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.