JT Supergravity, Minimal Strings, and Matrix Models

Understand

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.