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Bootstrapping 2D CFTs in the Semiclassical Limit: We study two dimensional conformal field theories in the semiclassical limit.
In this limit, the four-point function is dominated by intermediate primaries
of particular weights along with their descendants, and the crossing equations
simplify drastically. For a four-point function receiving sufficiently small
contributions from the light primaries, the structure constants involving heavy
primaries follow a universal formula. Applying our results to the four-point
function of the $\mathbb Z_2$ twist field in the symmetric product orbifold, we
produce the Hellerman bound and the logarithmically corrected Cardy formula
that is valid for $h \geq c/12$. | hep-th |
Geometric Aspects of the `Deformation Method': At the classical level, redefinitions of the field content of a Lagrangian
allow to rewrite an interacting model on a flat target space, in the form of a
free field model (no potential term) on a curved target space. In the present
work we extend the idea of the `deformation method' introduced in
\cite{defmet}, to show that it is possible to write an explicit correspondence
between the metrics of the curved target spaces that arise in the free versions
of distinct scalar field models. This is accomplished by obtaining an explicit
relation between the map function linking the fields and the free models'
metrics. By considering complex and even quaternionic field models, we extend
the procedure --initially proposed for models of a single scalar field-- to
systems with a content of two and four (despite constrained) real fields,
respectively, widening the range of applicability. We also analyze
supersymmetric models to illustrate more possibilities. In particular, we show
how to relate a flat Minkowskian metric to a Fubini-Study space. | hep-th |
Quantized Einstein-Rosen waves, AdS_2, and spontaneous symmetry breaking: 4D cylindrical gravitational waves with aligned polarizations (Einstein-Rosen
waves) are shown to be described by a weight 1/2 massive free field on the
double cover of AdS_2. Thorn's C-energy is one of the sl(2,R) generators, the
reconstruction from the (timelike) symmetry axis is the CFT_1 holography.
Classically the phase space is also invariant under a O(1,1) group action on
the metric coefficients that is a remnant of the original 4D diffeomorphism
invariance. In the quantum theory this symmetry is found to be spontaneously
broken while the AdS_2 conformal invariance remains intact. | hep-th |
Excitations in Hot Non-Commutative Theories: We study the dispersion relation for scalar excitations in supersymmetric,
non-commutative theories at finite temperature. In N=4 Yang-Mills the low
momenta modes have superluminous group velocity. In the massless Wess-Zumino
model the minimum of the dispersion relation is at non zero momentum for
temperatures above T_0 ~ (g \theta)^(-1\2). We briefly comment on N=2
Yang-Mills at finite density. | hep-th |
Primordial Black Hole Pair Creation Probability in Modified
Gravitational Theory: The probability for quantum creation of an inflationary universe with a pair
of black holes is computed in a modified gravitational theory. Considering a
gravitational action which includes a cosmological constant ($\Lambda$) in
addition to $ \alpha R^{2} $ and $ \delta R^{-1}$ terms, the probabilities have
been evaluated for two different kinds of spatial sections, one accommodating a
pair of black holes and the other without black hole. We adopt a technique
prescribed by Bousso and Hawking to calculate the above creation probability in
a semiclassical approximation with Hartle-Hawking boundary condition. Depending
on the parameters in the action some new and physically interesting instanton
solutions are presented here which may play an important role in the creation
of the early universe. We note that the probability of creation of a universe
with a pair of black holes is strongly suppressed with a positive cosmological
constant when $\delta = \frac{4 \Lambda^{2}}{3}$ for $\alpha > 0$ but it is
more probable for $\alpha < - \frac{1}{6 \Lambda}$. It is also found that
instanton solutions are allowed without a cosmological constant in the theory
provided $\delta < 0$. | hep-th |
Exactly solvable potentials of Calogero type for q-deformed Coxeter
groups: We establish that by parameterizing the configuration space of a
one-dimensional quantum system by polynomial invariants of q-deformed Coxeter
groups it is possible to construct exactly solvable models of Calogero type. We
adopt the previously introduced notion of solvability which consists of
relating the Hamiltonian to finite dimensional representation spaces of a Lie
algebra. We present explicitly the $G_2^q $-case for which we construct the
potentials by means of suitable gauge transformations. | hep-th |
Closed-form expression for cross-channel conformal blocks near the
lightcone: In the study of conformal field theories, conformal blocks in the lightcone
limit are fundamental to the analytic conformal bootstrap method. Here we
consider the lightcone limit of 4-point functions of generic scalar primaries.
Based on the nonperturbative pole structure in spin of Lorentzian inversion, we
propose the natural basis functions for cross-channel conformal blocks. In this
new basis, we find a closed-form expression for crossed conformal blocks in
terms of the Kamp\'e de F\'eriet function, which applies to intermediate
operators of arbitrary spin in general dimensions. We derive the general
Lorentzian inversion for the case of identical external scaling dimensions. Our
results for the lightcone limit also shed light on the complete analytic
structure of conformal blocks in the lightcone expansion. | hep-th |
Master Ward Identity for Nonlocal Symmetries in D=2 Principal Chiral
Models: We derive, in path integral approach, the (anomalous) master Ward identity
associated with an infinite set of nonlocal conservation laws in
two-dimensional principal chiral models | hep-th |
Gauging spacetime inversions in quantum gravity: Spacetime inversion symmetries such as parity and time reversal play a
central role in physics, but they are usually treated as global symmetries. In
quantum gravity there are no global symmetries, so any spacetime inversion
symmetries must be gauge symmetries. In particular this includes
$\mathcal{CRT}$ symmetry (in even dimensions usually combined with a rotation
to become $\mathcal{CPT}$), which in quantum field theory is always a symmetry
and seems likely to be a symmetry of quantum gravity as well. In this article
we discuss what it means to gauge a spacetime inversion symmetry, and we
explain some of the more unusual consequences of doing this. In particular we
argue that the gauging of $\mathcal{CRT}$ is automatically implemented by the
sum over topologies in the Euclidean gravity path integral, that in a closed
universe the Hilbert space of quantum gravity must be a real vector space, and
that in Lorentzian signature manifolds which are not time-orientable must be
included as valid configurations of the theory. In particular we give an
example of an asymptotically-AdS time-unorientable geometry which must be
included to reproduce computable results in the dual CFT. | hep-th |
Semiclassical partition function for strings dual to Wilson loops with
small cusps in ABJM: We compute the 1-loop partition function for strings in
$AdS_4\times\mathbb{CP}^3$, whose worldsheets end along a line with small cusp
angles in the boundary of AdS. We obtain these 1-loop results in terms of the
vacuum energy for on-shell modes. Our results verify the proposal by Lewkowycz
and Maldacena in arXiv:1312.5682 for the exact Bremsstrahlung function up to
the next to leading order in the strong coupling expansion. The agreement is
observed for cusps distorting either the 1/2 BPS or the 1/6 BPS Wilson line. | hep-th |
Abrikosov String in N=2 Supersymmetric QED: We study the Abrikosov-Nielsen-Olesen string in N=2 supersymmetric QED with
N=2-preserving superpotential, in which case the Abrikosov string is found to
be 1/2-BPS saturated. Adding a quadratic small perturbation in the
superpotential breaks N=2 supersymmetry to N=1 supersymmetry. Then the
Abrikosov string is no longer BPS saturated. The difference between the string
tensions for the non-BPS and BPS saturated situation is found to be negative to
the first order of the perturbation parameter. | hep-th |
Quasimodular instanton partition function and the elliptic solution of
Korteweg-de Vries equations: The Gauge/Bethe correspondence relates Omega-deformed N=2 supersymmetric
gauge theories to some quantum integrable models, in simple cases the
integrable models can be treated as solvable quantum mechanics models. For
SU(2) gauge theory with an adjoint matter, or with 4 fundamental matters, the
potential of corresponding quantum model is the elliptic function. If the mass
of matter takes special value then the potential is an elliptic solution of KdV
hierarchy. We show that the deformed prepotential of gauge theory can be
obtained from the average densities of conserved charges of the classical KdV
solution, the UV gauge coupling dependence is assembled into the Eisenstein
series. The gauge theory with adjoint mass is taken as the example. | hep-th |
Erasure of Strings and Vortexes: The interaction of defects can lead to a phenomenon of erasure. During this
process, a lower-dimensional object gets absorbed and dissolved by a
higher-dimensional one. The phenomenon is very general and has a wide range of
implications, both cosmological and fundamental. In particular, all types of
strings, such as cosmic strings, QCD flux tubes, or fundamental strings, get
erased when encountering a defect, either solitonic or a $D$-brane that
deconfines their fluxes. This leads to a novel mechanism of cosmic string
break-up, accompanied by gravitational and electromagnetic radiations. The
arguments based on loss of coherence and the entropy count suggest that the
erasure probability is very close to one, and strings never make it through the
deconfining layer. We confirm this by a numerical simulation of the system,
which effectively captures the essence of the phenomenon: a $2+1$-dimensional
