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Agujeros negros clasicos y cuanticos en teoria de cuerdas: Introductory lectures on classical and quantum string black holes
(supergravity, branes and dualities) given at the VII School "La Hechicera" of
Relativity, Fields and Astrophysics, held in the University of Los Andes,
Merida (Venezuela) 2001. Fully in Spanish. | hep-th |
Celestial Feynman Rules for Scalars: Off-shell celestial amplitudes with both time-like and space-like external
legs are defined. The Feynman rules for scalar amplitudes, viewed as a set of
recursion relations for off-shell momentum space amplitudes, are transformed to
the celestial sphere using the split representation. For four-point celestial
amplitudes, the Feynman expansion is shown to be equivalent to a conformal
partial wave decomposition, providing an interpretation of conformal partial
wave expansion coefficients as integrals over off-shell three-point structures.
A conformal partial wave decomposition for a simple four-point $s$-channel
massless scalar celestial amplitude is derived. | hep-th |
The supersymmetric extension of the replica model: We perform a $\mathcal{N}=1$ supersymmetric extension of the replica model
quantized in the Landau gauge and compute the gluon and gluino propagators at
tree-level, such results display a supersymmetric confined model very similar
to the supersymmetric version of the Gribov-Zwanziger approach. | hep-th |
Squeezing as a probe of the universality hypothesis: We compute analytically the radiative quantum corrections, up to
next-to-leading loop order, to the universal critical exponents for both
massless and massive O($N$) $\lambda\phi^{4}$ scalar squeezed field theories
for probing the universality hypothesis. For that, we employ six distinct and
independent methods. The outcomes for the universal squeezed critical exponents
obtained through these methods are identical among them and reduce to the
conventional ones where squeezing is absent. Although the squeezing mechanism
modifies the internal properties of the field, the squeezed critical indices
are not affected by the squeezing effect, thus implying the validity of the
universality hypothesis, at least at the loop level considered. At the end, we
present the corresponding physical interpretation for the results in terms of
the geometric symmetry properties of the squeezed field. | hep-th |
Four-modulus "Swiss Cheese" chiral models: We study the 'Large Volume Scenario' on explicit, new, compact, four-modulus
Calabi-Yau manifolds. We pay special attention to the chirality problem pointed
out by Blumenhagen, Moster and Plauschinn. Namely, we thoroughly analyze the
possibility of generating neutral, non-perturbative superpotentials from
Euclidean D3-branes in the presence of chirally intersecting D7-branes. We find
that taking proper account of the Freed-Witten anomaly on non-spin cycles and
of the Kaehler cone conditions imposes severe constraints on the models.
Nevertheless, we are able to create setups where the constraints are solved,
and up to three moduli are stabilized. | hep-th |
Holography in Lovelock Chern-Simons AdS Gravity: We analyse holographic field theory dual to Lovelock Chern-Simons AdS Gravity
in higher dimensions using first order formalism. We first find asymptotic
symmetries in the AdS sector showing that they consist of local translations,
local Lorentz rotations, dilatations and non-Abelian gauge transformations.
Then, we compute $1$-point functions of energy-momentum and spin currents in a
dual conformal field theory and write Ward identities. We find that the
holographic theory possesses Weyl anomaly and also breaks non-Abelian gauge
symmetry at the quantum level. | hep-th |
Local BRST cohomology in minimal D=4, N=1 supergravity: The local BRST cohomology is computed in old and new minimal supergravity,
including the coupling to Yang-Mills gauge multiplets. This covers the
determination of all gauge invariant local actions for these models, the
classification of all the possible counterterms that are invariant on-shell, of
all candidate gauge anomalies, and of the possible nontrivial (continuous)
deformations of the standard actions and gauge transformations. Among others it
is proved that in old minimal supergravity the most general gauge invariant
action can indeed be constructed from well-known superspace integrals, whereas
in new minimal supergravity there are only a few additional (but important)
contributions which cannot be constructed in this way without further ado.
Furthermore the results indicate that supersymmetry itself is not anomalous in
minimal supergravity and show that the gauge transformations are extremely
stable under consistent deformations of the models. There is however an unusual
deformation converting new into old minimal supergravity with local
R-invariance which is reminiscent of a duality transformation. | hep-th |
Conformal Bootstrap Analysis for Yang-Lee Edge Singularity: The Yang-Lee edge singularity is investigated by the determinant method of
the conformal field theory. The critical dimension Dc, for which the scale
dimension of scalar Delta_phi is vanishing, is discussed by this determinant
method. The result is incorporated in the Pade analysis of epsilon expansion,
which leads to an estimation of the value Delta_phi between three and six
dimensions. The structure of the minors is viewed from the fixed points. | hep-th |
The microscopic spectrum of the QCD Dirac operator with finite quark
masses: We compute the microscopic spectrum of the QCD Dirac operator in the presence
of dynamical fermions in the framework of random-matrix theory for the chiral
Gaussian unitary ensemble. We obtain results for the microscopic spectral
correlators, the microscopic spectral density, and the distribution of the
smallest eigenvalue for an arbitrary number of flavors, arbitrary quark masses,
and arbitrary topological charge. | hep-th |
An Origin Story for Amplitudes: We classify origin limits of maximally helicity violating multi-gluon
scattering amplitudes in planar $\mathcal{N}=4$ super-Yang-Mills theory, where
a large number of cross ratios approach zero, with the help of cluster
algebras. By analyzing existing perturbative data, and bootstrapping new data,
we provide evidence that the amplitudes become the exponential of a quadratic
polynomial in the large logarithms. With additional input from the
thermodynamic Bethe ansatz at strong coupling, we conjecture exact expressions
for amplitudes with up to 8 gluons in all origin limits. Our expressions are
governed by the tilted cusp anomalous dimension evaluated at various values of
the tilt angle. | hep-th |
Non-perturbative topological string theory on compact Calabi-Yau 3-folds: We obtain analytic and numerical results for the non-perturbative amplitudes
of topological string theory on arbitrary, compact Calabi-Yau manifolds. Our
approach is based on the theory of resurgence and extends previous special
results to the more general case. In particular, we obtain explicit
trans-series solutions of the holomorphic anomaly equations. Our results
predict the all orders, large genus asymptotics of the topological string free
energies, which we test in detail against high genus perturbative series
obtained recently in the compact case. We also provide additional evidence that
the Stokes constants appearing in the resurgent structure are closely related
to integer BPS invariants. | hep-th |
Covariance of WDVV equations: The (generalized) WDVV equations for the prepotentials in $2d$ topological
and $4,5d$ Seiberg-Witten models are covariant with respect to non-linear
transformations, described in terms of solutions of associated linear problem.
Both time-variables and the prepotential change non-trivially, but period
matrix (prepotential's second derivatives) remains intact. | hep-th |
Fermion states on domain wall junctions and the flavor number: In this paper we address the problem of localizing fermion states on stable
domain walls junctions. The study focus on the consequences of intersecting six
independent 8d domain walls to form 4d junctions in a ten-dimensional
spacetime. This is related to the mechanism of relaxing to three space
dimensions through the formation of domain wall junctions. The model is based
on six bulk real scalar fields, the phi-4 model in its broken phase, the
prototype of the Higgs field, and is such that the fermion and scalar modes
bound to the domain walls are the zero mode and a single massive bound state,
which can be regarded as a two level system, at least at sufficiently low
energy. Inside the junction, we use the fact that some states are statistically
more favored to address the possibility of constraining the flavor number of
the elementary fermions. | hep-th |
Quark mass correction to the string potential: A consistent method for calculating the interquark potential generated by the
relativistic string with massive ends is proposed. In this approach the
interquark potential in the model of the Nambu--Goto string with point--like
masses at its ends is calculated. At first the calculation is done in the
one--loop approximation and then the variational estimation is performed. The
quark mass correction results in decreasing the critical distance
(deconfinement radius). When quark mass decreases the critical distance also
decreases. For obtaining a finite result under summation over eigenfrequencies
of the Nambu--Goto string with massive ends a suitable mode--by--mode
subtraction is proposed. This renormalization procedure proves to be completely
unique. In the framework of the developed approach the one--loop interquark
potential in the model of the relativistic string with rigidity is also
calculated. | hep-th |
The Energy Loss of a Heavy Quark Moving Through a General Fluid
Dynamical Flow: We determine the most general form of the covariant drag force exerted on a
quark moving through a fluid dynamical flow. Up to first order in derivative
expansion, our general formula requires the specification of seven coefficient
functions. We use the perturbative method introduced in arXiv:1202.2737 and
find all these coefficients in the hydrodynamic regime of a $\mathcal{N}=4$ SYM
plasma. Having this general formula, we can obtain the rate of the energy and
momentum loss of a quark, namely the drag force, in a general flow. This result
makes it possible to perturbatively study the motion of heavy quarks moving
through the Bjorken flow up to first order in derivative expansion. | hep-th |
On the BRST approach to the description of a Regge trajectory: The free field theory for Regge trajectory is described in the framework of
the BRST - quantization method. The physical spectrum includes daugther
trajectories along with parent one. The applicability of the BRST approach to
the description of a single Regge trajectory without its daughter trajectories
is discussed. The simple example illustrates the appropriately modified BRST
construction for the needed second class constraints. | hep-th |
A new symmetry of the colored Alexander polynomial: We present a new conjectural symmetry of the colored Alexander polynomial,
that is the specialization of the quantum $\mathfrak{sl}_N$ invariant widely
known as the colored HOMFLY-PT polynomial. We provide arguments in support of
the existence of the symmetry by studying the loop expansion and the character
expansion of the colored HOMFLY-PT polynomial. We study the constraints this
symmetry imposes on the group theoretic structure of the loop expansion and
provide solutions to those constraints. The symmetry is a powerful tool for
research on polynomial knot invariants and in the end we suggest several
possible applications of the symmetry. | hep-th |
Thermal AdS(3), BTZ and competing winding modes condensation: We study the thermal physics of AdS(3) and the BTZ black hole when embedded
in String theory. The exact calculation of the Hagedorn temperature in TAdS(3)
is reinterpreted as the appearance of a winding tachyon both in AdS(3) and BTZ.
