We study three dimensional conformal field theories described by U (N ) Chern-Simons theory at level k coupled to massless fermions in the fundamental representation. By solving a Schwinger-Dyson equation in lightcone gauge, we compute the exact planar free energy of the theory at finite temperature on R 2 as a function of the 't Hooft coupling λ = N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at |λ| = 1; the conformal theory does not exist for |λ| > 1. We analyze the operator spectrum via the anomalous conservation relation for higher spin currents, and in particular show that the higher spin currents do not develop anomalous dimensions at leading order in 1/N . We present an integral equation whose solution in principle determines all correlators of these currents at leading order in 1/N and present explicit perturbative results for all three point functions up to two loops. We also discuss a lightcone Hamiltonian formulation of this theory where a W ∞ algebra arises. The maximally supersymmetric version of our theory is ABJ model with one gauge group taken to be U (1), demonstrating that a pure higher spin gauge theory arises as a limit of string theory.

In this Report we review the microscopic formulation of the five dimensional black hole of type IIB string theory in terms of the D1-D5 brane system. The emphasis here is more on the brane dynamics than on supergravity solutions. We show how the low energy brane dynamics, combined with crucial inputs from AdS/CFT correspondence, leads to a derivation of black hole thermodynamics and the rate of Hawking radiation. Our approach requires a detailed exposition of the gauge theory and conformal field theory of the D1-D5 system. We also discuss some applications of the AdS/CFT correspondence in the context of black hole formation in three dimensions by thermal transition and by collision of point particles.

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