# An exact quantization of Jackiw-Teitelboim gravity

## TL;DR

This paper presents an exact quantization of JT gravity by reformulating it as a 2D gauge theory with a central extension, matching the Schwarzian theory's partition function and correlators.

## Contribution

It introduces a novel gauge theory formulation of JT gravity with a central extension, enabling exact quantization and precise matching with Schwarzian theory results.

## Key findings

- Partition function matches Schwarzian theory on a disk.
- Wilson line correlators correspond to bi-local operators.
- Wilson lines are equivalent to massive particle world-lines.

## Abstract

We propose an exact quantization of two-dimensional Jackiw-Teitelboim (JT) gravity by formulating the JT gravity theory as a 2D gauge theory placed in the presence of a loop defect. The gauge group is a certain central extension of $PSL(2, \mathbb{R})$ by $\mathbb{R}$. We find that the exact partition function of our theory when placed on a Euclidean disk matches precisely the finite temperature partition function of the Schwarzian theory. We show that observables on both sides are also precisely matched: correlation functions of boundary-anchored Wilson lines in the bulk are given by those of bi-local operators in the Schwarzian theory. In the gravitational context, the Wilson lines are shown to be equivalent to the world-lines of massive particles in the metric formulation of JT gravity.