We construct a dual framework for analyzing the phases of the system. In this
dual framework, tachyon condensation and geometric capping appear on the same
footing, bridging the usual gap of connecting tachyon condensation to
modifications of geometry. This allows us to construct in a natural way a
candidate for the unstable phase, analogous to a small black hole in higher
dimensions. Additional peculiar effects associated with the Hagedorn
temperature and the Hawking-Page transition, some to do with the asymptotic
structure of AdS(3) and some with strong curvature effects, are analyzed and
explained. | hep-th |
Invariance of Unruh and Hawking radiation under matter-induced
supertranslations: Matter fields are supertranslated upon crossing a shock wave, which leads to
entanglement of the quantum vacuum between the two regions on either side of
the shock wave. We probe this entanglement for a scalar field in a planar shock
wave background by computing the Bogoliubov transformation between the inertial
and uniformly accelerated observer. The resulting Bogoliubov coefficients are
shown to reproduce the standard Unruh effect without dependence on the form
factor of the shock wave. In contrast, excited states lead to observables that
depend upon the form factor. In the context of nonspherical gravitational
collapse, we comment that the angular dependence of the limiting advanced time
leads to similar supertranslation effects that do not affect the Hawking
spectrum but do affect scattering amplitudes. | hep-th |
Dirac versus reduced phase space quantization for systems admitting no
gauge conditions: The constrained Hamiltonian systems admitting no gauge conditions are
considered. The methods to deal with such systems are discussed and developed.
As a concrete application, the relationship between the Dirac and reduced phase
space quantizations is investigated for spin models belonging to the class of
systems under consideration. It is traced out that the two quantization methods
may give similar, or essentially different physical results, and, moreover, a
class of constrained systems, which can be quantized only by the Dirac method,
is discussed. A possible interpretation of the gauge degrees of freedom is
given. | hep-th |
Gluonic fields of a static particle to all orders in 1/N: We determine the expectation value of the gauge invariant operator Tr
[F^2+... ] for N=4 SU(N) SYM, in the presence of an infinitely heavy static
particle in the symmetric representation of SU(N). We carry out the computation
in the context of the AdS/CFT correspondence, by considering the perturbation
of the dilaton field caused by the presence of a D3 brane dual to such an
external probe. We find that the effective chromo-electric charge of the probe
has exactly the same expression as the one recently found in the computation of
energy loss by radiation. | hep-th |
Anomalous U(1)'s in Type I and Type IIB D=4, N=1 string vacua: We study the cancellation of U(1) anomalies in Type I and Type IIB D=4, N=1
string vacua. We first consider the case of compact toroidal $Z_N$ Type IIB
orientifolds and then proceed to the non-compact case of Type IIB D3 branes at
orbifold and orientifold singularities. Unlike the case of the heterotic string
we find that for each given vacuum one has generically more than one U(1) with
non-vanishing triangle anomalies. There is a generalized Green-Schwarz
mechanism by which these anomalies are cancelled. This involves only the
Ramond-Ramond scalars coming from the twisted closed string spectrum but not
those coming from the untwisted sector. Associated to the anomalous U(1)'s
there are field-dependent Fayet-Illiopoulos terms whose mass scale is fixed by
undetermined vev's of the NS-NS partners of the relevant twisted RR fields.
Thus, unlike what happens in heterotic vacua, the masses of the anomalous
U(1)'s gauge bosons may be arbitrarily light. In the case of D3 branes at
singularities, appropriate factorization of the U(1)'s constrains the
Chan-Paton matrices beyond the restrictions from cancellation of non-abelian
anomalies. These conditions can be translated to constraints on the T-dual Type
IIB brane box configurations. We also construct a new large family of N=1
chiral gauge field theories from D3 branes at orientifold singularities, and
check its non-abelian and U(1) anomalies cancel. | hep-th |
Determination of critical exponents and equation of state by field
theory method: Path integrals have played a fundamental role in emphasizing the profound
analogies between Quantum Field Theory (QFT), and Classical as well as Quantum
Statistical Physics. Ideas coming from Statistical Physics have then led to a
deeper understanding of Quantum Field Theory and open the way for a wealth of
non-perturbative methods. Conversely QFT methods are become essential for the
description of the phase transitions and critical phenomena beyond mean field
theory. This is the point we want to illustrate here. We therefore review the
methods, based on renormalized phi^4_3 quantum field theory and renormalization
group, which have led to an accurate determination of critical exponents of the
N-vector model, and more recently of the equation of state of the 3D Ising
model. The starting point is the perturbative expansion for RG functions or the
effective potential to the order presently available. Perturbation theory is
known to be divergent and its divergence has been related to instanton
contributions. This has allowed to characterize the large order behaviour of
perturbation series, an information that can be used to efficiently "sum" them.
Practical summation methods based on Borel transformation and conformal mapping
have been developed, leading to the most accurate results available probing
field theory in a non perturbative regime. We illustrate the methods with a
short discussion of the scaling equation of state of the 3D Ising model.
Compared to exponents its determination involves a few additional (non-trivial)
technical steps, like the use of the parametric representation, and the
order-dependent mapping. | hep-th |
Field-enlarging transformations and chiral theories: A field-enlarging transformation in the chiral electrodynamics is performed.
This introduces an additional gauge symmetry to the model that is unitary and
anomaly-free and allows for comparison of different models discussed in the
literature. The problem of superfluous degrees of freedom and their influence
on quantization is discussed. Several "mysteries" are explained from this point
of view. | hep-th |
Looking at the Gregory-Laflamme instability through quasi-normal modes: We study evolution of gravitational perturbations of black strings. It is
well known that for all wavenumber less than some threshold value, the black
string is unstable against scalar type of gravitational perturbations, which is
named the Gregory-Laflamme instability. Using numerical methods, we find the
quasinormal modes and time-domain profiles of the black string perturbations in
the stable sector and also show the appearance of the Gregory-Laflamme
instability in the time domain. The dependence of the black string quasinormal
spectrum and late time tails on such parameters as the wave vector and the
number of extra dimensions is discussed. There is a numerical evidence that in
the threshold point of instability the static solution of the wave equation is
dominant. For wavenumbers slightly larger than the threshold value, in the
region of stability, we see tiny oscillations with very small damping rate.
While, for wavenumbers slightly smaller than the threshold value, in the region
of the Gregory-Laflamme instability, we observe tiny oscillations with very
small growth rate. We also find the level crossing of imaginary part of
quasinormal modes between the fundamental mode and the first overtone mode,
which accounts for the peculiar time domain profiles. | hep-th |
Non-Local Effects of Multi-Trace Deformations in the AdS/CFT
Correspondence: The AdS/CFT correspondence relates deformations of the CFT by "multi-trace
operators" to "non-local string theories". The deformed theories seem to have
non-local interactions in the compact directions of space-time; in the gravity
approximation the deformed theories involve modified boundary conditions on the
fields which are explicitly non-local in the compact directions. In this note
we exhibit a particular non-local property of the resulting space-time theory.
We show that in the usual backgrounds appearing in the AdS/CFT correspondence,
the commutator of two bulk scalar fields at points with a large enough distance
between them in the compact directions and a small enough time-like distance
between them in AdS vanishes, but this is not always true in the deformed
theories. We discuss how this is consistent with causality. | hep-th |
Casimir Energies for Spherically Symmetric Cavities: A general calculation of Casimir energies --in an arbitrary number of
dimensions-- for massless quantized fields in spherically symmetric cavities is
carried out. All the most common situations, including scalar and spinor
fields, the electromagnetic field, and various boundary conditions are treated
with care. The final results are given as analytical (closed) expressions in
terms of Barnes zeta functions. A direct, straightforward numerical evaluation
of the formulas is then performed, which yields highly accurate numbers of, in
principle, arbitrarily good precision. | hep-th |
Holography for Einstein-Maxwell-dilaton theories from generalized
dimensional reduction: We show that a class of Einstein-Maxwell-Dilaton (EMD) theories are related
to higher dimensional AdS-Maxwell gravity via a dimensional reduction over
compact Einstein spaces combined with continuation in the dimension of the
compact space to non-integral values (`generalized dimensional reduction').
