# Fine Structure of Jackiw-Teitelboim Quantum Gravity

## TL;DR

This paper explores the structural and physical aspects of Jackiw-Teitelboim (JT) gravity using its BF theory formulation, revealing new insights into its degrees of freedom, manifold configurations, and connections to other theories.

## Contribution

It demonstrates that JT gravity can be viewed as a coset of SL$^+$(2,R) BF theory and investigates its edge modes, factorization properties, and relation to Liouville CFT.

## Key findings

- JT gravity is described by SL$^+$(2,R) BF theory.
- Edge degrees of freedom include horizon SL$^+$(2,R) states.
- Configurations with two boundaries relate to Liouville CFT on a torus.

## Abstract

We investigate structural aspects of JT gravity through its BF description. In particular, we provide evidence that JT gravity should be thought of as (a coset of) the noncompact subsemigroup SL$^+$(2,R) BF theory. We highlight physical implications, including the famous sinh Plancherel measure. Exploiting this perspective, we investigate JT gravity on more generic manifolds with emphasis on the edge degrees of freedom on entangling surfaces and factorization. It is found that the one-sided JT gravity degrees of freedom are described not just by a Schwarzian on the asymptotic boundary, but also include frozen SL$^+$(2,R) degrees of freedom on the horizon, identifiable as JT gravity black hole states. Configurations with two asymptotic boundaries are linked to 2d Liouville CFT on the torus surface.