Extended JT supergravity and random matrix models: The power of the string equation

TL;DR

This paper demonstrates that the string equation effectively constrains the spectrum of extended JT supergravity models, supporting the conjecture that these models have corresponding matrix model descriptions.

Contribution

The authors refine the use of the string equation to analyze and constrain spectra of various extended JT supergravity theories, including new cases with N=3 and large N=4.

Findings

The string equation constrains supergravity spectra effectively.

The approach applies to N=2, N=3, N=4 supergravity models.

Supports the conjecture of matrix model descriptions for these theories.

Abstract

A number of supersymmetric Jackiw-Teitelboim (JT) gravity theories are known to be described (in the Euclidean path integral formulation) by double-scaled random matrix models. Such matrix models can be characterized using a certain ``string equation''. It was shown recently that in extended supergravity, when the number of BPS states scales as ${\rm e}^{S_0}$, where $S_0$ is the extremal entropy, a special ansatz for the leading order solution of the string equation yields the supergravity spectrum. Somewhat miraculously, the construction showed that the functional form of the non-BPS (continuum) sector predicts the precise form of the BPS sector, showing the robustness of the supergravity/matrix-model correspondence. In this paper, we refine the analysis and show that the string equation, combined with some simple requirements on solutions, are powerful tools for constraining the spectrum of extended JT supergravity theories. We re-explore the cases of ${N}{=}2$ and (small) ${N}{=}4$ JT supergravity, and then explore the new cases of spectra from ${N}{=}3$ and large ${N}{=}4$ JT supergravity (recently derived by Heydeman, Shi, and Turiaci) showing that our approach also works naturally for (nearly) all the models. Based on this success, we conjecture that these new supergravity models also have matrix model descriptions.