This relates (fairly complicated) black hole solutions of EMD theories to
simple black hole/brane solutions of AdS-Maxwell gravity and explains their
properties. The generalized dimensional reduction is used to infer the
holographic dictionary and the hydrodynamic behavior for this class of theories
from those of AdS. As a specific example, we analyze the case of a black brane
carrying a wave whose universal sector is described by gravity coupled to a
Maxwell field and two neutral scalars. At thermal equilibrium and finite
chemical potential the two operators dual to the bulk scalar fields acquire
expectation values characterizing the breaking of conformal and generalized
conformal invariance. We compute holographically the first order transport
coefficients (conductivity, shear and bulk viscosity) for this system. | hep-th |
Quasi-instantons in QCD with chiral symmetry restoration: We show, without using semiclassical approximations, that, in
high-temperature QCD with chiral symmetry restoration and U(1) axial symmetry
breaking, the partition function for sufficiently light quarks can be expressed
as an ensemble of noninteracting objects with topological charge that obey the
Poisson statistics. We argue that the topological objects are
"quasi-instantons" (rather than bare instantons) taking into account quantum
effects. Our result is valid even close to the (pseudo)critical temperature of
the chiral phase transition. | hep-th |
Entropy Function for Heterotic Black Holes: We use the entropy function formalism to study the effect of the Gauss-Bonnet
term on the entropy of spherically symmetric extremal black holes in heterotic
string theory in four dimensions. Surprisingly the resulting entropy and the
near horizon metric, gauge field strengths and the axion-dilaton field are
identical to those obtained by Cardoso et. al. for a supersymmetric version of
the theory that contains Weyl tensor squared term instead of the Gauss-Bonnet
term. We also study the effect of holomorphic anomaly on the entropy using our
formalism. Again the resulting attractor equations for the axion-dilaton field
and the black hole entropy agree with the corresponding equations for the
supersymmetric version of the theory. These results suggest that there might be
a simpler description of supergravity with curvature squared terms in which we
supersymmetrize the Gauss-Bonnet term instead of the Weyl tensor squared term. | hep-th |
$\mathcal{N} = (2,2)$ extended $\mathfrak{sl}(3|2)$ Chern-Simons $AdS_3$
supergravity with new boundaries: We present the first example of $\mathcal{N}=(2,2)$ formulation for the
extended higher-spin $AdS_3$ supergravity with the most general boundary
conditions as an extension of the $\mathcal{N} =\,(1,1)$ work, discovered
recently by us [1]. Using the method proposed by Grumiller and Riegler, we
construct a consistent class of the most general boundary conditions to extend
it. An important consequence of our method is that, for the loosest set of
boundary conditions it ensures that their asymptotic symmetry algebras consist
of two copies of the $\mathfrak{sl}(3|2)_k$. Moreover, we enjoin some certain
restrictions on the gauge fields for the most general boundary conditions,
leading to the supersymmetric extensions of the Brown and Henneaux boundary
conditions. Based on these results, we finally find out that the asymptotic
symmetry algebras are two copies of the super $\mathcal{W}_3$ algebra for
$\mathcal{N} = (2,2)$ extended higher-spin supergravity theory in $AdS_3$. | hep-th |
Exactly Marginal Deformations of N=4 SYM and of its Supersymmetric
Orbifold Descendants: In this paper we study exactly marginal deformations of field theories living
on D3-branes at low energies. These theories include N=4 supersymmetric
Yang-Mills theory and theories obtained from it via the orbifolding procedure.
We restrict ourselves only to orbifolds and deformations which leave some
supersymmetry unbroken. A number of new families of N=1 superconformal field
theories are found. We analyze the deformations perturbatively, and also by
using general arguments for the dimension of the space of exactly marginal
deformations. We find some cases where the space of perturbative exactly
marginal deformations is smaller than the prediction of the general analysis at
least up to three-loop order), and other cases where the perturbative result
(at low orders) has a non-generic form. | hep-th |
On the holographic duals of N=1 gauge dynamics: We analyze the holographic description of several properties of $\N=1$
confining gauge dynamics. In particular we discuss Wilson loops including the
issues of a Luscher term and the broadening of the flux tubes, 't Hooft loops,
baryons, instantons, chiral symmetry breaking, the gluino condensate and BPS
domain walls. | hep-th |
Holographic non-computers: We introduce the notion of holographic non-computer as a system which
exhibits parametrically large delays in the growth of complexity, as calculated
within the Complexity-Action proposal. Some known examples of this behavior
include extremal black holes and near-extremal hyperbolic black holes. Generic
black holes in higher-dimensional gravity also show non-computing features.
Within the $1/d$ expansion of General Relativity, we show that large-$d$
scalings which capture the qualitative features of complexity, such as a linear
growth regime and a plateau at exponentially long times, also exhibit an
initial computational delay proportional to $d$. While consistent for large AdS
black holes, the required `non-computing' scalings are incompatible with
thermodynamic stability for Schwarzschild black holes, unless they are tightly
caged. | hep-th |
Moving Domain Walls in $AdS_5$ and Graceful Exit from Inflation: We consider moving-brane-solutions in AdS type back ground. In the first
Randall-Sundrum configuration, there are two branes at fixed points of the
orbifold symmetry. We point out that if one brane is fixed and the other brane
is moving, the configuration is still a solution provided the moving brane has
a specific velocity determined by its tension and bulk cosmological constant.
In the absence of the $\bf Z_2$ symmetry, we can construct multi-brane
configurations by patching AdS-Schwarzshild solutions. In this case, we show
that the 4-dimensional effective cosmological constant on the brane world is
not well defined. We find a condition for a brane to be stationary. Using the
brane scattering, we suggest a scenario of inflation on the brane universe
during a finite time, i.e, a scenario of a graceful exit of inflation. | hep-th |
Dirac operators on the Taub-NUT space, monopoles and SU(2)
representations: We analyse the normalisable zero-modes of the Dirac operator on the Taub-NUT
manifold coupled to an abelian gauge field with self-dual curvature, and
interpret them in terms of the zero modes of the Dirac operator on the 2-sphere
coupled to a Dirac monopole. We show that the space of zero modes decomposes
into a direct sum of irreducible SU(2) representations of all dimensions up to
a bound determined by the spinor charge with respect to the abelian gauge
group. Our decomposition provides an interpretation of an index formula due to
Pope and provides a possible model for spin in recently proposed geometric
models of matter. | hep-th |
Directly from $H$-flux to the family of three nonlocal $R$-flux theories: In this article we consider T-dualization of the 3D closed bosonic string in
the weakly curved background - constant metric and Kalb-Ramond field with one
non-zero component, $B_{xy}=Hz$, where field strength $H$ is infinitesimal. We
use standard and generalized Buscher T-dualization procedure and make
T-dualization starting from coordinate $z$, via $y$ and finally along $x$
coordinate. All three theories are {\it nonlocal}, because variable $\Delta V$,
defined as line integral, appears as an argument of background fields. After
the first T-dualization we obtain commutative and associative theory, while
after we T-dualize along $y$, we get, $\kappa$-Minkowski-like, noncommutative
and associative theory. At the end of this T-dualization chain we come to the
theory which is both noncommutative and nonassociative. The form of the final
T-dual action does not depend on the order of T-dualization while
noncommutativity and nonassociativity relations could be obtained from those in
the $x\to y\to z$ case by replacing $H\to - H$. | hep-th |
Renormalization of Non-Semisimple Gauge Models with the Background Field
Method: We study the renormalization of non-semisimple gauge models quantized in the
`t Hooft-background gauge to all orders. We analyze the normalization
conditions for masses and couplings compatible with the Slavnov-Taylor and
Ward-Takahashi Identities and with the IR constraints. We take into account
both the problem of renormalization of CKM matrix elements and the problem of
CP violation and we show that the Background Field Method (BFM) provides proper
normalization conditions for fermion, scalar and gauge field mixings. We
discuss the hard and the soft anomalies of the Slavnov-Taylor Identities and
the conditions under which they are absent. | hep-th |
On RSOS models associated to Lie algebras and RCFT: RSOS models based on the Lie algebras $B_m$, $C_m$ and $D_m$ are derived from
the braiding of conformal field theory. This gives the first systematic
derivation of these models earlier described by Jimbo et al. The general two
field Boltzmann weights associated to any RCFT are described, giving in
particular the off critical thermalized Boltzmann weights. Crossing properties
are discussed and are shown to agree with the general theory which connects
these with toroidal modular transformations. The soliton systems based on these
lattice models are described and are conjectured based on the mass formulae and
the spins of the integrals of motions to describe perturbations of the RCFT
$G_k\times G_1\over G_{k+1}$, where $G$ is the corresponding Lie algebra. | hep-th |
Classical stability of stringy wormholes in flat and AdS spaces: We study small fluctuations of the stringy wormhole solutions of
graviton-dilaton-axion system in arbitrary dimensions. We show under
O($d$)-symmetric harmonic perturbation that the Euclidean wormhole solutions
are unstable in flat space irrespective of dimensions and in anti de Sitter
space of $d=3$. | hep-th |
Spin(7)-Manifolds as Generalized Connected Sums and 3d N=1 Theories: M-theory on compact eight-manifolds with $\mathrm{Spin}(7)$-holonomy is a
framework for geometric engineering of 3d $\mathcal{N}=1$ gauge theories
coupled to gravity. We propose a new construction of such
$\mathrm{Spin}(7)$-manifolds, based on a generalized connected sum, where the
building blocks are a Calabi-Yau four-fold and a $G_2$-holonomy manifold times
a circle, respectively, which both asymptote to a Calabi-Yau three-fold times a
cylinder. The generalized connected sum construction is first exemplified for
Joyce orbifolds, and is then used to construct examples of new compact
manifolds with $\mathrm{Spin}(7)$-holonomy. In instances when there is a
K3-fibration of the $\mathrm{Spin}(7)$-manifold, we test the spectra using
duality to heterotic on a $T^3$-fibered $G_2$-holonomy manifold, which are
shown to be precisely the recently discovered twisted-connected sum
constructions. | hep-th |
Reflection algebra, Yangian symmetry and bound-states in AdS/CFT: We present the `Heisenberg picture' of the reflection algebra by explicitly
constructing the boundary Yangian symmetry of an AdS/CFT superstring which ends
on a boundary with non-trivial degrees of freedom and which preserves the full
bulk Lie symmetry algebra. We also consider the spectrum of bulk and boundary
states and some automorphisms of the underlying algebras. | hep-th |
Argyres-Douglas Theories, the Macdonald Index, and an RG Inequality: We conjecture closed-form expressions for the Macdonald limits of the
superconformal indices of the (A_1, A_{2n-3}) and (A_1, D_{2n}) Argyres-Douglas
(AD) theories in terms of certain simple deformations of Macdonald polynomials.
