Phase transitions for deformations of JT supergravity and matrix models

TL;DR

This paper studies how adding defects to $ =1$ JT supergravity affects its phase structure, revealing a matrix model that captures these deformations and exhibits a phase transition resolving spectral issues.

Contribution

It introduces a matrix model for deformed $ =1$ JT supergravity, demonstrating a phase transition that resolves negative spectral densities and providing a non-perturbative completion.

Findings

Matrix model matches perturbative expansion of supergravity.

Negative spectral density is resolved by a phase transition.

Rich phase structure with both perturbative and non-perturbative analysis.

Abstract

We analyze deformations of $\mathcal{N}=1$ Jackiw-Teitelboim (JT) supergravity by adding a gas of defects, equivalent to changing the dilaton potential. We compute the Euclidean partition function in a topological expansion and find that it matches the perturbative expansion of a random matrix model to all orders. The matrix model implements an average over the Hamiltonian of a dual holographic description and provides a stable non-perturbative completion of these theories of $\mathcal{N}=1$ dilaton-supergravity. For some range of deformations, the supergravity spectral density becomes negative, yielding an ill-defined topological expansion. To solve this problem, we use the matrix model description and show the negative spectrum is resolved via a phase transition analogous to the Gross-Witten-Wadia transition. The matrix model contains a rich and novel phase structure that we explore in detail, using both perturbative and non-perturbative techniques.