Vectorial AdS/CFT and quantum higher spins

We will review recent work on  computing one-loop corrections
of quantum higher spins fields  in AdS  spaces
and   corresponding   tests  of vectorial  AdS/CFT  duality.
Part of this talk will be based on arXiv:1410.3273, arXiv:1412.0489

Refining Generalized Entropy

The Ryu-Takayanagi proposal in AdS/CFT hints to a deep role of
entanglement entropy in the mechanism of holography. Lewkowycz and
Maldacena have given a derivation of this proposal in a construction called
"generalized entropy". The ingredients of generalized entropy are Euclidean
quantum gravity and the replica trick in the dual theory. I will review the
original construction and some recent refinements of it. These refinements
(1) still use the replica trick, but drop the assumption of replica
symmetry---thus showing that Ryu-Takayangi follows independently from it;
and (2) are essential for the construction to work away from the general
relativity limit of holography.

Quantum entanglement and local excitations

Excitations in the form of local operators can be characterised from the perspective of quantum entanglement. I will describe the framework and results that illustrate this.
I will then show how local excitations above the thermal state describe a particle falling into a black hole and how to obtain the scrambling time in AdS/CFT.

Scaling in quantum quench and holography

In recent years the problem of quantum quench in the vicinity of
critical points  has been investigated using holographic methods. This
has led to an understanding of decoupling of length scales in the
dynamics of slow quench and the emergence of Kibble-Zurek scaling,
and provided predictions for corrections to the leading scaling
behavior. In the other limit, holographic calculations have led to the
discovery of new scaling laws for fast quench, which have been
subsequently shown to be generic properties of deformations  of any
conformal field theory regardless of holography. This talk will
discuss the salient aspects of this development.

OPE coefficients, string field theory vertex and integrability

One of the key open problems in solving N=4 Super-Yang-Mills theory
is the determination of OPE coefficients. We are searching for a framework
which could, in principle, serve to determine the OPE coefficients
at any value of the coupling. One such framework might be the
string field theory vertex which up till now could be determined
only for a free worldsheet theory. In this talk I will describe
a novel approach to the string field theory vertex which
should be applicable for any interacting but integrable worldsheet
theory.

QGP time formation in holographic shock waves model of heavy ion collisions

We estimate the thermalization time in two colliding shock waves
holographic model of heavy-ion collisions. For this purpose  we model the
process by  the Vaidya metric with a horizon defined by the trapped surface
location. We consider two bottom-up AdS/QCD models that give, within the
colliding shock waves approach,   the dependence of multiplicity on the
energy compatible with RHIC and LHC results.
One model is a bottom-up AdS/QCD confining model and the other is related
to an anisotropic thermalization. We estimate the thermalization time and
show that increasing the confining potential  decreases   the
thermalization time as well as an  anisotropy  accelerates the
thermalization.

Defect formation beyond Kibble-Zurek mechanism and holography

We study the dynamic after a smooth quench across a continuous transition from the disordered phase to the ordered phase. Based on scaling ideas, linear response and the
spectrum of unstable modes, we develop a theoretical framework, valid for any second order phase transition, for the early-time evolution of the condensate in the broken phase. Our analysis unveils a novel period of non-adiabatic evolution after the system passes through the phase transition, where a parametrically large amount of coarsening occurs before a well-defined condensate forms. Our formalism predicts a rate of defect formation parametrically smaller than the Kibble-Zurek prediction and yields a criterion for the break-down of Kibble-Zurek scaling for sufficiently fast quenches. We numerically test our formalism for a thermal quench in a 2 + 1 dimensional holographic superfluid.

Anomalies, Chern-Simons Terms and Black Hole Entropy

Recently, the hydrodynamic limit of the systems with quantum anomalies has been actively investigated, together with its holographic description by gravitational theories with Chern-Simons terms. In this presentation, I will start with a brief review on some recent results related to the anomalies in the hydrodynamic limit, and then reproduce these results systematically by using the dual gravitational description. In particular, I will explain the crucial roles of the anomaly polynomials there. I will also discuss the implication of our analysis to microscopic entropy counting for black holes in higher dimensions.