As checks of our conjectures, we demonstrate compatibility with two
S-dualities, we show symmetry enhancement for special values of n, and we argue
that our expressions encode a non-trivial set of renormalization group flows.
Moreover, we demonstrate that, for certain values of n, our conjectures imply
simple operator relations involving composites built out of the SU(2)_R
currents and flavor symmetry moment maps, and we find a consistent picture in
which these relations give rise to certain null states in the corresponding
chiral algebras. In addition, we show that the Hall-Littlewood limits of our
indices are equivalent to the corresponding Higgs branch Hilbert series. We
explain this fact by considering the S^1 reductions of our theories and showing
that the equivalence follows from an inequality on monopole quantum numbers
whose coefficients are fixed by data of the four-dimensional parent theories.
Finally, we comment on the implications of our work for more general N=2
superconformal field theories. | hep-th |
Scalar BCJ Bootstrap: In this letter, we study tree-level scattering amplitudes of scalar particles
in the context of effective field theories. We use tools similar to the soft
bootstrap to build an ansatz for cyclically ordered amplitudes and impose the
Bern-Carrasco-Johansson (BCJ) relations as a constraint. We obtain a set of
BCJ-satisfying amplitudes as solutions to our procedure, which can be thought
of as special higher-derivative corrections to SU(N) non-linear sigma model
amplitudes satisfying BCJ relations to arbitrary multiplicity at leading order.
The surprising outcome of our analysis is that BCJ conditions on higher-point
amplitudes impose constraints on lower-point amplitudes, and they relate
coefficients at different orders in the derivative expansion. This shows that
BCJ conditions are much more restrictive than soft limit behavior, allowing
only for a very small set of solutions. | hep-th |
Some approaches to 2+1-dimensional gravity coupled to point-particles: In these notes we will review some approaches to 2+1 dimensional gravity and
the way it is coupled to point-particles. First we look into some exact static
and stationary solutions with and without cosmological constant. Next we study
the polygon approach invented by 't Hooft. The third section treats the
Chern-Simonons formulation of 2+1-gravity. In the last part we map the problem
of finding the gravitational field around point-particles to the
Riemann-Hilbert problem. | hep-th |
Topologically Massive Spin-1 Particles and Spin-Dependent Potentials: We investigate the role played by particular field representations of an
intermediate massive spin-1 boson in the context of spin-dependent
interparticle potentials between fermionic sources in the limit of low momentum
transfer. The comparison between the well-known case of the Proca field and
that of an exchanged spin-1 boson (with gauge-invariant mass) described by a
2-form potential mixed with a 4-vector gauge field is established in order to
pursue an analysis of spin- as well as velocity-dependent profiles of the
interparticle potentials. We discuss possible applications and derive an upper
bound on the product of vector and pseudo-tensor coupling constants. | hep-th |
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. | hep-th |
Spin-Statistics for Black Hole Microstates: The gravitational path integral can be used to compute the number of black
hole states for a given energy window, or the free energy in a thermal
ensemble. In this article we explain how to use the gravitational path integral
to compute the separate number of bosonic and fermionic black hole microstates.
We do this by comparing the partition function with and without the insertion
of $(-1)^{\sf F}$. In particular we introduce a universal rotating black hole
that contributes to the partition function in the presence of $(-1)^{\sf F}$.
We study this problem for black holes in asymptotically flat space and in AdS,
putting constraints on the high energy spectrum of holographic CFTs (not
necessarily supersymmetric). Finally, we analyze wormhole contributions to
related quantities. | hep-th |
Duality between the massive sine-Gordon and the massive Schwinger models
at finite temperature: The massive Schwinger and the massive sine-Gordon models are proved to be
equivalent at finite temperature, using the path-integral framework. The well
known relations among the parameters of these models to establish the duality
at $T=0$, also remain valid at non zero temperature. | hep-th |
$L_\infty$-Algebras, the BV Formalism, and Classical Fields: We summarise some of our recent works on $L_\infty$-algebras and quasi-groups
with regard to higher principal bundles and their applications in twistor
theory and gauge theory. In particular, after a lightning review of
$L_\infty$-algebras, we discuss their Maurer-Cartan theory and explain that any
classical field theory admitting an action can be reformulated in this context
with the help of the Batalin-Vilkovisky formalism. As examples, we explore
higher Chern-Simons theory and Yang-Mills theory. We also explain how these
ideas can be combined with those of twistor theory to formulate maximally
superconformal gauge theories in four and six dimensions by means of
$L_\infty$-quasi-isomorphisms, and we propose a twistor space action. | hep-th |
Parity realization in Vector-like theories from Fermion Bilinears: We reconsider in this paper the old aim of trying to understand if the
observed realization of discrete symmetries as Parity or CP in the QCD vacuum
can be satisfied from first principles. We show how under the appropriate
assumptions implicitely done by Vafa and Witten in their old paper on parity
realization in vector-like theories, all parity and CP odd operators
constructed from fermion bilinears of the form $\bar\psi\tilde O\psi$ should
take a vanishing vacuum expectation value in a vector-like theory with N
degenerate flavours (N>1). In our analysis the Vafa-Witten theorem on the
impossibility to break spontaneously the flavour symmetry in a vector-like
theory plays a fundamental role. | hep-th |
Unitary Realizations of U-duality Groups as Conformal and Quasiconformal
Groups and Extremal Black Holes of Supergravity Theories: We review the current status of the construction of unitary representations
of U-duality groups of supergravity theories in five, four and three
dimensions. We focus mainly on the maximal supergravity theories and on the N=2
Maxwell-Einstein supergravity (MESGT) theories defined by Jordan algebras of
degree three in five dimensions and their descendants in four and three
dimensions. Entropies of the extremal black hole solutions of these theories in
five and four dimensions are given by certain invariants of their U-duality
groups. The five dimensional U-duality groups admit extensions to spectrum
generating generalized conformal groups which are isomorphic to the U-duality
groups of corresponding four dimensional theories. Similarly, the U-duality
groups of four dimensional theories admit extensions to spectrum generating
quasiconformal groups that are isomorphic to the corresponding U-duality groups
in three dimensions. We outline the oscillator construction of the unitary
representations of generalized conformal groups that admit positive energy
representations, which include the U-duality groups of N=2 MESGT's in four
dimensions. We conclude with a review of the minimal unitary realizations of
U-duality groups that are obtained by quantizations of their quasiconformal
actions. | hep-th |
Positivity, negativity, and entanglement: We explore properties of the universal terms in the entanglement entropy and
logarithmic negativity in 4d CFTs, aiming to clarify the ways in which they
behave like the analogous entanglement measures in quantum mechanics. We show
that, unlike entanglement entropy in finite-dimensional systems, the sign of
the universal part of entanglement entropy is indeterminate. In particular, if
and only if the central charges obey $a>c$, the entanglement across certain
classes of entangling surfaces can become arbitrarily negative, depending on
the geometry and topology of the surface. The negative contribution is
proportional to the product of $a-c$ and the genus of the surface. Similarly,
we show that in $a>c$ theories, the logarithmic negativity does not always
exceed the entanglement entropy. | hep-th |
BMS/GCA Redux: Towards Flatspace Holography from Non-Relativistic
Symmetries: The asymptotic group of symmetries at null infinity of flat spacetimes in
three and four dimensions is the infinite dimensional Bondi-Metzner-Sachs (BMS)
group. This has recently been shown to be isomorphic to non-relativistic
conformal algebras in one lower dimension, the Galilean Conformal Algebra (GCA)
in 2d and a closely related non-relativistic algebra in 3d [1]. We provide a
better understanding of this surprising connection by providing a spacetime
interpretation in terms of a novel contraction. The 2d GCA, obtained from a
linear combination of two copies of the Virasoro algebra, is generically
non-unitary. The unitary subsector previously constructed had trivial
correlation functions. We consider a representation obtained from a different
linear combination of the Virasoros, which is relevant to the relation with the
BMS algebra in three dimensions. This is realised by a new space-time
contraction of the parent algebra. We show that this representation has a
unitary sub-sector with interesting correlation functions. We discuss
implications for the BMS/GCA correspondence and show that the flat space limit
actually induces precisely this contraction on the boundary conformal field
theory. We also discuss aspects of asymptotic symmetries and the consequences
of this contraction in higher dimensions. | hep-th |
Lagrange Multiplier Modified Horava-Lifshitz Gravity: We consider RFDiff invariant Horava-Lifshitz gravity action with additional
Lagrange multiplier term that is a function of scalar curvature. We find its
Hamiltonian formulation and we show that the constraint structure implies the
same number of physical degrees of freedom as in General Relativity. | hep-th |
The Holomorphic Anomaly of Topological Strings: We show that the BRS operator of the topological string B model is not
holomorphic in the complex structure of the target space. This implies that the
so-called holomorphic anomaly of topological strings should not be interpreted
as a BRS anomaly. | hep-th |
Thermal Dark Energy: We present a novel source of dark energy, which is motivated by the
prevalence of hidden sectors in string theory models and is consistent with all
of the proposed swampland conjectures. Thermal effects hold a light hidden
sector scalar at a point in field space that is not a minimum of its zero
temperature potential. This leads to an effective "cosmological constant", with
an equation of state $w=-1$, despite the scalar's zero temperature potential
having only a 4D Minkowski or AdS vacuum. For scalar masses $\lesssim \mu$eV,
which could be technically natural via sequestering, there are large regions of
phenomenologically viable parameter space such that the induced vacuum energy
matches the measured dark energy density. Additionally, in many models a
standard cosmological history automatically leads to the scalar having the
required initial conditions. We study the possible observational signals of
such a model, including at fifth force experiments and through $\Delta N_{\rm
eff}$ measurements. Similar dynamics that are active at earlier times could
resolve the tension between different measurements of $H_0$ and can lead to a
detectable stochastic gravitational wave background. | hep-th |
Bit threads and holographic entanglement: The Ryu-Takayanagi (RT) formula relates the entanglement entropy of a region
in a holographic theory to the area of a corresponding bulk minimal surface.
