Potentials and Deformation Quantization: Systems built out of N-body interactions, beyond 2-body interactions, are
formulated on the plane, and investigated classically and quantum mechanically
(in phase space). Their Wigner Functions--the density matrices in phase-space
quantization--are given and analyzed. | hep-th |
Realization of symmetries and the c-theorem: We discuss the relation between the $c$--theorem and the the way various
symmetries are realized in quantum field theory. We review our recent proof of
the $c$--theorem in four dimensions. Based on this proof and further evidence,
we conjecture that the realization of chiral symmetry be irreversible, flowing
from the Wigner-Weyl realization at short distance to the Nambu--Goldstone
realization at long distance. We argue that three apparently independent
constraints based on the renormalization group, namely anomaly matching, the
c-theorem and the conjectured symmetry realization theorem, are particular
manifestations of a single underlying principle. | hep-th |
Analytic Results for Loop-Level Momentum Space Witten Diagrams: This paper presents an evaluation of the wave function coefficients for
conformally coupled scalars at both one and two-loop levels at leading order in
the coupling constant, in momentum space. We take cues from time-dependent
interactions in flat spacetime and under suitable approximations, these can
also be used to study the wave function coefficients for general cosmologies.
We make use of recursion relations developed in arxiv:\{1709.02813\} to
regularize certain bulk-point integrals and express the wave function
coefficients in a form that simplifies the loop integrals. We utilize
hard-cutoff regularization to regularize the loop integrals and further provide
a discussion on their renormalization. Our results can also be analytically
continued to obtain answers for transition amplitudes in AdS. | hep-th |
String theory in Lorentz-invariant time-like gauge: A theory of closed bosonic string in time-like gauge, related in
Lorentz-invariant way with the world sheet, is considered. Absence of quantum
anomalies in this theory is shown. | hep-th |
In quest of "just" the Standard Model on D-branes at a singularity: In this note we explore the possibility of obtaining gauge bosons and
fermionic spectrum as close as possible to the Standard Model content, by
placing D3-branes at a ZN orbifold-like singularity in the presence of
D7-branes. Indeed, we find that this is plausible provided a sufficiently high
N is allowed for and the singular point is also fixed by an orientifold action.
If extra charged matter is not permitted then the singularity should
necessarily be non-supersymmetric. Correct hypercharge assignments require a
dependence on some Abelian gauge D7-groups. In achieving such a construction we
follow a recent observation made in Ref. [hep-th/0105155] about the possibility
that, the three left handed quarks, would present different U(2) transformation
properties. | hep-th |
Worldline Formalism in Snyder Spaces: We study the $\phi_{\star}^4$ model for a scalar field in a linearization of
the Snyder model, using the methods of the Worldline Formalism. Our main result
is a master equation for the 1-loop n-point function. From this we derive the
renormalization of the coupling parameters of the theory and observe the
appearance of a $\phi^6$ divergent contribution that opens the question of
whether this theory is renormalizable or not. Additionally, we observe that
some terms in the renormalized action can be interpreted as coming from an
effective metric proportional to the square of the field. | hep-th |
A test of the circular Unruh effect using atomic electrons: We propose a test for the circular Unruh effect using certain atoms -
fluorine and oxygen. For these atoms the centripetal acceleration of the outer
shell electrons implies an effective Unruh temperature in the range 1000 - 2000
K. This range of Unruh temperatures is large enough to shift the expected
occupancy of the lowest energy level and nearby energy levels. In effect the
Unruh temperature changes the expected pure ground state, with all the
electrons in the lowest energy level, to a mixed state with some larger than
expected occupancy of states near to the lowest energy level. Examining these
atoms at low background temperatures and finding a larger than expected number
of electrons in low lying excited levels, beyond what is expected due to the
background thermal excitation, would provide experimental evidence for the
Unruh effect. | hep-th |
AdS scale separation and the distance conjecture: It has been argued that orientifold vacua with fluxes in type IIA string
theory can achieve moduli stabilisation and arbitrary decoupling between the
AdS and KK scales upon sending certain unconstrained RR-flux quanta to
infinity. In this paper, we find a novel scalar field in the open-string sector
that allows us to interpolate between such IIA vacua that differ in flux quanta
and find that the limit of large fluxes is nicely consistent with the distance
conjecture. This shows that the massive IIA vacua pass an important Swampland
criterion and suggests that scale-separated AdS vacua might not be in the
Swampland. Our analysis also naturally suggests a flux analogue of "Reid's
fantasy" where flux vacua that differ in quantised flux numbers can be
connected through trajectories in open-string field space and not just via
singular domain walls. | hep-th |
"Integrating in" and Effective Lagrangian for Non-Supersymmetric
Yang-Mills Theory: Recently a non-supersymmetric analog of Veneziano-Yankielowicz (VY) effective
Lagrangian has been proposed and applied for the analysis of the theta
dependence in pure Yang-Mills theory. This effective Lagrangian is similar in
many respects to the VY construction and, in particular, exhibits a kind of low
energy holomorphy which is absent in the full YM theory. Here we incorporate a
heavy fermion into this effective theory by using the "integrating in"
technique. We find that, in terms of this extended theory, holomorphy of the
effective Lagrangian for pure YM theory naturally implies a holomorphic
dependence on the heavy fermion mass.