problem of interaction between a Nielsen-Olesen vortex of a $U(1)$ Higgs model
and a domain wall inside which the $U(1)$ gauge group is unHiggsed and the
magnetic flux is deconfined. In accordance with the entropy argument, in our
simulation, the vortex never makes it across the wall. | hep-th |
Subleading-color contributions to gluon-gluon scattering in N=4 SYM
theory and relations to N=8 supergravity: We study the subleading-color (nonplanar) contributions to the four-gluon
scattering amplitudes in N=4 supersymmetric SU(N) Yang-Mills theory. Using the
formalisms of Catani and of Sterman and Tejeda-Yeomans, we develop explicit
expressions for the infrared-divergent contributions of all the
subleading-color L-loop amplitudes up to three loops, and make some conjectures
for the IR behavior for arbitrary L. We also derive several intriguing
relations between the subleading-color one- and two-loop four-gluon amplitudes
and the four-graviton amplitudes of N=8 supergravity. The exact one- and
two-loop N=8 supergravity amplitudes can be expressed in terms of the one- and
two-loop N-independent N=4 SYM amplitudes respectively, but the natural
generalization to higher loops fails, despite having a simple interpretation in
terms of the 't Hooft picture. We also find that, at least through two loops,
the subleading-color amplitudes of N=4 SYM theory have uniform
transcendentality (as do the leading-color amplitudes). Moreover, the N=4 SYM
Catani operators, which express the IR-divergent contributions of loop
amplitudes in terms of lower-loop amplitudes, are also shown to have uniform
transcendentality, and to be the maximum transcendentality piece of the QCD
Catani operators. | hep-th |
Lorentz-violating Chern-Simons action under high temperature in massless
QED: Lorentz and CPT violating QED with massless fermions at finite temperature is
studied. We show that there is no ambiguity in the induced coefficient of the
Chern-Simons-like term that defines the so-called Carroll-Field-Jackiw model at
high temperature. We also show that this system constitutes an example where
the breaking of CPT and Lorentz symmetries is more severe at high temperature
than in the zero temperature case thus precluding any naive expectations of
Lorentz symmetry restoration. | hep-th |
Null Vectors in Logarithmic Conformal Field Theory: The representation theory of the Virasoro algebra in the case of a
logarithmic conformal field theory is considered. Here, indecomposable
representations have to be taken into account, which has many interesting
consequences. We study the generalization of null vectors towards the case of
indecomposable representation modules and, in particular, how such logarithmic
null vectors can be used to derive differential equations for correlation
functions. We show that differential equations for correlation functions with
logarithmic fields become inhomogeneous. | hep-th |
Patterns of gauge symmetry in the background field method: The correlation functions of Yang-Mills theories formulated in the background
field method satisfy linear Slavnov-Taylor identities, which are naive
generalizations of simple tree level relations, with no deformations
originating from the ghost sector of the theory. In recent years, a stronger
version of these identities has been found to hold at the level of the
background gluon self-energy, whose transversality is enforced separately for
each special block of diagrams contributing to the gluon Schwinger-Dyson
equation. In the present work we demonstrate by means of explicit calculations
that the same distinct realization of the Slavnov-Taylor identity persists in
the case of the background three-gluon vertex. The analysis is carried out at
the level of the exact Schwinger-Dyson equation for this vertex, with no
truncations or simplifying assumptions. The demonstration entails the
contraction of individual vertex diagrams by the relevant momentum, which
activates Slavnov-Taylor identities of vertices and multi-particle kernels
nested inside these graphs; the final result emerges by virtue of a multitude
of extensive cancellations, without the need of performing explicit
integrations. In addition, we point out that background Ward identities amount
to replacing derivatives of propagators by zero-momentum background-gluon
insertions, in exact analogy to standard properties of Abelian gauge theories.
Finally, certain potential applications of these results are briefly discussed. | hep-th |
Dynamical realizations of l-conformal Newton-Hooke group: The method of nonlinear realizations and the technique previously developed
in arXiv:1208.1403 are used to construct a dynamical system without higher
derivative terms, which holds invariant under the l-conformal Newton-Hooke
group. A configuration space of the model involves coordinates, which
parametrize a particle moving in d spatial dimensions and a conformal mode,
which gives rise to an effective external field.The dynamical system describes
a generalized multi-dimensional oscillator, which undergoes
accelerated/decelerated motion in an ellipse in accord with evolution of the
conformal mode. Higher derivative formulations are discussed as well. It is
demonstrated that the multi-dimensional Pais-Uhlenbeck oscillator enjoys the
l=3/2-conformal Newton-Hooke symmetry for a particular choice of its
frequencies. | hep-th |
Yang-Mills and Born-Infeld actions on finite group spaces: Discretized nonabelian gauge theories living on finite group spaces G are
defined by means of a geometric action \int Tr F\wedge *F . This technique is
extended to obtain a discrete version of the Born-Infeld action. | hep-th |
Quasi-normal modes of dyonic black holes and magneto-hydrodynamics: We revisit the magneto-hydrodynamics in (2+1) dimensions and confirm that it
is consistent with the quasi-normal modes of the (3+1) dimensional dyonic black
holes in the most general set-up with finite density, magnetic field and wave
vector. We investigate all possible modes (sound, shear, diffusion, cyclotron
etc.) and their interplay. For the magneto-hydrodynamics we perform a complete
and detailed analysis correcting some prefactors in the literature, which is
important for the comparison with quasi-normal modes. For the quasi-normal mode
computations in holography we identify the independent fluctuation variables of
the dyonic black holes, which is nontrivial at finite density and magnetic
field. As an application of the quasi-normal modes of the dyonic black holes we
investigate a transport property, the diffusion constant. We find that the
diffusion constant at finite density and magnetic field saturates the lower
bound at low temperature. We show that this bound can be understood from the
pole-skipping point. | hep-th |
Statical Structures of the BCS-like Holographic Superfluid in AdS4
Spacetime: We investigate in detail the m^{2}=0 Abelian Higgs model in AdS4, which is
considered as the holographic dual of the most BCS-like superfluid. In
homogeneous and isotropic superfluid solutions, we calculate the sound speeds,
square of which approaches to 1/2 with increasing chemical potential (lowering
temperature). Then we present the single dark soliton solutions, which becomes
thinner with increasing chemical potential. For the first time, we also find
the interesting double and triple dark soliton solutions, which is unexpected
and shows the possibility of more complicated static configurations. Finally,
we investigate vortex solutions. For winding number n=1, the vortex becomes
thinner with increasing chemical potential. At a given chemical potential, with
increasing winding number, firstly the vortex becomes bigger and the charge
density depletion becomes larger, then the charge density depletion settles
down at a certain value and the growth of the vortex size is found to obey a
scaling symmetry. | hep-th |
A paucity of bulk entangling surfaces: AdS wormholes with de Sitter
interiors: We study and construct spacetimes, dubbed planar AdS-dS-wormholes, satisfying
the null energy condition and having two asymptotically AdS boundaries
connected through a (non-traversable) inflating wormhole. As for other
wormholes, it is natural to expect dual descriptions in terms of two
disconnected CFTs in appropriate entangled states. But for our cases certain
expected bulk entangling surfaces used by the Hubeny-Rangamani-Takayanagi (HRT)
prescription to compute CFT entropy do not exist. In particular, no real
codimension-2 extremal surface can run from one end of the wormhole to the
other. According to HRT, the mutual information between any two finite-sized
subregions (one in each CFT) must then vanish at leading order in large $N$ --
though the leading-order mutual information per unit area between the two CFTs
taken as wholes may be nonzero. Some planar AdS-dS-wormholes also fail to have
plane-symmetric surfaces that would compute the total entropy of either CFT. We
suggest this to remain true of less-symmetric surfaces so that the HRT entropy
is ill-defined and some modified prescription is required. It may be possible
to simply extend HRT or the closely-related maximin construction by a limiting
procedure, though complex extremal surfaces could also play an important role. | hep-th |
Cosmological String Backgrounds from Gauged WZW Models: We discuss the four-dimensional target-space interpretation of bosonic
strings based on gauged WZW models, in particular of those based on the
non-compact coset space $SL(2,{\bf R})\times SO(1,1)^2 /SO(1,1)$. We show that
these theories lead, apart from the recently broadly discussed black-hole type
of backgrounds, to cosmological string backgrounds, such as an expanding
Universe. Which of the two cases is realized depends on the sign of the level
of the corresponding Kac-Moody algebra. We discuss various aspects of these new
cosmological string backgrounds. | hep-th |
Renormalization Group Flows on D3 branes at an Orbifolded Conifold: We consider D3-branes at an orbifolded conifold whose horizon ${X_5}$
resolves into a smooth Einstein manifold which joins several copies of ${\bf
T}^{1,1}$. We describe in details the resolution of the singular horizon
${X_5}$ and describe different types of two-cycles appearing in the resolution.