Phases of Strong interactions: lattice results

QCD with Nf fundamental fermions has a rich phase structure which has been studied with analytic and numerical studies. I present recent lattice studies for Nf ranging from zero to twelve,  at zero and nonzero temperature. The results, which include the critical number of flavor, the approach to the conformal window and the nature of the thermal transition, are amenable to interesting comparisons with holographic analysis.

Black brane steady states

I will present the evolution of black brane solutions in the presence of a fixed spatial gradient of temperature until the formation of a steady state. The energy density and energy flux of the resulting steady state in the boundary theory are compared with the conjectured behaviour of steady states in conformal field theories. Very good agreement is found.

Aspects of entanglement of/between disjoint regions in CFT and holography

Mutual information and logarithmic negativity are important quantities to understand entanglement in pure and mixed states. In quantum field theories they are computed by employing a method based on the replica limit. We present a numerical method to compute the holographic mutual information in AdS4 for generic shapes and another numerical method to address the replica limit that turns out to be useful whenever the replica limit is not known analytically, like for the entanglement entropy of disjoint intervals in 2D CFTs. We also discuss the logarithmic negativity at finite temperature in 2D CFTs.

A Caveat for Applied Holography

After a brief review of holographic techniques derived from the
AdS-CFT correspondence, we specialize to a class of spacetimes proposed as
duals to non-relativistic systems. We highlight classical and quantum
features of these "Lifshitz spacetimes" which limit the reconstructability
of bulk spacetime information from boundary data.

Vacuum Alignment in Holographic Graphene

Somewhat inspired by graphene in which 2+1d Dirac fermions couple to strongly coupled 3+1d QED I investigate the D3/probe D5 holographic system. A magnetic field induces fermion condensation on the probe and there is a complex temperature vs chemical potential phase structure including a BKT transition at zero T with mu. The transition can be phenomenologically distorted into various non-mean field transitions.  When two layers are introduced an additional dynamical mass generation can occur with condensation of fermions between different layers. With a B field a dynamical vacuum alignment problem results and we investigate the phase structure. In the presence of chemical potential as well it is possible to realize a phase with both condensation mechanisms present. Finally I consider how to describe the holographic graphene between two mirrors that compactify the gauge theory mimicing ideas for how real graphene could be made more strongly coupled in the lab. Condensation with the mirror graphene sheet is possible and a complex phase struture again results.

Coulomb Branch Hilbert Series and the Moduli Space of Instantons

The moduli space of k G instantons on C^2, where G is a classical gauge group, has a well known HyperKahler quotient formulation known as the ADHM construction. The extension to exceptional groups is an open problem. In string theory this is realized using a system of branes, and the moduli space of instantons is identified with the Higgs branch of a particular supersymmetric gauge theory with 8 supercharges. A less known, and less studied aspect of moduli spaces of instantons is that they can be realized as the Coulomb branch of a supersymmetric gauge theory in 2+1 dimensions with 8 supercharges.
Recent developments on the understanding of the Coulomb branch gives us a nice solution to the problem where G is an exceptional group, thus allowing a systematic study of these moduli spaces. I will discuss these developments, and present the corresponding quivers, and the Coulomb branch Hilbert Series - the main tool which lead to the recent progress.

Exact results in supersymmetric field theories and holography

I will discuss some exact results in four dimensional supersymmetric field theories. After reviewing supersymmetric field theories on curved manifolds and the technique of localization, I will focus on the index and the Casimir energy in curved space. I will conclude discussing the holographic counterpart of these results and open problems. The talk will be based on results obtained during the last year as well as a paper recently submitted to the arxive.

2d N=(2,2) supersymmetry on curved space and localization on spheres

In this talk I will present exact results for two-dimensional N=(2,2) supersymmetric gauge theories, which can be used to study string compactifications on Calabi-Yau manifolds exactly in alpha". I will review the basic properties of these theories, explain how they can be formulated on curved space backgrounds, and finally present localisation formulas for their path integrals on two different supersymmetric backgrounds on the 2-sphere.

Universal identity in second order fluid dynamics

In 2008, Haack and Yarom demonstrated that there exists a relation
between second order transport coefficients which holds universally
for strongly interacting conformal fluids with gravity duals to
leading order in supergravity approximation. Later, Bigazzi and
Cotrone showed that the relation also holds for non-conformal
holographic liquids to leading order in the parameter of the
non-conformal deformation. We show that at least in some examples the
identity remains valid when higher-derivative corrections are taken
into account.