It is shown that this analysis fixes, under certain assumptions, a
dimensionless parameter which enters the effective Lagrangian and determines
the number of nondegenerate vacuum sectors in pure YM theory. We also compare
our results for the vacuum structure and theta dependence to those obtained
recently by Witten on the basis of AdS/CFT correspondence. | hep-th |
Holographic electrical and thermal conductivity in strongly coupled
gauge theory with multiple chemical potentials: We study transport coefficients of strongly coupled gauge theory in the
presence of multiple chemical potential which are dual to rotating D3, M2 and
M5 brane. Using the general form of the perturbation equations, we compute
DC-electrical conductivity at finite temperature as well as at zero
temperature. We also study thermal conductivity for the same class of black
holes and show that thermal conductivity and viscosity obeys Wiedemann-Franz
like law even in the presence of multiple chemical potential. | hep-th |
Adler-Bell-Jackiw anomaly, the Nieh-Yan form, and vacuum polarization: We show from first principles, using explicitly invariant Pauli-Villars
regularization of chiral fermions, that the Nieh-Yan form does contribute to
the Adler-Bell-Jackiw (ABJ) anomaly for spacetimes with generic torsion, and
comment on some of the implications. There are a number of interesting and
important differences with the usual ABJ contributions in the absence of
torsion. For dimensional reasons, the Nieh-Yan contribution is proportional to
the square of the regulator mass. In spacetimes with flat vierbein but
non-trivial torsion, the associated diagrams are actually vacuum polarization
rather than triangle diagrams, and the Nieh-Yan contribution to the ABJ anomaly
arises from the fact that the axial torsion "photon" is not transverse. | hep-th |
Vacuum Expectation Values of Products of Chiral Currents in $3+1$
Dimensions: An algebraic rule is presented for computing expectation values of products
of local nonabelian charge operators for fermions coupled to an external vector
potential in $3+1$ space-time dimensions. The vacuum expectation value of a
product of four operators is closely related to a cyclic cocycle in
noncommutative geometry of Alain Connes. The relevant representation of the
current is constructed using Kirillov's method of coadjoint orbits. | hep-th |
Free field representation and form factors of the chiral Gross-Neveu
model: The free field representation of the Zamolodchikov-Faddeev algebra for the
chiral Gross-Neveu model is analysed in detail, and used to construct an
integral representation for form factors of the model. | hep-th |
Towards the n-point one-loop superstring amplitude I: Pure spinors and
superfield kinematics: This is the first installment of a series of three papers in which we
describe a method to determine higher-point correlation functions in one-loop
open-superstring amplitudes from first principles. In this first part, we
exploit the synergy between the cohomological features of pure-spinor
superspace and the pure-spinor zero-mode integration rules of the one-loop
amplitude prescription. This leads to the study of a rich variety of
multiparticle superfields which are local, have covariant BRST variations, and
are compatible with the particularities of the pure-spinor amplitude
prescription. Several objects related to these superfields, such as their
non-local counterparts and the so-called BRST pseudo-invariants, are thoroughly
reviewed and put into new light. Their properties will turn out to be
mysteriously connected to products of one-loop worldsheet functions in packages
dubbed "generalized elliptic integrands", whose prominence will be seen in the
later parts of this series of papers. | hep-th |
Covariantly Constant Curvature Tensors and D=3, N=4, 5, 8 Chern-Simons
Matter Theories: We construct some examples of D=3, N=4 GW theory and N=5 superconformal
Chern-Simons matter theory by using the covariantly constant curvature of a
quaternionic-Kahler manifold to construct the symplectic 3-algebra in the
theories. Comparing with the previous theories, the N=4, 5 theories constructed
in this way possess a local Sp(2n) symmetry and a diffeomorphism symmetry
associated with the quaternionic-Kahler manifold. We also construct a
generalized N=8 BLG theory by utilizing the dual curvature operator of a
maximally symmetric space of dimension 4 to construct the Nambu 3-algebra.
