2D dilaton gravity and the Weil-Petersson volumes with conical defects

Understand

We derive the Weil-Petersson measure on the moduli space of hyperbolic surfaces with defects of arbitrary opening angles and use this to compute its volume.

• We conjecture a matrix integral computing the corresponding volumes and confirm agreement in simple cases.
• We combine this mathematical result with the equivariant localization approach to Jackiw-Teitelboim gravity to justify a proposed exact solution of pure 2d dilaton gravity for a large class of dilaton potentials.