Asymptotic symmetries and dual theories of (2+1) dimensional (super)gravity theories

Abstract

In this thesis we use the asymptotic symmetries of 3D (super)gravity theories to explore the dual theories.

Using the Chern-Simons formulation of (2+1)D gravity we have constructed a two dimensional theory dual to 3D asymptotically flat supergravity in presence of two supercharges with(out) internal R symmetry. In both cases, the dual theory is a Wess-Zumino-Witten type model. We then explore the symmetries of the dual theory and find the most generic, so far unknown, quantum N = 2 superBMS3 symmetry under which this is invariant. We have also commented on the phase space description of the duals.

Next, we use similar techniques to understand the dual dynamics of 3D asymptotically de-Sitter supergravity. We write down the Chern-Simons description of the bulk theory using OSp(1|2,C) as the gauge group. Next we describe the holographic screen of 3D de-Sitter and impose our boundary conditions. We finally end up with a super-Liouville theory at the boundary as the holographic dual of the bulk supergravity theory.

Finally we use conformal field theory techniques to write a Matrix model partition function with BMS3 constraints. We start from the free field realisation of the algebra in terms of a twisted beta−gamma system and solve the constraints through it. We end up with an eigenvalue representation of this partition function. Since BMS3 is the asymptotic symmetry algebra of the pure gravity in 3D flat background, we expect this partition function to illuminate our understanding of 3D holography. We comment on qualitative properties of this partition function.