Comparing with the previous N=8 BLG theory, the theory has a diffeomorphism
invariance and a local SO(4) invariance associated with the symmetric space. | hep-th |
Windings of twisted strings: Twistor string models have been known for more than a decade now but have
come back under the spotlight recently with the advent of the scattering
equation formalism which has greatly generalized the scope of these models. A
striking ubiquitous feature of these models has always been that, contrary to
usual string theory, they do not admit vibrational modes and thus describe only
conventional field theory. In this paper we report on the surprising discovery
of a whole new sector of one of these theories which we call "twisted strings,"
when spacetime has compact directions. We find that the spectrum is enhanced
from a finite number of states to an infinite number of interacting higher spin
massive states. We describe both bosonic and world sheet supersymmetric models,
their spectra and scattering amplitudes. These models have distinctive features
of both string and field theory, for example they are invariant under stringy
T-duality but have the high energy behavior typical of field theory. Therefore
they describe a new kind of field theories in target space, sitting on their
own halfway between string and field theory. | hep-th |
Non-Renormalization and Naturalness in a Class of Scalar-Tensor Theories: We study the renormalization of some dimension-4, 7 and 10 operators in a
class of nonlinear scalar-tensor theories. These theories are invariant under:
(a) linear diffeomorphisms which represent an exact symmetry of the full
non-linear action, and (b) global field-space Galilean transformations of the
scalar field. The Lagrangian contains a set of non-topological interaction
terms of the above-mentioned dimensionality, which we show are not renormalized
at any order in perturbation theory. We also discuss the renormalization of
other operators, that may be generated by loops and/or receive
loop-corrections, and identify the regime in which they are sub-leading with
respect to the operators that do not get renormalized. Interestingly, such
scalar-tensor theories emerge in a certain high-energy limit of the ghost-free
theory of massive gravity. One can use the non-renormalization properties of
the high-energy limit to estimate the magnitude of quantum corrections in the
full theory. We show that the quantum corrections to the three free parameters
of the model, one of them being the graviton mass, are strongly suppressed. In
particular, we show that having an arbitrarily small graviton mass is
technically natural. | hep-th |
Quark Condensates in Non-Supersymmetric MQCD: A set of non-supersymmetric minimal area embeddings of an M-theory 5-brane
are considered. The field theories on the surface of the 5-brane have the field
content of N=2 SQCD with fundamental representation matter fields. By suitable
choice of curve parameters the N=2 and N=1 superpartners may be decoupled
leaving a semi-classical approximation to QCD with massive quarks. As
supersymmetry breaking is introduced a quark condensate grows breaking the low
energy $Z_{F}$ flavour symmetry. At $\theta =$ (odd) $\pi$ spontaneous CP
violation is observed consistent with that of the QCD chiral lagrangian. | hep-th |
Chaos and Scrambling in Quantum Small Worlds: Quantum small-worlds are quantum many-body systems that interpolate between
completely ordered (nearest-neighbour, next-to-nearest-neighbour etc.) and
completely random interactions. As such, they furnish a novel new laboratory to
study quantum systems transitioning between regular and chaotic behaviour. In
this article, we introduce the idea of a quantum small-world network by
starting from a well understood integrable system, a spin-1 Heisenberg chain.