Renormalised 3-point functions in CFT

I will present a first principles analysis of the constraints of conformal invariance in momentum space. In particular, I will derive the form of the 3-point functions of scalar operators, conserved currents and the energy momentum tensor in momentum space and discuss renormalization and associated anomalies.

New 6d superconformal models from string theory, and their compactifications

I will describe three infinite classes of analytic AdS_d solutions in
massive IIA string theory, for d=7,5,4. The AdS7 solutions are conjectured
to be dual to a family of  (1,0)-supersymmetric CFT6’s living on an
NS5-D6-D8 system. The AdS5 and AdS4 classes are dual to twisted
compactifications of these (1,0) theories; their metrics and fluxes can be
obtained by a simple universal map from the AdS7 ones. I will then mention
an F-theoretical extension of the 6d CFT’s, which as a byproduct suggests
the existence of “fractional M5-branes”.

Superconformal Quantum Mechanics and Light Front Holographic QCD

An effective QCD light-front Hamiltonian for mesons and baryons is constructed from generalized supercharges of a superconformal algebra. The introduction of a scale inside the algebra fixes completely the light-front potential from a common general principle. The method can be applied in two formally very similar, but physically distinct ways. On one hand the supercharges can transform the different chiral components of the baryons into each other, on the other hand the positive chiral component of a baryon can be related with a meson wave function. With this construction the striking similarities between meson and baryon spectroscopy are explained. In particular the pion/b1 trajectory is identified as the superpartner of the nucleon trajectory. The lowest-lying state, however, on this trajectory, the pi-meson, is massless in the chiral limit and has no supersymmetric partner. Some preliminary results for the case of explicit breaking of conformal symmetry by (large) quark masses are presented.

Black holes in the 1/D expansion

When the number of dimensions is very large, the gravitational field of a black hole is strongly localized near the horizon. Therefore in this limit the black hole can be effectively identified with a surface in an empty background geometry. The Einstein equations determines the effective equations that this "black hole surface" must satisfy. When the black hole is static, they are the same as the equations for soap films. I will describe how this new effective theory of black holes can be used to solve for non-trivial black hole geometries in a very efficient way.

String-brane collisions: tidal excitations and time delays

We review some recent work on the high-energy scattering of a closed string
on a stack of D-branes. We first discuss the (tidal) excitation of the massive
string modes and show that the inelastic transition amplitudes are all given
by the matrix elements of a particularly simple operator, the eikonal operator.
We then analyze the time delay of the string-brane scattering process and show
that the potential causality violations due to higher-derivative corrections to
the Einstein-Hilbert action recently pointed out by Camanho et al. do not occur
in string theory as a consequence of its Regge behaviour.

Boost-invariant flow on non-conformal plasmas

I will report on a generalization of the Bjorken flow, a solution of
hydrodynamics under the assumption of boost-invariance, whose dual gravity solution was found by Janik and Peschanski, to a class of non-conformal theories described by
an Einstein+dilaton  model in the bulk. The results could be relevant to the thermalization of the quark-gluon plasma of QCD.

Ward identities and transport in 2+1 dimensions

 The Hall viscosity of chiral superfluids is determined by the angular
momentum density. One can understand and generalize this relation using
Ward identities of the energy-momentum tensor. Furthermore, the same
identities connect viscosities and conductivities. A preliminary analysis
in  AdS/CFT reveals that the identities seem to be non-trivial in the sense
that they cannot be derived simply from the asymptotic expansion of the
solutions.

Instabilities of finite density SYM theories from holography

Gauge field configurations carrying instanton number on the
worldvolume of probe branes on the geometry of a stack of Dp-branes are
dual to scalar operators with non-trivial vacuum expectation values in
supersymmetric Yang-Mills theories. This configurations do not change the
free energy of the theory and therefore describe a moduli space: the Higgs
branch. In the presence of a large charge density the background geometry
changes, and the moduli space is lifted. We will investigate whether in the
probe limit the configurations with non-trivial VEVs of the scalar
operators are energetically preferred and signal an instability of the
setup to a phase with condensation.