For a large number of D3 branes, the AdS/CFT conjecture becomes a duality
between type IIB string theory on $AdS_5 \times {X_5} $ and the ${\cal N} = 1$
field theory living on the D3 branes. We study the fractional branes as small
perturbations of the string background and we reproduce the logarithmic flow of
field theory couplings by studying fluxes of NS-NS and R-R two forms through
different 2-cycles of the resolved horizon. | hep-th |
An upper bound on transport: The linear growth of operators in local quantum systems leads to an effective
lightcone even if the system is non-relativistic. We show that consistency of
diffusive transport with this lightcone places an upper bound on the
diffusivity: $D \lesssim v^2 \tau_\text{eq}$. The operator growth velocity $v$
defines the lightcone and $\tau_\text{eq}$ is the local equilibration
timescale, beyond which the dynamics of conserved densities is diffusive. We
verify that the bound is obeyed in various weakly and strongly interacting
theories. In holographic models this bound establishes a relation between the
hydrodynamic and leading non-hydrodynamic quasinormal modes of planar black
holes. Our bound relates transport data --- including the electrical
resistivity and the shear viscosity --- to the local equilibration time, even
in the absence of a quasiparticle description. In this way, the bound sheds
light on the observed $T$-linear resistivity of many unconventional metals, the
shear viscosity of the quark-gluon plasma and the spin transport of unitary
fermions. | hep-th |
EFT and the SUSY Index on the 2nd Sheet: The counting of BPS states in four-dimensional ${\cal N}=1$ theories has
attracted a lot of attention in recent years. For superconformal theories,
these states are in one-to-one correspondence with local operators in various
short representations. The generating function for this counting problem has
branch cuts and hence several Cardy-like limits, which are analogous to
high-temperature limits. Particularly interesting is the second sheet, which
has been shown to capture the microstates and phases of supersymmetric black
holes in AdS$_5$. Here we present a 3d Effective Field Theory (EFT) approach to
the high-temperature limit on the second sheet. We use the EFT to derive the
behavior of the index at orders $\beta^{-2},\beta^{-1},\beta^0$. We also make a
conjecture for $O(\beta)$, where we argue that the expansion truncates up to
exponentially small corrections. An important point is the existence of vector
multiplet zero modes, unaccompanied by massless matter fields. The runaway of
Affleck-Harvey-Witten is however avoided by a non-perturbative confinement
mechanism. This confinement mechanism guarantees that our results are robust. | hep-th |
TCFHs, IIB warped AdS backgrounds and hidden symmetries: We present the twisted covariant form hierarchies (TCFHs) on the internal
spaces of all type IIB warped AdS backgrounds. As a result we demonstrate that
the form bilinears on the internal spaces satisfy a generalisation of the
conformal Killing-Yano equation. We also explore some of the properties of the
TCFHs, like for example the holonomy of the TCFH connections. In addition, we
present examples where the form bilinears generate hidden symmetries for
particle probes propagating on the internal spaces of some AdS backgrounds.
These include the maximally supersymmetric AdS$_5$ solution as well as some of
the near horizon geometries of intersecting IIB branes. | hep-th |
Quantizations of D=3 Lorentz symmetry: Using the isomorphism
$\mathfrak{o}(3;\mathbb{C})\simeq\mathfrak{sl}(2;\mathbb{C})$ we develop a new
simple algebraic technique for complete classification of quantum deformations
(the classical $r$-matrices) for real forms $\mathfrak{o}(3)$ and
$\mathfrak{o}(2,1)$ of the complex Lie algebra $\mathfrak{o}(3;\mathbb{C})$ in
terms of real forms of $\mathfrak{sl}(2;\mathbb{C})$: $\mathfrak{su}(2)$,
$\mathfrak{su}(1,1)$ and $\mathfrak{sl}(2;\mathbb{R})$. We prove that the $D=3$
Lorentz symmetry
$\mathfrak{o}(2,1)\simeq\mathfrak{su}(1,1)\simeq\mathfrak{sl}(2;\mathbb{R})$
has three different Hopf-algebraic quantum deformations which are expressed in
the simplest way by two standard $\mathfrak{su}(1,1)$ and
$\mathfrak{sl}(2;\mathbb{R})$ $q$-analogs and by simple Jordanian
$\mathfrak{sl}(2;\mathbb{R})$ twist deformations. These quantizations are
presented in terms of the quantum Cartan-Weyl generators for the quantized
algebras $\mathfrak{su}(1,1)$ and $\mathfrak{sl}(2;\mathbb{R})$ as well as in
terms of quantum Cartesian generators for the quantized algebra
$\mathfrak{o}(2,1)$. Finaly, some applications of the deformed $D=3$ Lorentz
symmetry are mentioned. | hep-th |
Is dark energy from cosmic Hawking radiation?: It is suggested that dark energy is the energy of the Hawking radiation from
a cosmic horizon. Despite of its extremely low Gibbons-Hawking temperature,
this radiation could have the appropriate magnitude $O(M_P^2 H^2)$ and the
equation of state to explain the observed cosmological data if there is a
Planck scale UV-cutoff, where $H$ is the Hubble parameter. | hep-th |
Excitation Spectra of Spin Models constructed from Quantized Affine
Algebras of type $B_n^{(1)}$, $D_n^{(1)}$: The energy and momentum spectrum of the spin models constructed from the
vector representation of the quantized affine algebras of type $\B$ and $\D$
are computed using the approach of Davies et al. \cite{DFJMN92}. The results
are for the anti-ferromagnetic (massive) regime, and they agree with the mass
spectrum found from the factorized S--matrix theory by Ogievetsky et al.
\cite{ORW87}. The other new result is the explicit realization of the fusion
construction for the quantized affine algebras of type $\B$ and $\D$.} | hep-th |
Supersymmetry and the Atiyah-Singer Index Theorem I: Peierls Brackets,
Green's Functions, and a Supersymmetric Proof of the Index Theorem: The Peierls bracket quantization scheme is applied to the supersymmetric
system corresponding to the twisted spin index theorem. A detailed study of the
quantum system is presented, and the Feynman propagator is exactly computed.
The Green's function methods provide a direct derivation of the index formula.
Note: This is essentially a new SUSY proof of the index theorem. | hep-th |
Shifted Homotopy Analysis of the Linearized Higher-Spin Equations in
Arbitrary Higher-Spin Background: Analysis of the first-order corrections to higher-spin equations is extended
to homotopy operators involving shift parameters with respect to the spinor $Y$
variables, the argument of the higher-spin connection $\omega(Y)$ and the
argument of the higher-spin zero-form $C(Y)$. It is shown that a relaxed
uniform $(y+p)$-shift and a shift by the argument of $\omega(Y)$ respect the
proper form of the free higher-spin equations and constitute a one-parametric
class of vertices that contains those resulting from the conventional (no
shift) homotopy. A pure shift by the argument of $\omega(Y)$ is shown not to
affect the one-form higher-spin field $W$ in the first order and, hence, the
form of the respective vertices. | hep-th |
Nilpotent Spinor Symmetry with Interacting Spin 3/2 Field: Consistent interactions of spin 3/2 field that realize a nilpotent spinorial
symmetry are presented. Based on our previous results on purely bosonic
non-Abelian tensor with consistent interactions, we present a new system for
interacting spin 3/2 field that realizes the nilpotent fermionic symmetry. | hep-th |
Positivity bounds on effective field theories with spontaneously broken
Lorentz invariance: We derive positivity bounds on EFT coefficients in theories where boosts are
spontaneously broken. We employ the analytic properties of the retarded Green's
function of conserved currents (or of the stress-energy tensor) and assume the
theory becomes conformal in the UV. The method is general and applicable to
both cosmology and condensed matter systems. As a concrete example, we look at
the EFT of conformal superfluids which describes the universal low-energy
dynamics of CFT's at large chemical potential and we derive inequalities on the
coefficients of the operators, in three dimensions, at NLO and NNLO. | hep-th |
Derivation of theories: structures of the derived system in terms of
those of the original system in classical mechanics: We present the technique of derivation of a theory to obtain an
$(n+1)f$-degrees-of-freedom theory from an $f$-degrees-of-freedom theory and
show that one can calculate all of the quantities of the derived theory from
those of the original one. Specifically, we show that one can use this
technique to construct, from an integrable system, other integrable systems
with more degrees of freedom. | hep-th |
Revisiting toric SU(3) structures: Three-dimensional smooth compact toric varieties (SCTV) admit SU(3)
structures, and may thus be relevant for string compactifications, if they have
even first Chern class (c1). This condition can be fulfilled by infinitely many
SCTVs, including CP3 and CP1 bundles over all two-dimensional SCTVs. We show
that as long as c1 is even, toric SU(3) structures can be constructed using a
method proposed in arXiv:1005.2194. We perform a systematic study of the
parametric freedom of the resulting SU(3) structures, with a particular focus
on the metric and the torsion classes. Although metric positivity constrains
the SU(3) parameters, we find that every SCTV admits several toric SU(3)
structures and that parametric choices can sometimes be made to match
requirements of string vacua. We also provide a short review on the constraints
that an SU(3) structure must meet to be relevant for four-dimensional,
maximally symmetric N=1 or N=0 string vacua. | hep-th |
UV-finite scalar field theory with unitarity: In this paper we show how to define the UV completion of a scalar field
theory such that it is both UV-finite and perturbatively unitary. In the UV
completed theory, the propagator is an infinite sum of ordinary propagators. To
eliminate the UV divergences, we choose the coefficients and masses in the
propagator to satisfy certain algebraic relations, and define the infinite sums
involved in Feynman diagram calculation by analytic continuation. Unitarity can
be proved relatively easily by Cutkosky's rules. The theory is equivalent to
infinitely many particles with specific masses and interactions. We take the
$\phi^4$ theory as an example and demonstrate our idea through explicit Feynman
diagram computation. | hep-th |
2-Group Symmetries and their Classification in 6d: We uncover 2-group symmetries in 6d superconformal field theories. These
symmetries arise when the discrete 1-form symmetry and continuous flavor
symmetry group of a theory mix with each other. We classify all 6d
superconformal field theories with such 2-group symmetries. The approach taken
in 6d is applicable more generally, with minor modifications to include
dimension specific operators (such as instantons in 5d and monopoles in 3d),
and we provide a discussion of the dimension-independent aspects of the
analysis. We include an ancillary mathematica code for computing 2-group
symmetries, once the dimension specific input is provided. We also discuss a
mixed 't Hooft anomaly between discrete 0-form and 1-form symmetries in 6d. | hep-th |
The spectral problem of the ABJ Fermi gas: The partition function on the three-sphere of ABJ theory can be rewritten
into a partition function of a non-interacting Fermi gas, with an accompanying
one-particle Hamiltonian. We study the spectral problem defined by this
Hamiltonian. We determine the exact WKB quantization condition, which involves
quantities from refined topological string theory, and test it successfully
against numerical calculations of the spectrum. | hep-th |
Partial duality in SU(N) Yang-Mills theory: Recently we have proposed a set of variables for describing the infrared
limit of four dimensional SU(2) Yang-Mills theory. here we extend these
variables to the general case of four dimensional SU(N) Yang-Mills theory. We
find that the SU(N) connection A decomposes according to irreducible
representations of SO(N-1) and the curvature two-form F is related to the
symplectic Kirillov two forms that characterize irreducible representations of
SU(N). We propose a general class of nonlinear chiral models that may describe
stable, soliton-like configurations with nontrivial topological numbers. | hep-th |
Regge trajectories of the charged string in a magnetic background: The set of Casimir operators associated with the global symmetries of a
charged string in a constant magnetic background are found. It is shown that
the string rest energy can be expressed as a combination of these invariants.
