Phase transitions for deformations of JT supergravity and matrix models

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.