We then inject a small number of long-range interactions into the spin chain
and study its ability to scramble quantum information using two primary
devices: the out-of-time-order correlator (OTOC) and the spectral form factor
(SFF). We find that the system shows increasingly rapid scrambling as its
interactions become progressively more random, with no evidence of quantum
chaos. | hep-th |
Interpolating Between $CP(N-1)$ and $S^{2N-1}$ Target Spaces: Some magnetic phenomena in correlated electron systems were recently shown to
be described in the continuum limit by a class of sigma models which present a
U(1) Hopf fibration over CP(1). In this paper we study a generalization of such
models with a target space given by a U(1) fibration over Grassmannian
manifolds, of which CP($N-1$) is a special case. The metric of our target space
is shown to be left-symmetric which implies that it is fully parametrized by
two constants: the first one -- the conventional coupling constant -- is
responsible for the overall scale while the second constant $\kappa$
parametrizes the strength of a deformation. In two dimensions these sigma
models are perturbatively renormalizable. We calculate their $\beta$ functions
to two loops and find the RG flow of the coupling constants. We calculate the
two-point function in the UV limit, which has a power law dependence with an
exponent dependent on the RG trajectory. | hep-th |
Unstoppable brane-flux decay of $\overline{\text{D6}}$ branes: We investigate $p$ $\overline{\text{D6}}$ branes inside a flux throat that
carries $K \times M$ D6 charges with $K$ the 3-form flux quantum and $M$ the
Romans mass. We find that within the calculable supergravity regime where $g_s
p$ is large, the $\overline{\text{D6}}$ branes annihilate immediately against
the fluxes despite the existence of a metastable state at small $p/M$ in the
probe approximation. The crucial property that causes this naive conflict with
effective field theory is a singularity in the 3-form flux, which we cut off at
string scale. Our result explains the absence of regular solutions at finite
temperature and suggests there should be a smooth time-dependent solution. We
also discuss the qualitative differences between $\overline{\text{D6}}$ branes
and $\overline{\text{D3}}$ branes, which makes it a priori not obvious to
conclude the same instability for $\overline{\text{D3}}$ branes. | hep-th |
Casimir force due to condensed vortices in a plane: The Casimir force between parallel lines in a theory describing condensed
vortices in a plane is determined. We make use of the relation between a
Chern-Simons-Higgs model and its dualized version, which is expressed in terms
of a dual gauge field and a vortex field. The dual model can have a phase of
condensed vortices and, in this phase, there is a mapping to a model of two
non-interacting massive scalar fields from which the Casimir force can readily
be obtained. The choice of boundary conditions required for the mapped scalar
fields and their association with those for the vectorial field and the issues
involved are discussed. We also briefly discuss the implications of our results
for experiments related to the Casimir effect when vortices can be present. | hep-th |
Protected Operators in N=2,4 Supersymmetric Theories: The anomalous dimension of single and multi-trace composite operators of
scalar fields is shown to vanish at all orders of the perturbative series. The
proof hold for theories with N=2 supersymmetry with any number of
hypermultiplets in a generic representation of the gauge group. It then applies
to the finite N=4 theory as well as to non conformal N=2 models. | hep-th |
Current correlators and AdS/CFT away from the conformal point: Using the AdS/CFT correspondence we study vacua of N=4 SYM for which part of
the gauge symmetry is broken by expectation values of scalar fields. A specific
subclass of such vacua can be analyzed with gauged supergravity and the
corresponding domain wall solutions lift to continuous distributions of
D3-branes in type IIB string theory. Due to the non-trivial expectation value
of the scalars, the SO(6) R-symmetry is spontaneously broken and field theory
predicts the existence of Goldstone bosons. We explicitly show that, in the
dual supergravity description, these emerge as massless poles in the current
two-point functions, while the bulk gauge fields which are dual to the broken
currents become massive via the Higgs mechanism. We find agreement with field
theory expectations and, hence, provide a non-trivial test of the AdS/CFT
correspondence far away from the conformal point. | hep-th |
Beyond the WKB approximation in PT-symmetric quantum mechanics: The mergings of energy levels associated with the breaking of PT symmetry in
the model of Bender and Boettcher, and in its generalisation to incorporate a
centrifugal term, are analysed in detail. Even though conventional WKB