Using this result, the Regge trajectories of the system are derived. The first
Regge trajectory is given by a family of infinitely many parallel
straight-lines, one for each spin projection along the magnetic field. | hep-th |
Nonlinear ${\cal N}=2$ Supersymmetry and 3D Supersymmetric Born-Infeld
Theory: D$p$-branes acquire effective nonlinear descriptions whose bosonic part is
related to the Born-Infeld action. This nonlinearity has been proven to be a
consequence of the partial ${\cal N}=2\to{\cal N}=1$ supersymmetry breaking,
originating from the solitonic nature of the branes. In this work, we focus on
the effective descriptions of D2-branes. Using the Goldstone multiplet
interpretation of the action and the method of nilpotent ${\cal N}=2$
superfields, we construct the 3D, ${\cal N}=1$ superspace effective action
which makes the first supersymmetry manifest and realizes the second,
spontaneously broken, supersymmetry nonlinearly. We show that there are two
such supersymmetric extensions of the 3D Born-Infeld action which correspond to
the dynamics of the 3D Maxwell-Goldstone multiplet and the 3D projection of the
Tensor-Goldstone multiplet respectively. Moreover, we demonstrate that these
results are derived by applying the constrained superfield approach on the
${\cal N}=2, D=3$ vector and chiral multiplets after expanding them around a
nontrivial vacuum. We find that these two descriptions are related by a duality
transformation which results in the inversion of a dimensionless parameter. For
both descriptions we derive the explicit bosonic and fermionic parts of the 3D
super Born-Infeld action. Finally, consider the deformation of the
Maxwell-Goldstone superspace action by the characteristic Chern-Simons-like,
gauge invariant, mass term. | hep-th |
Two-charge rotating black holes in four-dimensional gauged supergravity: We obtain an asymptotically AdS, non-extremal, electrically charged and
rotating black hole solution of 4-dimensional U(1)^4 gauged supergravity with 2
non-zero and independent U(1) charges. The thermodynamical quantities are
computed. We find BPS solutions that are nakedly singular. The solution is
generalized to include a NUT parameter and dyonic gauge fields. The string
frame metric has a rank-2 Killing-Stackel tensor and has completely integrable
geodesic motion, and the massless Klein-Gordon equation separates for the
Einstein frame metric. | hep-th |
Toroidal Compactification Without Vector Structure: Many important ideas about string duality that appear in conventional $\T^2$
compactification have analogs for $\T^2$ compactification without vector
structure. We analyze some of these issues and show, in particular, how
orientifold planes associated with $Sp(n)$ gauge groups can arise from
T-duality and how they can be interpreted in F-theory. We also, in an appendix,
resolve a longstanding puzzle concerning the computation of $\Tr (-1)^F$ in
four-dimensional supersymmetric Yang-Mills theory with gauge group SO(n). | hep-th |
Boundary K-matrix for the quantum Mikhailov-Shabat model: ( We present complete solutions of $K$-matrix for the quantum
Mikhailov-Shabat model. It has been known that there are three diagonal
solutions with no free parameters, one being trivial identity solution, the
others non-trivial. The most general solutions which we found consist of three
families corresponding to each diagonal solutions. One family of solutions
depends on two arbitrary parameters. If one of the parameters vanishes, the
other must also vanish so that the solutions reduces to trivial identity
solution. The other two families for each non-trivial diagonal solutions have
only one arbitrary parameter.) | hep-th |
Massive Spin-2 Scattering and Asymptotic Superluminality: We place model-independent constraints on theories of massive spin-2
particles by considering the positivity of the phase shift in eikonal
scattering. The phase shift is an asymptotic $S$-matrix observable, related to
the time delay/advance experienced by a particle during scattering. Demanding
the absence of a time advance leads to constraints on the cubic vertices
present in the theory. We find that, in theories with massive spin-2 particles,
requiring no time advance means that either: (i) the cubic vertices must appear
as a particular linear combination of the Einstein-Hilbert cubic vertex and an
$h_{\mu\nu}^3$ potential term or (ii) new degrees of freedom or strong coupling
must enter at parametrically the mass of the massive spin-2 field. These
conclusions have implications for a variety of situations. Applied to theories
of large-$N$ QCD, this indicates that any spectrum with an isolated massive
spin-2 at the bottom must have these particular cubic self-couplings. Applied
to de Rham-Gabadadze-Tolley massive gravity, the constraint is in accord with
and generalizes previous results obtained from a shockwave calculation: of the
two free dimensionless parameters in the theory there is a one parameter line
consistent with a subluminal phase shift. | hep-th |
Off-shell unimodular N=1, d=4 supergravity: We formulate a unimodular N=1, d=4 supergravity theory off shell. We see that
the infinitesimal Grassmann parameters defining the unimodular supergravity
transformations are constrained and show that the conmutator of two
infinitesinal unimodular supergravity transformations closes on transverse
diffeomorphisms, Lorentz transformations and unimodular supergravity
transformations. Along the way, we also show that the linearized theory is a
supersymmetric theory of gravitons and gravitinos. We see that de Sitter and
anti-de Sitter spacetimes are non-supersymmetric vacua of our unimodular
supergravity theory. | hep-th |
The Concept of Particle Weights in Local Quantum Field Theory: The concept of particle weights has been introduced by Buchholz and the
author in order to obtain a unified treatment of particles as well as (charged)
infraparticles which do not permit a definition of mass and spin according to
Wigner's theory. Particle weights arise as temporal limits of physical states
in the vacuum sector and describe the asymptotic particle content. Following a
thorough analysis of the underlying notion of localizing operators, we give a
precise definition of this concept and investigate the characteristic
properties. The decomposition of particle weights into pure components which
are linked to irreducible representations of the quasi-local algebra has been a
long-standing desideratum that only recently found its solution. We set out two
approaches to this problem by way of disintegration theory, making use of a
physically motivated assumption concerning the structure of phase space in
quantum field theory. The significance of the pure particle weights ensuing
from this disintegration is founded on the fact that they exhibit features of
improper energy-momentum eigenstates, analogous to Dirac's conception, and
permit a consistent definition of mass and spin even in an infraparticle
situation. | hep-th |
BV-Structure of the Cohomology of Nilpotent Subalgebras and the Geometry
of (W-) Strings: Given a simple, simply laced, complex Lie algebra $\bfg$ corresponding to the
Lie group $G$, let $\bfnp$ be the subalgebra generated by the positive roots.
