In the AdS/CFT correspondence, gauge theory calculations beyond the planar approximation correspond to quantum corrections in gravity or in string theory. Recently, the partition function on the three-sphere of Chern-Simons-matter theories has been computed at all orders in the 1/N expansion, and this leads to predictions for quantum corrections in M-theory/string theory. Using the ideas of effective field theory, we show that some of these corrections can be calculated reliably by doing one-loop calculations in supergravity. A similar reasoning has been used recently to calculate logarithmic corrections to black hole entropy, and we use it here to perform a successful test of AdS_4/CFT_3 beyond the leading, planar approximation.

Supersymmetry on curved spaces has recently attracted much attention, mainly as a tool towards the exact computation of quantum field theory observables via localization. Taking a holographic perspective, I will discuss how the conditions for rigid supersymmetry to be preserved on a curved boundary arise from the bulk supergravity Killing spinor equations. In particular, I will show that a four-dimensional superconformal field theory can be put on a curved, Lorentzian spacetime if and only if this admits a null conformal Killing vector. For a supersymmetric field theory with an R-symmetry, not necessarily conformal, the vector is further restricted to be Killing. After having presented some illustrative examples, I will conclude comparing with the Euclidean case.

Some issues of higher-spin (HS) gauge theory (in d+1>3) related to its cubic interactions and holography are discussed. After providing a very brief overview on the topic, I show how to construct all gauge consistent cubic interactions using the ambient-space formulation. Its number matches that of all possible 3pt functions, recently derived by other groups. However only one vertex corresponds to the free scalar CFT on the boundary, hence the metric-like version of the vertex encoded in Vasiliev's equation.

It will be shown that the dynamics of discrete (integer-valued) Hamiltonian cellular automata can only be consistently defined, if it is linear in the same sense that unitary evolution in quantum mechanics is linear. This suggests us to look for an invertible map between such automata and continuous quantum mechanical models. Based on sampling theory, such a map can indeed be constructed and leads to quantum mechanical models which incorporate a fundamental scale. The admissible observables, the one-to-one correspondence of the respective conservation laws, and the existence of solutions of the modified dispersion relation for stationary states are discussed. References: H.-T. Elze, Action principle for cellular automata and the linearity of quantum mechanics, Phys. Rev. A 89, 012111 (2014) [arXiv:1312.1615]; do., Journal of Physics: Conference Series 504 (2014) 012004 [arXiv:1403.2646].

The study of Superstring Theories on AdS backgrounds is important in the context of Gauge/Gravity correspondence. These theories can be reduced, under certain assumptions, to Sigma Models on semi-symmetric super-cosets. For a peculiar class of these cosets one can also introduce a WZW term. This correspond to study a Superstring Theory on a background supported by a mixture of RR and NSNS fluxes, as can happen for theories on $AdS_3\times S^3 \times M_4$. I will show the effect of this term on Integrability, Kappa symmetry and conformality of the theory, computing also the BMN spectrum in some relevant case for $AdS_3/CFT_2$ correspondence.

BPS states in N=2 gauge theories or string vacua are generically stable but liable to decay across certain codimension-one loci in moduli space. This process is easily understood by viewing BPS states as a bound state of more elementary BPS constituents, described classically by multi-centered solutions of the low energy effective action. The semi-classical quantization of the space of such solutions agrees with the wall-crossing formulae derived in the mathematical literature on BPS invariants, providing a physically elementary justification of the latter. Using this intuition, it is possible to express the BPS index, at any point in moduli space, in terms of indices associated to elementary (or single-centered) constituents. If time permits, I will present evidence for this idea in the case of BPS states described by quiver representations.

In the setting of integrability in AdS/CFT, in the typical approach to the AdS_5 x S^5 string a light-cone gauge is fixed, breaking Lorentz invariance on the worldsheet. One attempt to avoid the need for this goes under the name of Pohlmeyer reduction. Recently an S-matrix was conjectured to describe the scattering of solitons in this theory. Now as I will explain in my talk, the S-matrix of an integrable quantum field theory together with its dispersion relation are enough to find its finite volume spectrum exactly, through the so-called thermodynamic Bethe ansatz. I will work this out for an S-matrix and dispersion that interpolate between the standard light-cone gauge fixed superstring and this conjectured Pohlmeyer S-matrix, by analogy to a simpler model. Viewed as a deformation of the light-cone gauge fixed superstring TBA, this story is very similar to deforming the XXX spin chain to the XXZ one, which I will concretely discuss. I will finish by emphasizing important differences to this simple toy model, and discuss surprises in the so-called Y-system associated to the TBA equations.

