Understanding the phases of string theory in the strong curvature and high temperature regime, which is inaccessible to the field theory approximation, may provide insights about the physics of the very early Universe. Cosmological solutions can be described at the perturbative string level, arising as quantum or thermal instabilities of an initially flat background. Two major obstacles that typically prevent a perturbative treatment of the backreaction are the Hagedorn/tachyonic divergences that occur in such strong curvature and/or high temperature regions and the initial gravitational singularity (Big Bang), that always appears in the field theory approach. In this talk, I will present recent progress in tackling these problems within the framework of perturbative string theory. In particular, I will consider a special toy model whose high degree of symmetry may help uncover the stringy mechanism that protects the cosmological evolution from Hagedorn or gravitational type singularities.

Abstract: There has recently been considerable discussion of holographic backgrounds with Schrodinger and Lifshitz symmetry, motivated by condensed matter applications. Since the bulk spacetimes are not asymptotically AdS, there are however many subtleties in setting up a holographic dictionary. In this talk we will argue that Schrodinger spacetimes (along with some realizations of Lifshitz) can be understood in terms of deformations of conformal field theories which break the relativistic scaling symmetry, but preserve an anisotropic/non-relativistic scale symmetry. We will highlight how this fact restricts which condensed matter systems can be well modeled holographically, and we will briefly discuss how the entropy of Schrodinger black holes (so-callsed null warped black holes) in three dimensions can be understood in this framework.

In the context of gauge-gravity duality, consistent truncations have proved to be powerful solution-generating tools, their latest application being to the holographic description of condensed matter systems. In the talk, I will discuss a rich class of consistent truncations of type IIB supergravity on squashed Sasaki-Einstein manifolds, leading to N=4 or N=2 gauged supergravity in five dimensions. As examples of the several possible applications, I will present an approach to domain wall gradient flows, as well as a new class of AdS5 backgrounds on the T(1,1) coset, with a comment on some related Lifshitz solutions.

Various aspects of the geometry and the thermodynamics of black holes in gauged supergravities are explored. In such theories, where the gauge coupling or the cosmological constant can be thought of as an integration constant arising from a higher-dimensional origin, it becomes appropriate to think of it as an additional thermodynamic variable associated with a pressure. The conjugate variable defines a volume for the black hole, although its geometric interpretation becomes quite subtle if the black hole is rotating. Further geometric properties of the black holes are also explored, including an intriguing universal structure for the product of the horizon areas, which is suggestive of a possible dual field theory explanation for the microscopic entropy. Isoperimetric and hoop inequalities are also discussed.

Using 3-algebras we obtain a nonabelian system of equations that furnish a representation of the (2,0)-supersymmetric tensor multiplet. The on-shell conditions are quite restrictive so that the system can be reduced to five-dimensional super-Yang-Mills theory along with six-dimensional abelian (2,0) tensor multiplets. Possible applications to D4-branes and M5-branes are discussed.

We review a method of the construction of cubic off-shell interaction vertices for Higher Spin fields. This method is based on the BRST approach and is valid both for flat and AdS backgrounds. As a particular illustration of this method we construct an off-shell extension of the vertices which are related to perturbative bosonic string theory. We discus a generalization of this method for higher order vertices and examine whether BCFW recursion relations are applicable for interacting Higher Spin gage theories.

Recently the Skyrme model has been derived from string theory in the context of holographic QCD. Inspired by this work, I shall introduce a BPS Skyrme model derived from Yang-Mills theory. This explains and extends the construction of Skyrmions from the holonomy of Yang-Mills instantons, introduced some time ago by Atiyah and Manton

The current status of realistic particle physics models and cosmology in heterotic string theory, and their potential predictions for the LHC and cosmological observations, will be discussed.

I will review some recent attempts at providing a microscopic description for extremal black holes. First, I will explain a constituent model for extremal non-rotating non-BPS asymptoticaly flat black holes. Second, I will summarise the main claims in the so called extremal BH/CFT correspondence, pointing out how a chiral CFT can emerge as a limit of a non-chiral CFT. Finally, I will use R-charge AdS black holes to derive the existence of emergent IR CFTs, similar to the ones that have been argued to capture some interesting quantum criticality phenomena in some strongly coupled condensed matter systems.