techniques fail, it is shown how the ODE/IM correspondence can be used to
obtain a systematic approximation scheme which captures all previously-observed
features. Nonperturbative effects turn out to play a crucial role, governing
the behaviour of almost all levels once the symmetry-breaking transition has
been passed. In addition, a novel treatment of the radial Schrodinger equation
is used to recover the values of local and non-local conserved charges in the
related integrable quantum field theories, without any need for resummation
even when the angular momentum is nonzero. | hep-th |
Quantum Inverse Scattering and the Lambda Deformed Principal Chiral
Model: The lambda model is a one parameter deformation of the principal chiral model
that arises when regularizing the non-compactness of a non-abelian T dual in
string theory. It is a current-current deformation of a WZW model that is known
to be integrable at the classical and quantum level. The standard techniques of
the quantum inverse scattering method cannot be applied because the Poisson
bracket is non ultra-local. Inspired by an approach of Faddeev and Reshetikhin,
we show that in this class of models, there is a way to deform the symplectic
structure of the theory leading to a much simpler theory that is ultra-local
and can be quantized on the lattice whilst preserving integrability. This
lattice theory takes the form of a generalized spin chain that can be solved by
standard algebraic Bethe Ansatz techniques. We then argue that the IR limit of
the lattice theory lies in the universality class of the lambda model implying
that the spin chain provides a way to apply the quantum inverse scattering
method to this non ultra-local theory. This points to a way of applying the
same ideas to other lambda models and potentially the string world-sheet theory
in the gauge-gravity correspondence. | hep-th |
Relative entropy of excited states in conformal field theories of
arbitrary dimensions: Extending our previous work, we study the relative entropy between the
reduced density matrices obtained from globally excited states in conformal
field theories of arbitrary dimensions. We find a general formula in the small
subsystem size limit. When one of the states is the vacuum of the CFT, our
result matches with the holographic entanglement entropy computations in the
corresponding bulk geometries, including AdS black branes. We also discuss the
first asymmetric part of the relative entropy and comment on some implications
of the results on the distinguishability of black hole microstates in AdS/CFT. | hep-th |
Conformal and Superconformal Mechanics: We investigate the conformal and superconformal properties of a
non-relativistic spinning particle propagating in a curved background coupled
to a magnetic field and with a scalar potential. We derive the conditions on
the couplings for a large class of such systems which are necessary in order
their actions admit conformal and superconformal symmetry. We find that some of
these conditions can be encoded in the conformal and holomorphic geometry of
the background. Several new examples of conformal and superconformal models are
also given. | hep-th |
On the Casimir interaction between two smoothly deformed cylindrical
surfaces: We generalize the derivative expansion (DE) approach to the interaction
between almost-flat smooth surfaces, to the case of surfaces which are
optimally described in cylindrical coordinates. As in the original form of the
DE, the obtained method does not depend on the nature of the interaction. We
apply our results to the study of the static, zero-temperature Casimir effect
between two cylindrical surfaces, obtaining approximate expressions which are
reliable under the assumption that the distance between those surfaces is
always much smaller than their local curvature radii. To obtain the zero-point
energy, we apply known results about the thermal Casimir effect for a planar
geometry. To that effect, we relate the time coordinate in the latter to the
angular variable in the cylindrical case, as well as the temperature to the
radius of the cylinders. We study the dependence of the applicability of the DE
on the kind of interaction, considering the particular cases where Dirichlet or
Neumann conditions are applied to a scalar field. | hep-th |
KK Spectroscopy of Type IIB Supergravity on AdS_5 x T^{11}: We give full details for the computation of the Kaluza--Klein mass spectrum
of Type IIB Supergravity on AdS_5 x T^{11}, with T^{11}=SU(2)xSU(2)/U(1), that
has recently lead to both stringent tests and interesting predictions on the
AdS_5/CFT_4 correspondence for N=1 SCFT's (hep-th/9905226). We exhaustively
explain how KK states arrange into SU(2,2|1) supermultiplets, and stress some
relevant features of the T^{11} manifold, such as the presence of topological
modes in the spectrum originating from the existence of non-trivial 3-cycles.
