Solvable Systems in 3D Gravity and Holography

Objective

The project investigates exactly solvable models of quantum gravity in three-dimensions, with the aim of deepening our understanding of the holographic principle, and particularly the AdS/CFT correspondence. My research will focus on two complementary goals: the solution of string theory in AdS3 backgrounds and the inclusion of matter in pure 3D gravity. In the context of string theory, I will exploit recent advances in worldsheet techniques to compute scattering amplitudes in string theory on AdS3 backgrounds, both in pure NS-NS flux backgrounds as well as in backgrounds with mixed NS-NS and Ramond-Ramond flux, with an end goal of providing an analytically testable framework for proving the AdS3/CFT2 correspondence within string theory. In parallel, I will study the quantization of pure 3D gravity with negative cosmological constant, minimally coupled to matter. I will utilize the recent discovery of a topological field theoretic description of 3D gravity (the so-called Virasoro TQFT), which provides a nonperturbative definition of the gravitational path integral. The end goal of this direction will be to refine the duality between pure 3D gravity and random ensembles of CFT data, and to understand how this ensemble is altered when the gravitational path integral is supplemented with nontrivial bulk matter. Together, these two approaches aim to expand the space of known solvable systems in quantum gravity and to serve as laboratories for answering fundamental questions in holography.