Higher spin JT gravity and a matrix model dual

We propose a generalization of the Saad-Shenker-Stanford duality relating matrix models and JT gravity to case in which bulk includes higher spin fields. Using $\textsf{PSL}(N,\mathbb{R})$ BF theory we compute disk trumpet partition function this theory. then study genus corrections show how differs from usual calculations. In particular, quotient by mapping class group is not enough ensure finite answers so extend with additional elements that make gluing integrals finite. These can be thought as large diffeomorphisms. The cylinder contribution spectral form factor behaves $T^{N-1}$ at late times $T$, signaling deviation conventional random To account for deviation, dual model consisting $N-1$ commuting matrices associated conserved charges. find further evidence existence interpreting gauge geometrically employing formalism developed Gomis et al. nineties. This introduces (auxiliary) boundary each charge generates translations those new directions. allows us an explicit description $\textsf{PSL}(3,\mathbb{R})$ Schwarzian view ordinary Dehn twists, but dimensions.