A TQFT Approach to 3d Gravity

The connection between 3d pure gravity and Chern-Simons theory has been proposed and studied for decades. In this talk, I will give a brief review of the works 2304.13650 and 2401.13900 with Scott Collier and Lorenz Eberhardt, where we sharpen this idea into a precise correspondence and propose the Virasoro TQFT formulation of pure AdS3 gravity. I will start with a discussion of the identification between gravity phase space and Teichmuller space and show that the quantization of Teichmuller space leads to the construction of Virasoro TQFT. Then I will illustrate some useful algorithms (Heegaard splitting, Surface bundle construction, etc.) to compute the Virasoro TQFT partition functions on a fixed topology. Finally, I will discuss the calculation of gravity partition functions on manifolds with multiple boundaries and its holographic implications.