I present arguments that suggest that string theory should be viewed as an effective framework just like quantum field theory. The open/closed string and UV/IR correspondence indicate that gravity is emergent. I introduce the concept of entropic force and discuss it's subtleties. Next I present the case for the entropic origin of gravity and outline a route toward its derivation. Finally, I discuss some of the possible implications on this new view on gravity.

Effective Holographic Theories are employed in order to classify and study the critical dynamics at low temperature of quantum field theoritec systems in 2 and 3 spacial dimensions at finite charge density. The relevant dynamics variables involve the energy momentum tensor, a scalar relevant or marginal operator and the charge density current. A wealth of scaling phases are found with interesting and sometimes counterintuitive properties.

Strange metals are materials with numerous anomalous properties. The flow of electricity cannot be explained in the familiar language of a fluid of individual electrons, but instead requires a new strongly interacting description. In this talk, I will review some basic facts about these materials. With this as motivation, I will explain how to compute conductivity in certain strongly interacting, non-relativistic field theories which are defined holographically.

I will explain a gradient formula for beta functions of two-dimensional quantum field theories. The gradient formula has the form derivative c = - (gij+Delta gij+bij) bj where bj are the beta functions, c and gij are the Zamolodchikov c-function and metric, bij is an antisymmetric tensor introduced by H. Osborn and Delta gij is a certain metric correction. The formula is derived under the assumption of stress-energy conservation and certain conditions on the infrared behaviour the most significant of which is the condition that the large distance limit of the field theory does not exhibit spontaneously broken global conformal symmetry. Being specialized to non-linear sigma models this formula implies a one-to-one correspondence between renormalization group fixed points and critical points of c.

I will present the 1/2 BPS Wilson loop operator of N=6 super Chern- Simons-matter (ABJM theory) which is dual to the simplest macroscopic open string in AdS4 x CP3. The Wilson loop couples, in addition to the gauge and scalar fields of the theory, also to the fermions in the bi-fundamental representation of the U(N) x U(M) gauge group. These ingredients are naturally combined into a superconnection whose holonomy gives the Wilson loop, which can be defined for any representation of the supergroup U(NlM). Using the localization calculation of Kapustin et al. I will then show that the circular loop is computed by a supermatrix model and discuss the connection to pure Chern-Simons theory with supergroup U(NlM).

Recently there has been great interest in calculating transport coefficients for field theories at large coupling, using AdS/CFT. In this talk I will discuss recent work showing how to use the membrane paradigm to easily compute the shear viscosity and conductivity in arbitrary gravity theories. In a certain sense these can be thought of as effective couplings at the black hole horizon dual to the field theory plasma. An explicit Wald-like formula for these couplings is given for a large class of generalized gravity theories.

We discuss a couple of topics motivated by the Chern-Simons type gauge theory description of M2-branes in nontrivial backgrounds. In the first part we start by briefly reviewing the 3-algebra construction of Bagger, Lambert and Gustavsson. Then we propose an orbifold truncation prescription of 3-algebra, and show how one can 'derive' the ABJM model through matrix regularization. In the second part, we report on some explicit classical solutions of rotating membranes in Sasaki-Einstein 7-manifold M(111). We discuss the dual operators on the CS side, for several different class of spinning membranes.

Recently Kazakov, Vieira and the author conjectured the Y system set of equations describing the planar spectrum of AdS/CFT. In this paper we solve the Y system equations in the strong coupling scaling limit. We show that the quasiclassical spectrum of string moving inside AdS3 x S1 matches precisely with the prediction of the Y system. Thus the Y system, unlike the asymptotic Bethe ansatz, describes correctly the spectrum of one-loop string energies including all exponential finite size corrections. This gives a very non-trivial further support in favor of the conjecture. We also discuss how the generalization to the full AdS5 x S5 can be easily constructed using the PSU(2,2 4) symmetry of the problem.

Based on the results of 0906.4393 and 0910.5771, this talk will discuss the formulation of general 4D N=2 superconformal sigma-model in N=2 and N=1 superspace settings.