Using the max flow-min cut principle, a theorem from network theory, we rewrite
the RT formula in a way that does not make reference to the minimal surface.
Instead, we invoke the notion of a "flow", defined as a divergenceless
norm-bounded vector field, or equivalently a set of Planck-thickness "bit
threads". The entanglement entropy of a boundary region is given by the maximum
flux out of it of any flow, or equivalently the maximum number of bit threads
that can emanate from it. The threads thus represent entanglement between
points on the boundary, and naturally implement the holographic principle. As
we explain, this new picture clarifies several conceptual puzzles surrounding
the RT formula. We give flow-based proofs of strong subadditivity and related
properties; unlike the ones based on minimal surfaces, these proofs correspond
in a transparent manner to the properties' information-theoretic meanings. We
also briefly discuss certain technical advantages that the flows offer over
minimal surfaces. In a mathematical appendix, we review the max flow-min cut
theorem on networks and on Riemannian manifolds, and prove in the network case
that the set of max flows varies Lipshitz continuously in the network
parameters. | hep-th |
Neutrino mixing and cosmological constant: We report on the recent result that the non--perturbative vacuum structure
associated with neutrino mixing leads to a non--zero contribution to the value
of the cosmological constant. Its value is estimated by using the natural
cut--off appearing in the quantum field theory formalism for neutrino mixing. | hep-th |
Bogoliubov Renormalization Group and Symmetry of Solution in
Mathematical Physics: Evolution of the concept known in the theoretical physics as the
Renormalization Group (RG) is presented. The corresponding symmetry, that has
been first introduced in QFT in mid-fifties, is a continuous symmetry of a
solution with respect to transformation involving parameters (e.g., of boundary
condition) specifying some particular solution.
After short detour into Wilson's discrete semi-group, we follow the expansion
of QFT RG and argue that the underlying transformation, being considered as a
reparameterisation one, is closely related to the self-similarity property. It
can be treated as its generalization, the Functional Self-similarity (FS).
Then, we review the essential progress during the last decade of the FS
concept in application to boundary value problem formulated in terms of
differential equations. A summary of a regular approach recently devised for
discovering the RG = FS symmetries with the help of the modern Lie group
analysis and some of its applications are given.
As a main physical illustration, we give application of new approach to
solution for a problem of self-focusing laser beam in a non-linear medium. | hep-th |
The GUP and quantum Raychaudhuri equation: In this paper, we compare the quantum corrections to the Schwarzschild black
hole temperature due to quadratic and linear-quadratic generalized uncertainty
principle, with the corrections from the quantum Raychaudhuri equation. The
reason for this comparison is to connect the deformation parameters $\beta_0$
and $ \alpha_0$ with $\eta$ which is the parameter that characterizes the
quantum Raychaudhuri equation. The derived relation between the parameters
appears to depend on the relative scale of the system (black hole), which could
be read as a beta function equation for the quadratic deformation parameter
$\beta_0$. This study shows a correspondence between the two phenomenological
approaches and indicates that quantum Raychaudhuri equation implies the
existence of a crystal-like structure of spacetime. | hep-th |
Enhanced Gauge Symmetry in Type II String Theory: We show how enhanced gauge symmetry in type II string theory compactified on
a Calabi--Yau threefold arises from singularities in the geometry of the target
space. When the target space of the type IIA string acquires a genus $g$ curve
$C$ of $A_{N-1}$ singularities, we find that an $SU(N)$ gauge theory with $g$
adjoint hypermultiplets appears at the singularity. The new massless states
correspond to solitons wrapped about the collapsing cycles, and their dynamics
is described by a twisted supersymmetric gauge theory on $C\times \R^4$. We
reproduce this result from an analysis of the $S$-dual $D$-manifold. We check
that the predictions made by this model about the nature of the Higgs branch,
the monodromy of period integrals, and the asymptotics of the one-loop
topological amplitude are in agreement with geometrical computations. In one of
our examples we find that the singularity occurs at strong coupling in the
heterotic dual proposed by Kachru and Vafa. | hep-th |
Derivative self-interactions for a massive vector field: In this work we revisit the construction of theories for a massive vector
field with derivative self-interactions such that only the 3 desired
polarizations corresponding to a Proca field propagate. We start from the
decoupling limit by constructing healthy interactions containing second
derivatives of the Stueckelberg field with itself and also with the transverse
modes. The resulting interactions can then be straightforwardly generalized
beyond the decoupling limit. We then proceed to a systematic construction of
the interactions by using the Levi-Civita tensors. Both approaches lead to a
finite family of allowed derivative self-interactions for the Proca field. This
construction allows us to show that some higher order terms recently introduced
as new interactions trivialize in 4 dimensions by virtue of the Cayley-Hamilton
theorem. Moreover, we discuss how the resulting derivative interactions can be
written in a compact determinantal form, which can also be regarded as a
generalization of the Born-Infeld lagrangian for electromagnetism. Finally, we
generalize our results for a curved background and give the necessary
non-minimal couplings guaranteeing that no additional polarizations propagate
even in the presence of gravity. | hep-th |
The double cone geometry is stable to brane nucleation: In gauge/gravity duality, the bulk double cone geometry has been argued to
account for a key feature of the spectral form factor known as the ramp. This
feature is deeply associated with quantum chaos in the dual field theory. The
connection with the ramp has been demonstrated in detail for two-dimensional
theories of bulk gravity, but it appears natural in higher dimensions as well.
In a general bulk theory the double cone might thus be expected to dominate the
semiclassical bulk path integral for the boundary spectral form factor in the
ramp regime. While other known spacetime wormholes have been shown to be
unstable to brane nucleation when they dominate over known disconnected
(factorizing) solutions, we argue that the double cone is stable to
semiclassical brane nucleation at the probe-brane level in a variety of string-
and M-theory settings. Possible implications for the AdS/CFT factorization
problem are briefly discussed. | hep-th |
Flow of shear response functions in hyperscaling violating Lifshitz
theories: We study the flow equations of the shear response functions for hyperscaling
violating Lifshitz (hvLif) theories, with Lifshitz and hyperscaling violating
exponents $z$ and $\theta$. Adapting the membrane paradigm approach of
analysing response functions as developed by Iqbal and Liu, we focus
specifically on the shear gravitational modes which now are coupled to the
perturbations of the background gauge field. Restricting to the zero momenta
sector, we make further simplistic assumptions regarding the hydrodynamic
expansion of the perturbations. Analysing the flow equations shows that the
shear viscosity at leading order saturates the Kovtun-Son-Starinets (KSS) bound
of $\frac{1}{4\pi}$. When $z=d_i-\theta$, ($d_i$ being the number of spatial
dimension in the dual field theory) the first-order correction to shear
viscosity exhibits logarithmic scaling, signalling the emergence of a scale in
the UV regime for this class of hvLif theories. We further show that the
response function associated to the gauge field perturbations diverge near the
boundary when $z>d_i+2-\theta$. This provides a holographic understanding of
the origin of such a constraint and further vindicates results obtained in
previous works that were obtained through near horizon and quasinormal mode
analysis. | hep-th |
θ-angle monodromy in two dimensions: "\theta-angle monodromy" occurs when a theory possesses a landscape of
metastable vacua which reshuffle as one shifts a periodic coupling \theta by a
single period. "Axion monodromy" models arise when this parameter is promoted
to a dynamical pseudoscalar field. This paper studies the phenomenon in
two-dimensional gauge theories which possess a U(1) factor at low energies: the
massive Schwinger and gauged massive Thirring models, the U(N) 't Hooft model,
and the {\mathbb CP}^N model. In all of these models, the energy dependence of
a given metastable false vacuum deviates significantly from quadratic
dependence on \theta just as the branch becomes completely unstable (distinct
from some four-dimensional axion monodromy models). In the Schwinger, Thirring,
and 't Hooft models, the meson masses decrease as a function of \theta. In the
U(N) models, the landscape is enriched by sectors with nonabelian \theta terms.
