JT Supergravity, Minimal Strings, and Matrix Models

Abstract

It is proposed that a family of Jackiw-Teitelboim supergravites, recently discussed in connection with matrix models by Stanford and Witten, can be given a complete definition, to all orders in the topological expansion and beyond, in terms of a specific combination of minimal string theories. This construction defines non-perturbative physics for the supergravity that is well-defined and stable. The minimal models come from double-scaled complex matrix models and correspond to the cases $(2\Gamma{+}1,2)$ in the Altland-Zirnbauer $(\boldsymbol{\alpha},\boldsymbol{\beta})$ classification of random matrix ensembles, where $\Gamma$ is a parameter. A central role is played by a non-linear `string equation' that naturally incorporates $\Gamma$, usually taken to be an integer, counting e.g., D-branes in the minimal models. Here, half-integer $\Gamma$ also has an interpretation. In fact, $\Gamma{=}{\pm}\frac12$ yields the cases $(0,2)$ and $(2,2)$ that were shown by Stanford and Witten to have very special properties. These features are manifest in this definition because the relevant solutions of the string equation have special properties for $\Gamma{=}{\pm}\frac12$. Additional special features for other half-integer $\Gamma$ suggest new surprises in the supergravity models.