Matrix Models and Deformations of JT Gravity

TL;DR

This paper explores how deformations of JT gravity correspond to specific matrix models, providing a method to determine the eigenvalue density of the dual matrix ensemble based on the deformation function.

Contribution

It extends the duality between JT gravity and matrix models to include deformations with arbitrary potentials W(φ), detailing how to compute the eigenvalue density.

Findings

Derived the eigenvalue density for deformed JT gravity.

Provided a simple solution when W(0)=0.

Presented a complex eigenvalue density for general W(φ).

Abstract

Recently, it has been found that JT gravity, which is a two-dimensional theory with bulk action $ -\frac{1}{2}\int {\mathrm d}^2x \sqrt g\phi(R+2)$, is dual to a matrix model, that is, a random ensemble of quantum systems rather than a specific quantum mechanical system. In this article, we argue that a deformation of JT gravity with bulk action $ -\frac{1}{2}\int {\mathrm d}^2x \sqrt g(\phi R+W(\phi))$ is likewise dual to a matrix model. With a specific procedure for defining the path integral of the theory, we determine the density of eigenvalues of the dual matrix model. There is a simple answer if $W(0)=0$, and otherwise a rather complicated answer.