Wormholes, branes and finite matrices in sine dilaton gravity

Abstract

We compute the double trumpet in sine dilaton gravity via WdW quantization. The wormhole size is discretized. The wormhole amplitude matches the spectral correlation of a finite-cut matrix integral, where matrices have large but finite dimensions. This strongly suggests an identification of the sine dilaton gravity theory with the q-deformed JT gravity matrix integral. At the very least, it captures all universal content of that matrix model. The disk decomposes into the physical (gauge invariant) solutions of the WdW equation, which are trumpets with discrete sizes. This decomposition modifies the usual no-boundary wavefunction to a normalizable one in sine dilaton gravity. We furthermore present an exact quantization of sine dilaton gravity with open and closed end of the world branes. These EOW branes correspond with FZZT branes for the two Liouville theories that make up sine dilaton gravity. The WdW equation implies redundancies in this space of branes, leaving a one parameter family of gauge invariant branes. One gauge choice corresponds with branes discussed by Okuyama in the context of chord diagrams and of DSSYK. Legendre transforming the EOW brane amplitude reproduces the trumpet, independent of the WdW quantization calculation. One could read our work as fleshing out the Hilbert space of closed universes in sine dilaton gravity.