In this paper we construct a BV-algebra $\fA[\bfg]$ whose underlying graded
commutative algebra is given by the cohomology, with respect to $\bfnp$, of the
algebra of regular functions on $G$ with values in $\mywedge
(\bfnp\backslash\bfg)$. We conjecture that $\fA[\bfg]$ describes the algebra of
{\it all} physical (i.e., BRST invariant) operators of the noncritical
$\cW[\bfg]$ string. The conjecture is verified in the two explicitly known
cases, $\bfg=\sltw$ (the Virasoro string) and $\bfg=\slth$ (the $\cW_3$
string). | hep-th |
Correlation functions on a curved background: We investigate gravitational correlation functions in a curved background
with the help of nonperturbative renormalization group methods. Beta functions
for eleven couplings are derived, two of which correspond to running gauge
parameters. A unique ultraviolet fixed point is found, suitable for a UV
completion in the sense of Asymptotic Safety. To arrive at a well-behaved flow
in a curved background, the regularization must be chosen carefully. We provide
two admissible choices to solve this issue in the present approximation. We
further demonstrate by an explicit calculation that the Landau limit is a fixed
point also for quantum gravity, and additionally show that in this limit, the
gauge parameter $\beta$ does not flow. | hep-th |
Multidimensional Dirac strings and the Witten index of SYMCS theories
with groups of higher rank: We discuss generalized Dirac strings associated with a given Lie group. They
live in r-dimensional complex space (r being the rank of the group). Such
strings show up in the effective Born-Oppenheimer Hamiltonian for 3d
supersymmetric Yang-Mills-Chern-Simons theories, brought up by the gluon loops.
We calculate accurately the number of the vacuum states in the effective
Hamiltonian associated with these strings. We also show that these states are
irrelevant for the final SYMCS vacuum counting. The Witten index of SYMCS
theories depends thus only on the strings generated by fermion loops and
carrying fractional generalized fluxes. | hep-th |
Witten Diagrams for Torus Conformal Blocks: We give a holographic description of global conformal blocks in two
dimensional conformal field theory on the sphere and on the torus. We show that
the conformal blocks for one-point functions on the torus can be written as
Witten diagrams in thermal AdS. This is accomplished by deriving a general
conformal Casimir equation for global conformal blocks, and showing that Witten
diagrams obey the same equation. We study the semi-classical limit of n-point
conformal blocks, and show that these equal the action of a network of bulk
world-lines obeying appropriate geodesic equations. We give an alternate
description in the Chern-Simons formulation of 3D gravity, where the conformal
blocks are described by networks of Wilson lines, and argue that these
formulations are equivalent. | hep-th |
Solutions of massive gravity theories in constant scalar invariant
geometries: We solve massive gravity field equations in the framework of locally
homogenous and vanishing scalar invariant (VSI) Lorentzian spacetimes, which in
three dimensions are the building blocks of constant scalar invariant (CSI)
spacetimes. At first, we provide an exhaustive list of all Lorentzian
three-dimensional homogeneous spaces and then we determine the Petrov type of
the relevant curvature tensors. Among these geometries we determine for which
values of their structure constants they are solutions of the field equations
of massive gravity theories with cosmological constant. The homogeneous
solutions founded are of all various Petrov types : I_C, I_R, II, III, D_t,
D_s, N, O; the VSI geometries which we found are of Petrov type III. The Petrov
types II and III are new explicit CSI spacetimes solutions of these types. We
also examine the conditions under which the obtained anti-de Sitter solutions
are free of tachyonic massive graviton modes. | hep-th |
Fractional space-like branes: We discuss construction and applications of instanton-like objects which we
call fractional space-like branes. These objects are localised at a fixed point
of a time-like (or more generally space-time) orbifold which is a string
theoretical toy model of a cosmological singularity. We formulate them in
boundary state, adsorption, and fermionisation approaches. | hep-th |
Fermionic quantization of Hopf solitons: In this paper we show how to quantize Hopf solitons using the
Finkelstein-Rubinstein approach. Hopf solitons can be quantized as fermions if
their Hopf charge is odd. Symmetries of classical minimal energy configurations
induce loops in configuration space which give rise to constraints on the wave
function. These constraints depend on whether the given loop is contractible.
Our method is to exploit the relationship between the configuration spaces of
the Faddeev-Hopf and Skyrme models provided by the Hopf fibration. We then use
recent results in the Skyrme model to determine whether loops are contractible.
We discuss possible quantum ground states up to Hopf charge Q=7. | hep-th |
Some aspects of self-duality and generalised BPS theories: If a scalar field theory in (1+1) dimensions possesses soliton solutions
obeying first order BPS equations, then, in general, it is possible to find an
infinite number of related field theories with BPS solitons which obey closely
related BPS equations. We point out that this fact may be understood as a
simple consequence of an appropriately generalised notion of self-duality. We
show that this self-duality framework enables us to generalize to higher
dimensions the construction of new solitons from already known solutions. By
performing simple field transformations our procedure allows us to relate
solitons with different topological properties. We present several interesting
examples of such solitons in two and three dimensions. | hep-th |
Symmetry Breaking in Coupled SYK or Tensor Models: We study a large $N$ tensor model with $O(N)^3$ symmetry containing two
flavors of Majorana fermions, $\psi_1^{abc}$ and $\psi_2^{abc}$. We also study
its random counterpart consisting of two coupled Sachdev-Ye-Kitaev models, each
one containing $N_{\rm SYK}$ Majorana fermions. In these models we assume
tetrahedral quartic Hamiltonians which depend on a real coupling parameter
$\alpha$. We find a duality relation between two Hamiltonians with different
values of $\alpha$, which allows us to restrict the model to the range of
$-1\leq \alpha\leq 1/3$. The scaling dimension of the fermion number operator
$Q=i\psi_1^{abc} \psi_2^{abc}$ is complex and of the form $1/2 +i f(\alpha)$ in
the range $-1\leq \alpha<0$, indicating an instability of the conformal phase.
Using Schwinger-Dyson equations to solve for the Green functions, we show that
in the true low-temperature phase this operator acquires an expectation value.
This demonstrates the breaking of an anti-unitary particle-hole symmetry and
other discrete symmetries. We also calculate spectra of the coupled SYK models
for values of $N_{\rm SYK}$ where exact diagonalizations are possible. For
negative $\alpha$ we find a gap separating the two lowest energy states from
the rest of the spectrum; this leads to exponential decay of the
zero-temperature correlation functions. For $N_{\rm SYK}$ divisible by $4$, the
two lowest states have a small splitting. They become degenerate in the large
$N_{\rm SYK}$ limit, as expected from the spontaneous breaking of a
$\mathbb{Z}_2$ symmetry. | hep-th |
Axion Inflation in Type II String Theory: Inflationary models driven by a large number of axion fields are discussed in
the context of type IIB compactifications with N=1 supersymmetry. The inflatons
arise as the scalar modes of the R-R two-forms evaluated on vanishing
two-cycles in the compact geometry. The vanishing cycles are resolved by small
two-volumes or NS-NS B-fields which sit together with the inflatons in the same
supermultiplets. String world-sheets wrapping the vanishing cycles correct the
metric of the R-R inflatons. They can help to generate kinetic terms close to
the Planck scale and a mass hierarchy between the axions and their non-axionic
partners during inflation. At small string coupling, D-brane corrections are
subleading in the metric of the R-R inflatons. However, an axion potential can
be generated by D1 instantons or gaugino condensates on D5 branes. Models with
sufficiently large number of axions admit regions of chaotic inflation which
can stretch over the whole axion field range for potentials from gaugino
condensates. These models could allow for a possibly detectable amount of
gravitational waves with tensor to scalar ratio as high as r<0.14. | hep-th |
Exact partition functions for the $Ω$-deformed $\mathcal N=2^{*}$
$SU(2)$ gauge theory: We study the low energy effective action of the $\Omega$-deformed $\mathcal N
=2^{*}$ $SU(2) $ gauge theory. It depends on the deformation parameters
$\epsilon_{1},\epsilon_{2}$, the scalar field expectation value $a$, and the
hypermultiplet mass $m$. We explore the plane $(\frac{m}{\epsilon_{1}},
\frac{\epsilon_{2}}{\epsilon_{1}})$ looking for special features in the
multi-instanton contributions to the prepotential, motivated by what happens in
the Nekrasov-Shatashvili limit $\epsilon_{2}\to 0$. We propose a simple
condition on the structure of poles of the $k$-instanton prepotential and show
that it is admissible at a finite set of points in the above plane. At these
special points, the prepotential has poles at fixed positions independent on
the instanton number. Besides and remarkably, both the instanton partition
function and the full prepotential, including the perturbative contribution,
may be given in closed form as functions of the scalar expectation value $a$
and the modular parameter $q$ appearing in special combinations of Eisenstein
series and Dedekind $\eta$ function. As a byproduct, the modular anomaly
equation can be tested at all orders at these points. We discuss these special
features from the point of view of the AGT correspondence and provide explicit
toroidal 1-blocks in non-trivial closed form. The full list of solutions with
1, 2, 3, and 4 poles is determined and described in details. | hep-th |
Superstrings on AdS3 at k=1: We study superstring theory in three dimensional Anti-de Sitter spacetime
with NS-NS flux, focusing on the case where the radius of curvature is equal to
the string length. This corresponds to the critical level k=1 in the
Wess-Zumino-Witten description. Previously, it was argued that a transition
takes place at this special radius, from a phase dominated by black holes at
larger radius to one dominated by long strings at smaller radius. We argue that
the infinite tower of modes that become massless at k=1 is a signal of this
transition. We propose a simple two-dimensional conformal field theory as the
holographic dual to superstring theory at k=1. As evidence for our conjecture,
we demonstrate that at large N our putative dual exactly reproduces the full
spectrum of the long strings of the weakly coupled string theory, including
states unprotected by supersymmetry. | hep-th |
Quantum Wilson surfaces and topological interactions: We introduce the description of a Wilson surface as a 2-dimensional
topological quantum field theory with a 1-dimensional Hilbert space. On a
closed surface, the Wilson surface theory defines a topological invariant of
the principal $G$-bundle $P \to \Sigma$. Interestingly, it can interact
topologically with 2-dimensional Yang-Mills and BF theories modifying their
partition functions. We compute explicitly the partition function of the
2-dimensional Yang-Mills theory with a Wilson surface. The Wilson surface turns
out to be nontrivial for the gauge group $G$ non-simply connected (and trivial
for $G$ simply connected). In particular we study in detail the cases
$G=SU(N)/\mathbb{Z}_m$, $G=Spin(4l)/(\mathbb{Z}_2\oplus\mathbb{Z}_2)$ and
obtain a general formula for any compact connected Lie group. | hep-th |
Role of Various Entropies in the Black Hole Information Loss Problem: In a recent paper Hawking has argued that there is no information loss in
black holes in asymptotically AdS spacetimes. We remind that there are several
types of information (entropy) in statistical physics -- fine grained
(microscopic) and coarse grained (macroscopic) ones which behave differently
under unitary evolution. We suggest that the coarse grained information of the
rest of the Universe is lost while fine grained information is preserved. A
possibility to develop in quantum gravity an analogue of the Bogoliubov
derivation of the irreversible Boltzmann and Navier - Stokes equations from the
reversible mechanical equations is discussed. | hep-th |
Computation of D-brane instanton induced superpotential couplings -
Majorana masses from string theory: We perform a detailed conformal field theory analysis of D2-brane instanton
effects in four-dimensional type IIA string vacua with intersecting D6-branes.
