Matrix models and deformations of JT gravity

Recently, it has been found that Jackiw-Teitelboim (JT) gravity, which is a two-dimensional theory with bulk action $$ , is dual to a matrix model, that is, a random ensemble of quantum systems rather than a specific quantum mechanical system. In this article, we argue that a deformation of JT gravity with bulk action $$ 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.