  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.