In particular, we explicitly compute instanton induced fermion two-point
couplings which play the role of perturbatively forbidden Majorana mass terms
for right-handed neutrinos or MSSM mu-terms. These results can readily be
extended to higher-dimensional operators. In concrete realizations of such
non-perturbative effects, the Euclidean D2-brane has to wrap a rigid,
supersymmetric cycle with strong constraints on the zero mode structure. Their
implications for Type IIA compactifications on the T^6/(Z_2 x Z_2) orientifold
with discrete torsion are analyzed. We also construct a local supersymmetric
GUT-like model allowing for a class of Euclidean D2-branes whose fermionic zero
modes meet all the constraints for generating Majorana masses in the
phenomenologically allowed regime. Together with perturbatively realized Dirac
masses, these non-perturbative couplings give rise to the see-saw mechanism. | hep-th |
Quantum Fluctuations of Effective Fields and the Correspondence
Principle: The question of Bohr correspondence in quantum field theory is considered
from a dynamical point of view. It is shown that the classical description of
particle interactions is inapplicable even in the limit of large particles'
masses because of finite quantum fluctuations of the fields produced. In
particular, it is found that the relative value of the root mean square
fluctuation of the Coulomb and Newton potentials of a massive particle is equal
to 1/sqrt{2}. It is shown also that in the case of a macroscopic body, the
quantum fluctuations are suppressed by a factor 1/sqrt{N}, where N is the
number of particles in the body. An adequate macroscopic interpretation of the
correspondence principle is given. | hep-th |
The Role of Conformal Symmetry in Abelian Bosonization of the Massive
Thirring Model: We show equivalence between the massive Thirring model and the sine-Gordon
theory by gauge fixing a wider gauge invariant theory in two different ways.
The exact derivation of the equivalence hinges on the existence of an
underlying conformal symmetry. Previous derivations were all perturbative in
mass (althought to all orders). | hep-th |
The Local Structure of Anomaly Inflow: Anomaly cancellation for M-theory fivebranes requires the introduction of a
"bump-form" which smoothes out the five-brane source. We discuss the physical
origin of this bump-form in the simpler case of axion strings in 3+1 dimensions
and construct it in terms of the radial profile of the fermion zero modes. Our
treatment allows for a clearer understanding of the role played by covariant
rather than consistent anomalies when anomalies are canceled by inflow from the
bulk. We briefly discuss the generalization of these results to fivebrane
anomalies in M theory. | hep-th |
Crystal bases and three-dimensional $ \mathcal{N}=4 $ Coulomb branches: We establish and develop a correspondence between certain crystal bases
(Kashiwara crystals) and the Coulomb branch of three-dimensional $ \mathcal{N}
=4 $ gauge theories. The result holds for simply-laced, non-simply laced and
affine quivers. Two equivalent derivations are given in the non-simply laced
case, either by application of the axiomatic rules or by folding a simply-laced
quiver. We also study the effect of turning on real masses and the ensuing
simplification of the crystal. We present a multitude of explicit examples of
the equivalence. Finally, we put forward a correspondence between infinite
crystals and Hilbert spaces of theories with isolated vacua. | hep-th |
Consistent boundary conditions for cosmological topologically massive
gravity at the chiral point: We show that cosmological topologically massive gravity at the chiral point
allows not only Brown-Henneaux boundary conditions as consistent boundary
conditions, but slightly more general ones which encompass the logarithmic
primary found in 0805.2610 as well as all its descendants. | hep-th |
Universal Thermal Corrections to Symmetry-Resolved Entanglement Entropy
and Full Counting Statistics: We consider the symmetry-resolved R\'{e}nyi and entanglement entropies for
two-dimensional conformal field theories on a circle at nonzero temperature. We
assume a unique ground state with a nonzero mass gap induced by the system's
finite size and then calculate the leading corrections to the contributions of
individual charge sectors in a low-temperature expansion. Besides the size of
the mass gap and the degeneracy of the first excited state, these universal
corrections depend only on the four-point correlation function of the primary
fields. We also obtain thermal corrections to the full counting statistics of
the ground state and define the \textit{probability fluctuations} function. It
scales as $e^{-2 \pi \Delta_{\psi} \beta /L}$, where $\Delta_{\psi}$ is the
scaling dimension of the lowest weight states. As an example, we explicitly
evaluate the thermal corrections to the symmetry-resolved entanglement entropy
and FCS for the spinless fermions. | hep-th |
Nonextremal black holes in gauged supergravity and the real formulation
of special geometry II: In arXiv:1207.2679 a new prescription for finding nonextremal black hole
solutions to N=2, D=4 Fayet-Iliopoulos gauged supergravity was presented, and
explicit solutions of various models containing one vector multiplet were
constructed. Here we use the same method to find new nonextremal black holes to
more complicated models. We also provide a general recipe to construct non-BPS
extremal solutions for an arbitrary prepotential, as long as an axion-free
condition holds. These follow from a set of first-order conditions, and are
related to the corresponding supersymmetric black holes by a multiplication of
the charge vector with a constant field rotation matrix S. The fake
superpotential driving this first-order flow is nothing else than Hamilton's
characteristic function in a Hamilton-Jacobi formalism, and coincides in the
supersymmetric case (when S is plus or minus the identity) with the
superpotential proposed by Dall'Agata and Gnecchi in arXiv:1012.3756. For the
nonextremal black holes that asymptote to (magnetic) AdS, we compute both the
mass coming from holographic renormalization and the one appearing in the
superalgebra. The latter correctly vanishes in the BPS case, but also for
certain values of the parameters that do not correspond to any known
supersymmetric solution of N=2 gauged supergravity. We finally show that the
product of all horizon areas depends only on the charges and the asymptotic
value of the cosmological constant. | hep-th |
Domain Walls and Decay Rate of the Excited Vacua in the Large N
Yang-Mills Theory: In the (non-supersymmetric) Yang-Mills theory in the large N limit there
exists an infinite set of non-degenerate vacua. The distinct vacua are
separated by domain walls whose tension determines the decay rate of the false
vacua. I discuss the phenomenon from a field-theoretic point of view, starting
from supersymmetric gluodynamics and then breaking supersymmetry, by
introducing a gluino mass. By combining previously known results, the decay
rate of the excited vacua is estimated, \Gamma \sim \exp (-const \times N^4).
The fourth power of N in the exponent is a consequence of the fact that the
wall tension is proportional to N. | hep-th |
On the Geometry on Antisymmetric Fields: The geometry of antisymmetric fields with nontrivial transitions over a base
manifold is described in terms of exact sequences of cohomology groups. This
formulation leads naturally to the appearance of nontrivial topological charges
associated to the periods of the curvature of the antisymmetric fields. The
relation between the partition functions of dual theories is carefully studied
under the most general assumptions, and new topological factors related to zero
modes and the Ray Singer torsion are found. | hep-th |
Equivalence of A-Maximization and Volume Minimization: The low energy effective theory on a stack of D3-branes at a Calabi-Yau
singularity is an $\mathcal{N} = 1$ quiver gauge theory. The AdS/CFT
correspondence predicts that the strong coupling dynamics of the gauge theory
is described by weakly coupled type IIB supergravity on $AdS_5 \times L^5,$
where $L^5$ is a Sasaki-Einstein manifold. Recent results on Calabi-Yau
algebras efficiently determine the Hilbert series of any superconformal quiver
gauge theory. We use the Hilbert series to determine the volume of the horizon
manifold in terms of the fields of the quiver gauge theory. One corollary of
the AdS/CFT conjecture is that the volume of the horizon manifold $L^5$ is
inversely proportional to the a-central charge of the gauge theory. By direct
comparison of the volume determined from the Hilbert series and the a-central
charge, this prediction is proved independently of the AdS/CFT conjecture. | hep-th |
AdS twistors for higher spin theory: We construct spectra of supersymmetric higher spin theories in D=4, 5 and 7
from twistors describing massless (super-)particles on AdS spaces. A massless
twistor transform is derived in a geometric way from classical kinematics.