Chiral anomalies have profound impact on the transport properties of relativistic fluids. They are closely related to the creation of currents by magnetic fields or vortices in the fluid via the so called Chiral Magnetic Conductivity and the Chiral Vortical Conductivity. Both can be computed by Kubo type formulae from special kinematic limits of two point functions of currents. I will review the calculation of these conductivites in a gas of free Weyl fermions and at strong coupling via a holographic model. A special and somewhat mysterious role is played by the mixed gauge-gravitational anomaly.

3d N=4 superconformal quiver theories arise as the low energy description of intersecting D3/D5/NS5 branes. I will discuss the backreacted solutions describing the near horizon geometry of such configurations. A map between the CFT and supergravity solutions is proposed. As a check, the CFT partition function on S^3 is computed using localization technqiues and matched to the supergravity results.

The AdS/CFT correspondence has recently allowed the computation of gauge theory quantities in the strong coupled regime (for certain particular theories). One important such quantity is the Wilson loop which is related to the quark/ anti-quark potential, scattering amplitudes, etc. The computation is reduced to finding minimal area surfaces in hyperbolic space. Although this is a classical problem in mathematics its solution is not easy since it involves non-linear partial differential equations. In this talk I will describe some recent work where we found an infinite parameter family of such surfaces by using Riemann Theta functions to analytically solve the equations.

I will discuss recent work on the supergravity description of the fully localized orthogonal black M2-M5 intersection using blackfold theory. Special emphasis will be given to the near-extremal thermodynamics of this system from which we can read off, for the first time, the large-N scaling of the central charge of the two-dimensional superconformal field theory that lives at the intersection. The resulting formula for this central charge is suggestive for the underlying M2 and M5 brane physics.

I will review the recent progress in the study of three dimensional U(N)_k Chern-Simons theories coupled to a massless boson or fermion in the fundamental representation. In particular, in the planar limit, one can determine the conformal fixed points and spectrum of local primary operators of these theories. In addition, the planar 3-point functions can be computed exactly as a function of the 't Hooft coupling, and the results agree with the general predictions of Maldacena and Zhiboedov for the correlators of theories that have high-spin symmetries in the large N limit. It has been suggested in the past that the fermionic and bosonic theories are dual to each other at large N. Using the exact expressions of the planar 3-point functions, one can find the precise mapping between the two theories. In particular, it was found that the theory of N scalars coupled to a U(N)_k Chern-Simons theory is equivalent to the Gross-Neveu model of k fermions coupled to a U(k)_N Chern-Simons theory, thus providing a bosonization of the latter theory.

We will discuss methods of computing instanton partition functions for arbitrary gauge groups including the exceptional ones. Even though there is no explicit algebraic construction of instanton moduli space available for the EFG groups beyond 1-instanton, we're able to evaluate the partition function using the blow-up recursion relations derived by Nakajima and Yoshioka. We compare this result with the recent proposal based on the superconformal index of SCFTs with E6, E7 global symmetry. We also compare our result with the norm of certain coherent states of W-algebras and thereby extending the AGT correspondence for pure YM theory to all gauge groups. Reference: 1111.5624, 1205.4722.

An exact solution representing black holes in an expanding universe is found. The black holes are maximally charged and the universe is expanding with arbitrary equation of state. It is an exact solution of the Einstein-scalar-Maxwell system, in which we have two Maxwell-type U(1) fields coupled to the scalar field. The potential of the scalar field is an exponential. The solution depends on two parameters, the charge Q and one parameter (the ratio of the energy density of U(1) fields to that of the scalar field). We find a regular horizon, which is static because of the balance on the horizon between gravitational attractive force and U(1) repulsive force acting on the scalar field. We also calculate the black hole temperature. For the case without a potential, we can derive such a solution from a time-dependent intersecting M-brane solution in eleven dimensions by the dimensional reduction.