Higher spin JT gravity and a matrix model dual

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In this talk I will propose and discuss a generalization of the Saad-Shenker-Stanford duality between matrix models and JT gravity to the case in which the bulk includes higher spin fields. Using an PSL(N,R) BF theory we compute the disk and generalization of the trumpet partition function in this theory. Using an appropriate subspace of the moduli space of flat PSL(N,R) connections on a Riemann surface $\Sigma$ we propose a recipe for computing the cylinder contribution. This gives a $T^{N-1}$ behaviour at late times $T$, signaling a deviation from conventional random matrix theory. To account for this deviation, we propose that the bulk theory is dual to a matrix model consisting of N-1 commuting matrices associated to the N-1 conserved charges in the boundary theory. Due to its modified eigenvalue repulsion, the spectral two-point function reproduces the late time gravitational answer.