Relaxing the spin-shell constraints on twistor space gives an infinite tower of
massless states of a ``higher spin particle'', generalising previous work of
Bandos et al. This can generically be done in a number of ways, each defining
the states of a distinct higher spin theory, and the method provides a
systematic way of finding these. We reproduce known results in D=4, minimal
supersymmetric 5- and 7-dimensional models, as well as supersymmetrisations of
Vasiliev's Sp-models as special cases. In the latter models a dimensional
enhancement takes place, meaning that the theory lives on a space of higher
dimension than the original AdS space, and becomes a theory of doubletons. This
talk was presented at the XIXth Max Born Symposium ``Fundamental Interactions
and Twistor-Like Methods'', September 2004, in Wroclaw, Poland. | hep-th |
Derivative Expansion of the Effective Action for QED in 2+1 and 3+1
dimensions: The derivative expansion of the one-loop effective action in QED$_3$ and
QED$_4$ is considered. The first term in such an expansion is the effective
action for a constant electromagnetic field. An explicit expression for the
next term containing two derivatives of the field strength $F_{\mu\nu}$, but
exact in the magnitude of the field strength, is obtained. The general results
for fermion and scalar electrodynamics are presented. The cases of pure
electric and pure magnetic external fields are considered in details. The
Feynman rules for the perturbative expansion of the one-loop effective action
in the number of derivatives is developed. | hep-th |
On the Mutual Information in Hawking Radiation: We compute the mutual information of two Hawking particles emitted
consecutively by an evaporating black hole. Following Page, we find that the
mutual information is of order exp(-S) where S is the entropy of the black
hole. We speculate on implications for black hole unitarity, in particular on a
possible failure of locality at large distances. | hep-th |
On Classical de Sitter Vacua in String Theory: We review the prospect of obtaining tree-level de Sitter (dS) vacua and
slow-roll inflation models in string compactifications. Restricting ourselves
to the closed string sector and assuming the absence of NSNS-sources, we
classify the minimal classical ingredients that evade the simplest no-go
theorems against dS vacua and inflation. Spaces with negative integrated
curvature together with certain combinations of low-dimensional orientifold
planes and low-rank RR-fluxes emerge as the most promising setups of this
analysis. We focus on two well-controlled classes that lead to an effective 4D,
N=1 supergravity description: Type IIA theory on group or coset manifolds with
SU(3)-structure and O6-planes, as well as type IIB compactifications on
SU(2)-structure manifolds with O5- and O7-planes. While fully stabilized AdS
vacua are generically possible, a number of problems encountered in the search
for dS vacua are discussed. | hep-th |
A method for solve integrable $A_2$ spin chains combining different
representations: A non homogeneous spin chain in the representations $ \{3 \}$ and $ \{3^*\}$
of $A_2$ is analyzed. We find that the naive nested Bethe ansatz is not
applicable to this case. A method inspired in the nested Bethe ansatz, that can
be applied to more general cases, is developed for that chain. The solution for
the eigenvalues of the trace of the monodromy matrix is given as two coupled
Bethe equations different from that for a homogeneous chain. A conjecture about
the form of the solutions for more general chains is presented.
PACS: 75.10.Jm, 05.50+q 02.20 Sv | hep-th |
Isotropic Lifshitz Scaling in four dimensions: The presence of isotropic Lifshitz points for a O(N)-symmetric scalar theory
is investigated with the help of the Functional Renormalization Group. In
particular, at the supposed lower critical dimension d=4, evidence for a
continuous line of fixed points is found for the O(2) theory, and the observed
structure presents clear similarities with the properties observed in the
2-dimensional Berezinskii-Kosterlitz-Thouless phase. | hep-th |
Abelian Zero Modes in Odd Dimensions: We show that the Loss-Yau zero modes of the 3d abelian Dirac operator may be
interpreted in a simple manner in terms of a stereographic projection from a 4d
Dirac operator with a constant field strength of definite helicity. This is an
alternative to the conventional viewpoint involving Hopf maps from S^3 to S^2.
Furthermore, our construction generalizes in a straightforward way to any odd
dimension. The number of zero modes is related to the Chern-Simons number in a
nonlinear manner. | hep-th |
A differential relation between the energy and electric charge of a dyon: The differential relation between the energy and electric charge of a dyon is
derived. The relation expresses the derivative of the energy with respect to
the electric charge in terms of the boundary value for the temporal component
of the dyon's electromagnetic potential. The use of the Hamiltonian formalism
and transition to the unitary gauge make it possible to show that this
derivative is proportional to the phase frequency of the electrically charged
massive gauge fields forming the dyon's core. It follows from the differential
relation that the energy and electric charge of the non-BPS dyon cannot be
arbitrarily large. Finally, the dyon's properties are investigated numerically
at different values of the model parameters. | hep-th |
RR charges of D2-branes in the WZW model: We consider the contribution of the B-field into the RR charge of a spherical
D2-brane. Extending a recent analysis of Taylor, we show that the boundary and
bulk contributions do not cancel in general. Instead, they add up to an integer
as observed by Stanciu. The general formula is applied to compute the RR
charges of spherical D-branes of the SU(2) WZW model at level k and it shows
that these RR charges are only defined modulo k+2. We support this claim by
studying bound state formation of D0-branes using boundary conformal field
theory. | hep-th |
Topology and geometry of elliptic Feynman amplitudes: We report on the analytic computation of the 2-loop amplitude for Bhabha
scattering in QED. We study the analytic structure of the amplitude, and reveal
its underlying connections to hyperbolic Coxeter groups and arithmetic
geometries of elliptic curves. | hep-th |
The Geometer's Toolkit to String Compactifications: These lecture notes are meant to serve as an introduction to some geometric
constructions and techniques (in particular the ones of toric geometry) often
employed by the physicist working on string theory compactifications. The
emphasis is wholly on the geometry side, not on the physics.
The treated topics include toroidal orbifolds, methods of toric geometry,
desinglularization of toroidal orbifolds and their orientifold quotients. | hep-th |
Exact late time Hawking radiation and the information loss problem for
evaporating near-extremal black holes: In this paper we investigate the effects of gravitational backreaction for
the late time Hawking radiation of evaporating near-extremal black holes. This
problem can be studied within the framework of an effective one-loop solvable
model on AdS_2. We find that the Hawking flux goes down exponentially and it is
proportional to a parameter which depends on details of the collapsing matter.
This result seems to suggest that the information of the initial state is not
lost and that the boundary of AdS_2 acts, at least at late times, as a sort of
stretched horizon in the Reissner-Nordstrom spacetime. | hep-th |
On quantum mechanics as constrained N=2 supersymmetric classical
mechanics: The Schr\"odinger equation is shown to be equivalent to a constrained
Liouville equation under the assumption that phase space is extended to
Grassmann algebra valued variables. For onedimensional systems, the underlying
Hamiltonian dynamics has a N=2 supersymmetry. Potential applications to more
realistic theories are briefly discussed. | hep-th |
Quantized Nambu-Poisson Manifolds in a 3-Lie Algebra Reduced Model: We consider dimensional reduction of the Bagger-Lambert-Gustavsson theory to
a zero-dimensional 3-Lie algebra model and construct various stable solutions
corresponding to quantized Nambu-Poisson manifolds. A recently proposed Higgs
mechanism reduces this model to the IKKT matrix model. We find that in the
strong coupling limit, our solutions correspond to ordinary noncommutative
spaces arising as stable solutions in the IKKT model with D-brane backgrounds.
In particular, this happens for S^3, R^3 and five-dimensional Neveu-Schwarz
Hpp-waves. We expand our model around these backgrounds and find effective
noncommutative field theories with complicated interactions involving
higher-derivative terms. We also describe the relation of our reduced model to
a cubic supermatrix model based on an osp(1|32) supersymmetry algebra. | hep-th |
The Lifshitz black branes and DC transport coefficients in massive
Einstein-Maxwell-dilaton gravity: We construct analytical Lifshitz massive black brane solutions in massive
Einstein-Maxwell-dilaton gravity theory. We also study the thermodynamics of
these black brane solutions and obtain the thermodynamical stability
conditions. On the dual nonrelativistic boundary field theory with Lifshitz
symmetry, we analytically compute the DC transport coefficients, including the
electric conductivity, thermoelectric conductivity, and thermal conductivity.