In the {\mathbb CP}^N model, we compute the effective action and the size of
the mass gap is computed along a metastable branch. | hep-th |
The Universe as a Nonuniform Lattice in the Finite-Dimensional Hypercube
II.Simple Cases of Symmetry Breakdown and Restoration: This paper continues a study of field theories specified for the nonuniform
lattice in the finite-dimensional hypercube with the use of the earlier
described deformation parameters. The paper is devoted to spontaneous breakdown
and restoration of symmetry in simple quantum-field theories with scalar
fields. It is demonstrated that an appropriate deformation opens up new
possibilities for symmetry breakdown and restoration. To illustrate, at low
energies it offers high-accuracy reproducibility of the same results as with a
nondeformed theory. In case of transition from low to higher energies and vice
versa it gives description for new types of symmetry breakdown and restoration
depending on the rate of the deformation parameter variation in time, and
indicates the critical points of the previously described lattice associated
with a symmetry restoration. Besides, such a deformation enables one to find
important constraints on the initial model parameters having an explicit
physical meaning. | hep-th |
Monopole-fermion scattering and varying Fock space: We propose a four-dimensional interpretation of the outgoing state of the
scattering of a massless fermion off a Dirac monopole. It has been known that
such a state has fractional fermion numbers and is necessarily outside the Fock
space on top of ordinary perturbative vacuum, when more than two flavours of
charged Dirac fermions are considered. In this paper, we point out that the
Fock space of the fermions depends on the rotor degree of freedom of the
monopole and changes by a monopole-fermion s-wave scattering. By uplifting the
fermion-rotor system introduced by Polchinski, from two to four dimensions, we
argue that the outgoing state can be understood as a state in a different Fock
space. | hep-th |
Topologically massive gravity and complex Chern-Simons terms: This paper is withdrawn because its results have been previously reported in
arxiv hep-th/0507200. | hep-th |
Entropic destruction of heavy quarkonium in non-Abelian plasma from
holography: Lattice QCD indicates a large amount of entropy associated with the heavy
quark-antiquark pair immersed in the quark-gluon plasma. This entropy grows as
a function of the inter-quark distance giving rise to an entropic force that
can be very effective in dissociating the bound quarkonium states. In addition,
the lattice data show a very sharp peak in the heavy quark-antiquark entropy at
the deconfinement transition. Since the quark-gluon plasma around the
deconfinement transition is strongly coupled, we employ the holographic
correspondence to study the entropy associated with the heavy quark-antiquark
pair in two theories: i) ${\cal{N}}=4$ supersymmetric Yang-Mills and ii) a
confining Yang-Mills theory obtained by compactification on a Kaluza-Klein
circle. In both cases we find the entropy growing with the inter-quark distance
and evaluate the effect of the corresponding entropic forces. In the case ii),
we find a sharp peak in the entropy near the deconfinement transition, in
agreement with the lattice QCD results. This peak in our holographic
description arises because the heavy quark pair acts as an eyewitness of the
black hole formation in the bulk -- the process that describes the
deconfinement transition. In terms of the boundary theory, this entropy likely
emerges from the entanglement of a "long string" connecting the quark and
antiquark with the rest of the system. | hep-th |
Perturbative instabilities in Horava gravity: We investigate the scalar and tensor perturbations in Horava gravity, with
and without detailed balance, around a flat background. Once both types of
perturbations are taken into account, it is revealed that the theory is plagued
by ghost-like scalar instabilities in the range of parameters which would
render it power-counting renormalizable, that cannot be overcome by simple
tricks such as analytic continuation. Implementing a consistent flow between
the UV and IR limits seems thus more challenging than initially presumed,
regardless of whether the theory approaches General Relativity at low energies
or not. Even in the phenomenologically viable parameter space, the tensor
sector leads to additional potential problems, such as fine-tunings and
super-luminal propagation. | hep-th |
Lattice W algebras and quantum groups: We represent Feigin's construction [11] of lattice W algebras and give some
simple results: lattice Virasoro and $W_3$ algebras. For simplest case
$g=sl(2)$ we introduce whole $U_q(sl(2))$ quantum group on this lattice. We
find simplest two-dimensional module as well as exchange relations and define
lattice Virasoro algebra as algebra of invariants of $U_q(sl(2))$. Another
generalization is connected with lattice integrals of motion as the invariants
of quantum affine group $U_q(\hat{n}_{+})$. We show that Volkov's scheme leads
to the system of difference equations for the function from non-commutative
variables.Continium limit of this lattice algebras are considered. | hep-th |
Galilean Conformal Electrodynamics: Maxwell's Electrodynamics admits two distinct Galilean limits called the
Electric and Magnetic limits. We show that the equations of motion in both
these limits are invariant under the Galilean Conformal Algebra in D=4, thereby
exhibiting non-relativistic conformal symmetries. Remarkably, the symmetries
are infinite dimensional and thus Galilean Electrodynamics give us the first
example of an infinitely extended Galilean Conformal Field Theory in D>2. We
examine details of the theory by looking at purely non-relativistic conformal
methods and also use input from the limit of the relativistic theory. | hep-th |
BPS Boojums in N=2 supersymmetric gauge theories II: We continue our study of 1/4 Bogomol'nyi-Prasad-Sommerfield (BPS) composite
solitons of vortex strings, domain walls and boojums in N=2 supersymmetric
Abelian gauge theories in four dimensions. In this work, we numerically confirm
that a boojum appearing at an end point of a string on a thick domain wall
behaves as a magnetic monopole with a fractional charge in three dimensions. We
introduce a "magnetic" scalar potential whose gradient gives magnetic fields.
Height of the magnetic potential has a geometrical meaning that is shape of the
domain wall. We find a semi-local extension of boojum which has an additional
size moduli at an end point of a semi-local string on the domain wall. Dyonic
solutions are also studied and we numerically confirm that the dyonic domain
wall becomes an electric capacitor storing opposite electric charges on its
skins. At the same time, the boojum becomes fractional dyon whose charge
density is proportional to ${\vec E} \cdot {\vec B}$. We also study dual
configurations with an infinite number of boojums and anti-boojums on parallel
lines and analyze the ability of domain walls to store magnetic charge as
magnetic capacitors. In understanding these phenomena, the magnetic scalar
potential plays an important role. We study the composite solitons from the
viewpoints of the Nambu-Goto and Dirac-Born-Infeld actions, and find the
semi-local BIon as the counterpart of the semi-local Boojum. | hep-th |
Strong obstruction of the Berends-Burgers-van Dam spin-3 vertex: In the eighties, Berends, Burgers and van Dam (BBvD) found a nonabelian cubic
vertex for self-interacting massless fields of spin three in flat spacetime.
However, they also found that this deformation is inconsistent at higher order
for any multiplet of spin-three fields. For arbitrary symmetric gauge fields,
we severely constrain the possible nonabelian deformations of the gauge algebra
and, using these results, prove that the BBvD obstruction cannot be cured by
any means, even by introducing fields of spin higher (or lower) than three. | hep-th |
Explicit Formulae for Yang-Mills-Einstein Amplitudes from the Double
Copy: Using the double-copy construction of Yang-Mills-Einstein theories formulated
in our earlier work, we obtain compact presentations for single-trace
Yang-Mills-Einstein tree amplitudes with up to five external gravitons and an
arbitrary number of gluons. These are written as linear combinations of
color-ordered Yang-Mills trees, where the coefficients are given by
color/kinematics-satisfying numerators in a Yang-Mills+\phi^3 theory. The
construction outlined in this paper holds in general dimension and extends
straightforwardly to supergravity theories. For one, two, and three external
gravitons, our expressions give identical or simpler presentations of
amplitudes already constructed through string-theory considerations or the
scattering equations formalism. Our results are based on color/kinematics
duality and gauge invariance, and strongly hint at a recursive structure
underlying the single-trace amplitudes with an arbitrary number of gravitons.
