Supersymmetric localization of (higher-spin) JT gravity: a bulk perspective

TL;DR

This paper uses supersymmetric localization to compute exact partition functions of (higher-spin) JT gravity, providing a bulk perspective that aligns with boundary Schwarzian theory results and extends to Wilson line correlators.

Contribution

It introduces a supersymmetric formulation of JT gravity with boundary terms and computes exact partition functions, extending the approach to higher-spin generalizations.

Findings

Exact partition function matches Schwarzian theory results.

Supersymmetric localization simplifies calculations in JT gravity.

Method extends to higher-spin and Wilson line correlators.

Abstract

We study two-dimensional Jackiw-Teitelboim gravity on the disk topology by using a BF gauge theory in the presence of a boundary term. The system can be equivalently written in a supersymmetric way by introducing auxiliary gauginos and scalars with suitable boundary conditions on the hemisphere. We compute the exact partition function thanks to supersymmetric localization and we recover the result obtained from the Schwarzian theory by accurately identifying the physical scales. The calculation is then easily extended to the higher-spin generalization of Jackiw-Teitelboim gravity, finding perfect agreement with previous results. We argue that our procedure can also be applied to boundary-anchored Wilson line correlators.