The novel property of our model is that the massive term supports the Lifshitz
black brane solutions with $z\neq 1$ in such a way that the DC transport
coefficients in the dual field theory are finite. We also find that the
Wiedemann-Franz law in this dual boundary field theory is violated, which
indicates that it may involve strong interactions. | hep-th |
S-duality transformation of $\mathcal{N}$ $=4$ SYM theory at the
operator level: We consider the S-duality transformation of gauge invariant operators and
states in $\mathcal{N}$ $=4$ SYM theory. The transformation is realized through
an operator $ S $ which is the $ SL(2,Z) $ canonical transformation in loop
space with the gauge invariant electric and the magnetic flux operators
composing the canonical variables. Based on $ S $, S-duals for all of the
physical operators and states can be defined. The criterion for the theory to
be S-duality invariant is that the superconformal charges and their S-duals
differ by a $ U(1)_{Y} $ phase. The verification can be done by checking the S
transformation for supersymmetry and special supersymmetry variations of the
loop operators. The fact that supercharges preserved by BPS Wilson operators
and the S-dual BPS 't Hooft operators differ by a $4d $ chiral rotation could
in some sense serve as a proof. | hep-th |
A finite model of two-dimensional ideal hydrodynamics: A finite-dimensional su($N$) Lie algebra equation is discussed that in the
infinite $N$ limit (giving the area preserving diffeomorphism group) tends to
the two-dimensional, inviscid vorticity equation on the torus. The equation is
numerically integrated, for various values of $N$, and the time evolution of an
(interpolated) stream function is compared with that obtained from a simple
mode truncation of the continuum equation. The time averaged vorticity moments
and correlation functions are compared with canonical ensemble averages. | hep-th |
Gauge Theory on Twisted $κ$-Minkowski: Old Problems and Possible
Solutions: We review the application of twist deformation formalism and the construction
of noncommutative gauge theory on $\kappa$-Minkowski space-time. We compare two
different types of twists: the Abelian and the Jordanian one. In each case we
provide the twisted differential calculus and consider ${U}(1)$ gauge theory.
Different methods of obtaining a gauge invariant action and related
problems are thoroughly discussed. | hep-th |
Gauge Symmetry Enhancement by Wilson Lines in Twisted Compactification: We point out a simple realization of gauge symmetry enhancement by Wilson
lines in QFT with twisted compactification in extra dimensions. We illustrate
this in the field contents taken from heterotic supergravity in arbitrary
dimensions toroidally compactified. | hep-th |
The Seven-sphere and its Kac-Moody Algebra: We investigate the seven-sphere as a group-like manifold and its extension to
a Kac-Moody-like algebra. Covariance properties and tensorial composition of
spinors under $S^7$ are defined. The relation to Malcev algebras is
established. The consequences for octonionic projective spaces are examined.
Current algebras are formulated and their anomalies are derived, and shown to
be unique (even regarding numerical coefficients) up to redefinitions of the
currents. Nilpotency of the BRST operator is consistent with one particular
expression in the class of (field-dependent) anomalies. A Sugawara construction
is given. | hep-th |
Holographic Representation of Local Operators In De Sitter Space: Assuming the existence of the dS/CFT correspondence, we construct local
scalar fields with $m^2>\left( \frac{d}{2} \right)^2$ in de Sitter space by
smearing over conformal field theory operators on the future/past boundary. To
maintain bulk micro-causality and recover the bulk Wightman function in the
Euclidean vacuum, the smearing prescription must involve two sets of
single--trace operators with dimensions $\Delta$ and $d-\Delta$. Thus the local
operator prescription in de Sitter space differs from the analytic continuation
from the prescription in anti--de Sitter space. Pushing a local operator in the
global patch to future/past infinity is shown to lead to an operator relation
between single--trace operators in conformal field theories at
$\mathcal{I}^\pm$, which can be interpreted as a basis transformation, also
identified as the relation between an operator in CFT and its shadow operator.
Construction of spin$-s$ gauge field operators is discussed, it is shown that
the construction of higher spin gauge fields in de Sitter space is equivalent
to constructing scalar fields with specific values of mass parameter
$m^2<\left( \frac{d}{2} \right)^2$. An acausal higher spin bulk operator which
matches onto boundary higher spin current is constructed. Implementation of the
scalar operator constructions in AdS and dS with embedding formalism is briefly
described. | hep-th |
Exploring the Tensor Networks/AdS Correspondence: In this paper we study the recently proposed tensor networks/AdS
correspondence. We found that the Coxeter group is a useful tool to describe
tensor networks in a negatively curved space. Studying generic tensor network
populated by perfect tensors, we find that the physical wave function
generically do not admit any connected correlation functions of local
operators. To remedy the problem, we assume that wavefunctions admitting such
semi-classical gravitational interpretation are composed of tensors close to,
but not exactly perfect tensors. Computing corrections to the connected two
point correlation functions, we find that the leading contribution is given by
structures related to geodesics connecting the operators inserted at the
boundary physical dofs. Such considerations admit generalizations at least to
three point functions. This is highly suggestive of the emergence of the
analogues of Witten diagrams in the tensor network. The perturbations alone
however do not give the right entanglement spectrum. Using the Coxeter
construction, we also constructed the tensor network counterpart of the BTZ
black hole, by orbifolding the discrete lattice on which the network resides.
We found that the construction naturally reproduces some of the salient
features of the BTZ black hole, such as the appearance of RT surfaces that
could wrap the horizon, depending on the size of the entanglement region A. | hep-th |
Spatial correlations of primordial density fluctuations in the standard
cosmological model: We revisit the {\it origin of structures problem} of standard
Friedmann-Robertson-Walker cosmology to point out an unjustified approximation
in the prevalent analysis. We follow common procedures in statistical mechanics
to revise the issue without the disputed approximation. Our conclusions
contradict the current wisdom and reveal and unexpected scenario for the origin
of primordial cosmological structures. We show that standard physics operating
in the cosmic plasma during the radiation dominated expansion of the universe
produce at the time of decoupling scale invariant density anisotropies over
cosmologically large comoving volumes. Scale invariance is shown to be a direct
consequence of the causality constrains imposed by the short FRW comoving
horizon at decoupling, which strongly suppress the power spectrum of density
fluctuations with cosmologically large comoving wavelength. The global
amplitude of these cosmological density anisotropies is fixed by the power
spectrum in comoving modes whose wavelength is shorter than the causal horizon
at the time and can be comparable to the amplitude of the primordial
cosmological inhomogeneities imprinted in the cosmic microwave background
radiation. | hep-th |
Faddeev-Jackiw formalism for a topological-like oscillator in planar
dimensions: The problem of a harmonic oscillator coupling to an electromagnetic potential
plus a topological-like (Chern-Simons) massive term, in two-dimensional space,
is studied in the light of the symplectic formalism proposed by Faddeev and
Jackiw for constrained systems. | hep-th |
Superconformal Sigma Models in Higher Than Two Dimensions: Rigidly superconformal sigma models in higher than two dimensions are
constructed. These models rely on the existence of conformal Killing spinors on
the $p+1$ dimensional worldvolume $(p\le 5)$, and homothetic conformal Killing
vectors in the $d$--dimensional target space. In the bosonic case, substituting
into the action a particular form of the target space metric admitting such
Killing vectors, we obtain an action with manifest worldvolume conformal
symmetry, which describes the coupling of $d-1$ scalars to a conformally flat
metric on the worldvolume. We also construct gauged sigma models with
worldvolume conformal supersymmetry. The models considered here are
generalizations of the singleton actions on $S^p\times S^1$, constructed
sometime ago by Nicolai and these authors. | hep-th |
Anisotropic Asymptotics and High Energy Scattering: Recently E.Verlinde and H.Verlinde have suggested an effective
two-dimensional theory describing the high-energy scattering in QCD. In this
report we attempt to clarify some issues of this suggestion. We consider {\it
anisotropic asymptotics} of correlation functions for scalar and gauge theories
in four dimensions. Anisotropic asymptotics describe behaviour of correlation
functions when some components of coordinates are large as compare with others
components. It is occurred that (2+2) anisotropic asymptotics for 4-points
functions are related with the well known Regge regime of scattering
amplitudes. We study an expansion of correlation functions with respect to the
rescaling parameter $\lambda$ over a part of variables (anisotropic
$\lambda$-expansion). An effective theory describing the anisotropic limit of
free scalar field contains two 2 dim conformal theories. One of them is a
conformal theory in configuration space and another one is a conformal theory
in momentum space. In some special cases ,in particular for the Wilson line
correlators in gauge theories, the leading term of the anisotropic expansion
involves only one of the conformal theories and it can be described by an
effective theory with an action being a dimensional reduction of the original
action. | hep-th |
Fermions with spin 1/2 as global SO(3) vortices: In this paper we show that the nontrivial fundamental group $\pi_1 SO(3)
={\Bbb Z}_2$ for the group SO(3) of global proper rotations of a
four-dimensional Euclidian space (when a spin structure is introduced
preliminarily in that space) implies always fermions as global SO(3) vortices,
while bosons can be reduced to trivial lines (contracted into a point) in the
SO(3) group space. | hep-th |
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