For the single-graviton case, we give amplitudes to any loop order and obtain,
through gauge invariance, new loop-level amplitude relations for Yang-Mills
theory. | hep-th |
Analytical study of superradiant instability for five-dimensional
Kerr-Gödel black hole: We present an analytical study of superradiant instability of rotating
asymptotically G\"{o}del black hole (Kerr-G\"{o}del black hole) in
five-dimensional minimal supergravity theory. By employing the matched
asymptotic expansion method to solve Klein-Gordon equation of scalar field
perturbation, we show that the complex parts of quasinormal frequencies are
positive in the regime of superradiance. This implies the growing instability
of superradiant modes. The reason for this kind of instability is the Dirichlet
boundary condition at asymptotic infinity, which is similar to that of rotating
black holes in anti-de Sitter (AdS) spacetime. | hep-th |
A differential-geometry approach to operator mixing in massless QCD-like
theories and Poincaré-Dulac theorem: We review recent progress on operator mixing in the light of the theory of
canonical forms for linear systems of differential equations and, in
particular, of the Poincar\'e-Dulac theorem. We show that the matrix $A(g) =
-\frac{\gamma(g)}{\beta(g)} =\frac{\gamma_0}{\beta_0}\frac{1}{g} + \cdots $
determines which different cases of operator mixing can occur, and we review
their classification. We derive a sufficient condition for $A(g)$ to be set in
the one-loop exact form $A(g) = \frac{\gamma_0}{\beta_0}\frac{1}{g}$. Finally,
we discuss the consequences of the unitarity requirement in massless QCD-like
theories, and we demonstrate that $\gamma_0$ is always diagonalizable if the
theory is conformal invariant and unitary in its free limit at $g =0$. | hep-th |
Scaling Exponents for Lattice Quantum Gravity in Four Dimensions: In this work nonperturbative aspects of quantum gravity are investigated
using the lattice formulation, and some new results are presented for critical
exponents, amplitudes and invariant correlation functions. Values for the
universal scaling dimensions are compared with other nonperturbative approaches
to gravity in four dimensions, and specifically to the conjectured value for
the universal critical exponent $\nu =1 /3$. It is found that the lattice
results are generally consistent with gravitational anti-screening, which would
imply a slow increase in the strength of the gravitational coupling with
distance, and here detailed estimates for exponents and amplitudes
characterizing this slow rise are presented. Furthermore, it is shown that in
the lattice approach (as for gauge theories) the quantum theory is highly
constrained, and eventually by virtue of scaling depends on a rather small set
of physical parameters. Arguments are given in support of the statement that
the fundamental reference scale for the growth of the gravitational coupling
$G$ with distance is represented by the observed scaled cosmological constant
$\lambda$, which in gravity acts as an effective nonperturbative infrared
cutoff. In the vacuum condensate picture a fundamental relationship emerges
between the scale characterizing the running of $G$ at large distances, the
macroscopic scale for the curvature as described by the observed cosmological
constant, and the behavior of invariant gravitational correlation functions at
large distances. Overall, the lattice results suggest that the infrared slow
growth of $G$ with distance should become observable only on very large
distance scales, comparable to $\lambda$. It is hoped that future high
precision satellite experiments will possibly come within reach of this small
quantum correction, as suggested by a vacuum condensate picture of quantum
gravity. | hep-th |
Comment on `Index-free Heat Kernel Coefficients': The article by Anton E. M. van de Ven, Class. Quantum Grav. \textbf{15}
(1998), is one of the fundamental references for higher-order heat kernel
coefficients in curved backgrounds and with non-abelian gauge connections. In
this manuscript, we point out two errors and ambiguities in the $\mathsf{a}_5$
coefficient, which may also affect the higher-order ones. | hep-th |
Conformal Symmetry, Rindler Space and The AdS/CFT Correspondence: Field theories in black hole spacetimes undergo dimensional reduction near
horizon (in the Rindler limit) to two dimensional conformal field theories. We
investigate this enhancement of symmetries in the context of gauge/gravity
duality by considering Rindler space as boundary of Anti-de Sitter space in
three spacetime dimensions. We show that the loxodromy conjugacy class of the
SO(2,2) isometry group is responsible for generating the special conformal
transformations on the boundary under RG flow. We use this approach to present
an alternative derivation of the two-point function in Rindler space using
AdS/CFT correspondence. | hep-th |
Optics, Mechanics and Quantization of Reparametrization Systems: In this paper we regard the dynamics obtained from Fermat principle as begin
the classical theory of light. We (first-)quantize the action and show how
close we can get to the Maxwell theory. We show that Quantum Geometric Optics
is not a theory of fields in curved space. Considering Classical Mechanics to
be on the same footing, we show the parallelism between Quantum Mechanics and
Quantum Geometric Optics. We show that, due to the reparametrization invariance
of the classical theories, the dynamics of the quantum theories is given by a
Hamiltonian constraint. Some implications of the above analogy in the
quantization of true reparameterization invariant systems are discussed. | hep-th |
Do the gravitational corrections to the beta functions of the quartic
and Yukawa couplings have an intrinsic physical meaning?: We study the beta functions of the quartic and Yukawa couplings of General
Relativity and Unimodular Gravity coupled to the $\lambda\phi^4$ and Yukawa
theories with masses. We show that the General Relativity corrections to those
beta functions as obtained from the 1PI functional by using the standard MS
multiplicative renormalization scheme of Dimensional Regularization are gauge
dependent and, further, that they can be removed by a non-multiplicative,
though local, field redefinition. An analogous analysis is carried out when
General Relativity is replaced with Unimodular Gravity. Thus we show that any
claim made about the change in the asymptotic behaviour of the quartic and
Yukawa couplings made by General Relativity and Unimodular Gravity lack
intrinsic physical meaning. | hep-th |
Flat space (higher spin) gravity with chemical potentials: We introduce flat space spin-3 gravity in the presence of chemical potentials
and discuss some applications to flat space cosmology solutions, their entropy,
free energy and flat space orbifold singularity resolution. Our results include
flat space Einstein gravity with chemical potentials as special case. We
discover novel types of phase transitions between flat space cosmologies with
spin-3 hair and show that the branch that continuously connects to spin-2
gravity becomes thermodynamically unstable for sufficiently large temperature
or spin-3 chemical potential. | hep-th |
Relative scale separation in orbifolds of $S^2$ and $S^5$: In orbifold vacua containing an $S^q/\Gamma$ factor, we compute the relative
order of scale separation, $r$, defined as the ratio of the eigenvalue of the
lowest-lying $\Gamma$-invariant state of the scalar Laplacian on $S^q$, to the
eigenvalue of the lowest-lying state. For $q=2$ and $\Gamma$ finite subgroup of
$SO(3)$, or $q=5$ and $\Gamma$ finite subgroup of $SU(3)$, the maximal relative
order of scale separation that can be achieved is $r=21$ or $r=12$,
respectively. For smooth $S^5$ orbifolds, the maximal relative scale separation
is $r=4.2$. Methods from invariant theory are very efficient in constructing
$\Gamma$-invariant spherical harmonics, and can be readily generalized to other
orbifolds. | hep-th |
Special holonomy sigma models with boundaries: A study of (1,1) supersymmetric two-dimensional non-linear sigma models with
boundary on special holonomy target spaces is presented. In particular, the
consistency of the boundary conditions under the various symmetries is studied.
Models both with and without torsion are discussed. | hep-th |
Further comments on BPS systems: We look at BPS systems involving two interacting Sine-Gordon like fields both
when one of them has a kink solution and the second one either a kink or an
antikink solution. The interaction between the two fields is controlled by a
parameter $\lambda$ which has to satisfy $| \lambda|< 2$. We then take these
solitonic static solutions (with solitons well localised) and construct from
them systems involving two solitons in each field (kinks and antikinks) and
then use them as initial conditions for their evolution in Lorentz covariant
versions of such models. This way we study their interactions and compare them
with similar interactions involving only one Sine-Gordon field. In particular,
we look at the behaviour of two static kinks in each field (which for one field
repel each other) and of a system involving kinks and anti-kinks (which for one
field attract each other) and look how their behaviour depends on the strength
of the interaction $\lambda$ between the two fields. Our simulations have led
us to look again at the static BPS solutions of systems involving more fields.
We have found that such ostensibly 'static' BPS solutions can exhibit small
motions due to the excitation of their zero modes. These excitations arise from
small unavoidable numerical errors (the overall translation is cancelled by the
conservation of momentum) but as systems of two or more fields have more that
one zero mode such motions can be generated and are extremely small. The energy
of our systems has been conserved to within $10^{-5}\%$. | hep-th |
Nonlinear Fluid Dynamics from Gravity: Black branes in AdS5 appear in a four parameter family labeled by their
velocity and temperature. Promoting these parameters to Goldstone modes or
collective coordinate fields -- arbitrary functions of the coordinates on the
boundary of AdS5 -- we use Einstein's equations together with regularity
requirements and boundary conditions to determine their dynamics. The resultant
equations turn out to be those of boundary fluid dynamics, with specific values
for fluid parameters. Our analysis is perturbative in the boundary derivative
expansion but is valid for arbitrary amplitudes. Our work may be regarded as a
derivation of the nonlinear equations of boundary fluid dynamics from gravity.