The corresponding Betti vector multiplet is responsible for the extra baryonic
symmetry in the boundary CFT. More generally, we use the simple T^{11} coset as
a laboratory to revive the technique and show the power of KK harmonic
expansion, in view of the present attempts to probe along the same lines also
M-theory compactifications and the AdS_4/CFT_3 map. | hep-th |
From Topological to Quantum Entanglement: Entanglement is a special feature of the quantum world that reflects the
existence of subtle, often non-local, correlations between local degrees of
freedom. In topological theories such non-local correlations can be given a
very intuitive interpretation: quantum entanglement of subsystems means that
there are "strings" connecting them. More generally, an entangled state, or
similarly, the density matrix of a mixed state, can be represented by
cobordisms of topological spaces. Using a formal mathematical definition of
TQFT we construct basic examples of entangled states and compute their von
Neumann entropy. | hep-th |
Average Effective Potential for the Conformal Factor: In a four dimensional theory of gravity with lagrangian quadratic in
curvature and torsion, we compute the effective action for metrics of the form
$g_{\mu\nu}=\rho^2\delta_{\mu\nu}$, with $\rho$ constant. Using standard
field-theoretic methods we find that one loop quantum effects produce a
nontrivial effective potential for $\rho$. We explain this unexpected result by
showing how our regularization procedure differs from the one that is usually
adopted in Quantum Gravity. Using the method of the average effective
potential, we compute the scale dependence of the v.e.v. of the conformal
factor. | hep-th |
Charged seven-dimensional spacetimes with spherically symmetric
extra-dimensions: We derive exact solutions of the seven-dimensional Einstein-Maxwell equations
for a spacetime exhibiting Poincare invariance along four-dimensions and
spherical symmetry in the extra-dimensions. Such topology generically arises in
the context of braneworld models. Our solutions generalise previous results on
Ricci-flat spacetimes admitting the two-sphere and are shown to include
wormhole configurations. A regular coordinate system suitable to describe the
whole spacetime is singled-out and we discuss the physical relevance of the
derived solutions. | hep-th |
Non-Abelian discrete gauge symmetries in F-theory: The presence of non-Abelian discrete gauge symmetries in four-dimensional
F-theory compactifications is investigated. Such symmetries are shown to arise
from seven-brane configurations in genuine F-theory settings without a weak
string coupling description. Gauge fields on mutually non-local seven-branes
are argued to gauge both R-R and NS-NS two-form bulk axions. The gauging is
completed into a generalisation of the Heisenberg group with either additional
seven-brane gauge fields or R-R bulk gauge fields. The former case relies on
having seven-brane fluxes, while the latter case requires torsion cohomology
and is analysed in detail through the M-theory dual. Remarkably, the M-theory
reduction yields an Abelian theory that becomes non-Abelian when translated
into the correct duality frame to perform the F-theory limit. The reduction
shows that the gauge coupling function depends on the gauged scalars and
transforms non-trivially as required for the groups encountered. This field
dependence agrees with the expectations for the kinetic mixing of seven-branes
and is unchanged if the gaugings are absent. | hep-th |
Asymptotic Quasinormal Frequencies of Brane-Localized Black Hole: The asymptotic quasinormal frequencies of the brane-localized
$(4+n)$-dimensional black hole are computed. Since the induced metric on the
brane is not an exact vacuum solution of the Einstein equation defined on the
brane, the real parts of the quasinormal frequencies $ \omega$ do not approach
to the well-known value $T_H \ln 3$ but approach to $T_H \ln k_n$, where $k_n$
is a number dependent on the extra dimensions. For the scalar perturbation
$Re(\omega / T_H) = \ln 3$ is reproduced when $n = 0$. For $n \neq 0$, however,
$Re(\omega / T_H)$ is smaller than $\ln 3$. It is shown also that when $n > 4$,
$Im(\omega / T_H)$ vanishes in the scalar perturbation. For the gravitational
perturbation it is shown that $Re(\omega / T_H) = \ln 3$ is reproduced when $n
= 0$ and $n = 4$. For different $n$, however, $Re(\omega / T_H)$ is smaller
than $\ln 3$. When $n = \infty$, for example, $Re(\omega / T_H)$ approaches to
$\ln (1 + 2 \cos \sqrt{5} \pi) \approx 0.906$. Unlike the scalar perturbation
$Im(\omega / T_H)$ does not vanish regradless of the number of extra
dimensions. | hep-th |
Towards Natural Inflation in String Theory: We provide type IIB string embeddings of two axion variants of natural
inflation. We use a combination of RR 2 form axions as the inflaton field and
have its potential generated by non perturbative effects in the superpotential.
Besides giving rise to inflation, the models developed take into account the
stabilization of the compact space, both in the KKLT and large volume scenario
regimes, an essential condition for any semi-realistic model of string
inflation. | hep-th |
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