Solving 3d Gravity with Virasoro TQFT

Understand

We propose a precise reformulation of 3d quantum gravity with negative cosmological constant in terms of a topological quantum field theory based on the quantization of the Teichm\"uller space of Riemann surfaces that we refer to as ``Virasoro TQFT.'' This TQFT is similar, but importantly not equivalent, to $\text{SL}(2,\mathbb{R})$ Chern-Simons theory.

• This sharpens the folklore that 3d gravity is related to $\text{SL}(2,\mathbb{R})$ Chern-Simons theory into a precise correspondence, and resolves some well-known issues with this lore at the quantum level.
• Our proposal is computationally very useful and provides a powerful tool for the further study of 3d gravity.
• In particular, we explain how together with standard TQFT surgery techniques this leads to a fully algorithmic procedure for the computation of the gravity partition function on a fixed topology exactly in the central charge.