As a concrete application we find an explicit expression for the expansion of
this fluid stress tensor including terms up to second order in the derivative
expansion. | hep-th |
The periodic sl(2|1) alternating spin chain and its continuum limit as a
bulk Logarithmic Conformal Field Theory at c=0: The periodic sl(2|1) alternating spin chain encodes (some of) the properties
of hulls of percolation clusters, and is described in the continuum limit by a
logarithmic conformal field theory (LCFT) at central charge c=0. This theory
corresponds to the strong coupling regime of a sigma model on the complex
projective superspace $\mathbb{CP}^{1|1} = \mathrm{U}(2|1) / (\mathrm{U}(1)
\times \mathrm{U}(1|1))$, and the spectrum of critical exponents can be
obtained exactly. In this paper we push the analysis further, and determine the
main representation theoretic (logarithmic) features of this continuum limit by
extending to the periodic case the approach of [N. Read and H. Saleur, Nucl.
Phys. B 777 316 (2007)]. We first focus on determining the representation
theory of the finite size spin chain with respect to the algebra of local
energy densities provided by a representation of the affine Temperley-Lieb
algebra at fugacity one. We then analyze how these algebraic properties carry
over to the continuum limit to deduce the structure of the space of states as a
representation over the product of left and right Virasoro algebras. Our main
result is the full structure of the vacuum module of the theory, which exhibits
Jordan cells of arbitrary rank for the Hamiltonian. | hep-th |
Teleparallel Geroch geometry: We construct the teleparallel dynamics for extended geometry where the
structure algebra is (an extension of) an untwisted affine Kac-Moody algebra.
This provides a geometrisation of the Geroch symmetry appearing on dimensional
reduction of a gravitational theory to two dimensions. The formalism is adapted
to the underlying tensor hierarchy algebra, and will serve as a stepping stone
towards the geometrisation of other infinite-dimensional, e.g. hyperbolic,
symmetries. | hep-th |
Shadow multiplets and superHiggs mechanism: We discuss a general feature of Freund Rubin compactifications that was
previously overlooked. It consist in a curious pairing, which we call a shadow
relation, of completely different (in terms of spin and mass) fields of the
dimensionally reduced theory. Particularly interesting is the case where the
compactification preserves a certain amount of supersymmetry, giving rise to a
shadowing phenomenon between whole supermultiplets of fields. In particular,
there are strong suggestions about the consistency of a massive truncation of
11D supergravity to the massless modes of the graviton supermultiplet plus the
massive modes of its shadow partner. This fact has important consequences in
the ${\cal N}=2$ and ${\cal N}=3$ cases, which seem to realize respectively a
Higgs or a superHiggs phenomenon. In other words, we are led to reinterpret the
dimensionally reduced theory as a spontaneously broken phase of some higher
(super)symmetric theory. | hep-th |
The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories: We consider N = 3 supersymmetric Chern-Simons gauge theories with product
unitary and orthosymplectic groups and bifundamental and fundamental fields. We
study the partition functions on an S^3 by using the Kapustin-Willett-Yaakov
matrix model. The saddlepoint equations in a large N limit lead to a constraint
that the long range forces between the eigenvalues must cancel; the resulting
quiver theories are of affine Dynkin type. We introduce a folding/unfolding
trick which lets us, at the level of the large N matrix model, (i) map quivers
with orthosymplectic groups to those with unitary groups, and (ii) obtain
non-simply laced quivers from the corresponding simply laced quivers using a
Z_2 outer automorphism. The brane configurations of the quivers are described
in string theory and the folding/unfolding is interpreted as the
addition/subtraction of orientifold and orbifold planes. We also relate the
U(N) quiver theories to the affine ADE quiver matrix models with a
Stieltjes-Wigert type potential, and derive the generalized Seiberg duality in
2 + 1 dimensions from Seiberg duality in 3 + 1 dimensions. | hep-th |
High temperature asymptotics of thermodynamic functions of
electromagnetic field subjected to boundary conditions on a sphere and
cylinder: The high temperature asymptotics of thermodynamic functions of
electromagnetic field subjected to boundary conditions with spherical and
cylindrical symmetries are constructed by making use of a general expansion in
terms of heat kernel coefficients and the related determinant. For this, some
new heat kernel coefficients and determinants had to be calculated for the
boundary conditions under consideration. The obtained results reproduce all the
asymptotics derived by other methods in the problems at hand and involve a few
new terms in the high temperature expansions. An obvious merit of this approach
is its universality and applicability to any boundary value problem correctly
formulated. | hep-th |
Banana integrals in configuration space: We reconsider the computation of banana integrals at different loops, by
working in the configuration space, in any dimension. We show how the 2-loop
banana integral can be computed directly from the configuration space
representation, without the need to resort to differential equations, and we
include the analytic extension of the diagram in the space of complex masses.
We also determine explicitly the $\varepsilon$ expansion of the two loop banana
integrals, for $d=j-2\varepsilon$, $j=2,3,4$. | hep-th |
Oscillators from nonlinear realizations: We construct the systems of the harmonic and Pais-Uhlenbeck oscillators,
which are invariant with respect to arbitrary noncompact Lie algebras. The
equations of motion of these systems can be obtained with the help of the
formalism of nonlinear realizations. We prove that it is always possible to
choose time and the fields within this formalism in such a way that the
equations of motion become linear and, therefore, reduce to ones of ordinary
harmonic and Pais-Uhlenbeck oscillators. The first-order actions, that produce
these equations, can also be provided. As particular examples of this
construction, we discuss the $so(2,3)$ and $G_{2(2)}$ algebras. | hep-th |
Self-dual solutions of a field theory model of two linked rings: In this work the connection established in [7, 8] between a model of two
linked polymers rings with fixed Gaussian linking number forming a 4-plat and
the statistical mechanics of non-relativistic anyon particles is explored. The
excluded volume interactions have been switched off and only the interactions
of entropic origin arising from the topological constraints are considered. An
interpretation from the polymer point of view of the field equations that
minimize the energy of the model in the limit in which one of the spatial
dimensions of the 4-plat becomes very large is provided. It is shown that the
self-dual contributions are responsible for the long-range interactions that
are necessary for preserving the global topological properties of the system
during the thermal fluctuations. The non self-dual part is also related to the
topological constraints, and takes into account the local interactions acting
on the monomers in order to prevent the breaking of the polymer lines. It turns
out that the energy landscape of the two linked rings is quite complex.
Assuming as a rough approximation that the monomer densities of half of the
4-plat are constant, at least two points of energy minimum are found. Classes
of non-trivial self-dual solutions of the self-dual field equations are
derived. ... . | hep-th |
Supergravity backgrounds of the eta-deformed AdS2 x S2 x T6 and AdS5 x
S5 superstrings: We construct supergravity backgrounds for the integrable eta-deformations of
the AdS2 x S2 x T6 and AdS5 x S5 superstring sigma models. The eta-deformation
is governed by an R-matrix that solves the non-split modified classical
Yang-Baxter equation on the superisometry algebra of the model. Such R-matrices
include those of Drinfel'd-Jimbo type, which are constructed from a Dynkin
diagram and the associated Cartan-Weyl basis. Drinfel'd-Jimbo R-matrices
associated with inequivalent bases will typically lead to different deformed
backgrounds. For the two models under consideration we find that the
unimodularity condition, implying that there is no Weyl anomaly, is satisfied
if and only if all the simple roots are fermionic. For AdS2 x S2 x T6 we
construct backgrounds corresponding to the three Dynkin diagrams. When all the
simple roots are fermionic we find a supergravity background previously
obtained by directly solving the supergravity equations. For AdS5 x S5 we
construct a supergravity background corresponding to the Dynkin diagram with
all fermionic simple roots. | hep-th |
11d Electric-Magnetic Duality and the Dbrane Spectrum: We consider the gedanken calculation of the pair correlation function of
spatially-separated macroscopic string solitons in strongly coupled type IIA
string/M theory, with the macroscopic strings wrapping the eleventh dimension.
The supergravity limit of this correlation function with well-separated,
pointlike macroscopic strings corresponds to having also taken the IIA string
coupling constant to zero. Thus, the pointlike limit of the gedanken
correlation function can be given a precise worldsheet description in the 10D
weakly-coupled type IIA string theory, analysed by us in hep-th/0007056 [Nucl.
Phys. B591 (2000) 243]. The requisite type IIA string amplitude is the
supersymmetric extension of the worldsheet formulation of an off-shell closed
string tree propagator in bosonic string theory, a 1986 analysis due to Cohen,
Moore, Nelson, and Polchinski. We point out that the evidence for pointlike
sources of the zero-form field strength provided by our worldsheet results
clarifies that the electric-magnetic duality in the Dirichlet-brane spectrum of
type II string theories is eleven-dimensional. | hep-th |
Remarks on the harmonic oscillator with a minimal position uncertainty: We show that this problem gives rise to the same differential equation of a
well known potential of ordinary quantum mechanics. However there is a subtle
difference in the choice of the parameters of the hypergeometric function
solving the differential equation which changes the physical discussion of the
spectrum. | hep-th |
On first order formulations of supergravities: Supergravities are usually presented in a so-called 1.5 order formulation.
Here we present a general scheme to derive pure 1^{st} order formulations of
supergravities from the 1.5 order ones. The example of N_4=1 supergravity will
be rederived and new results for N_4=2 and N_11=1 will be presented. It seems
that beyond four dimensions the auxiliary fields introduced to obtain first
order formulations of SUGRA theories do not admit supergeometrical
transformation laws at least before a full superfield treatment. On the other
hand first order formalisms simplify eventually symmetry analysis and the study
of dimensional reductions. | hep-th |