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

TL;DR

This paper derives the Weil-Petersson measure for hyperbolic surfaces with conical defects, computes their volumes, and connects these mathematical results to an exact solution in 2D dilaton gravity using matrix integrals and localization techniques.

Contribution

It introduces a new measure for moduli spaces with defects, proposes a matrix integral for their volumes, and applies this to solve 2D dilaton gravity exactly for various potentials.

Findings

Derived Weil-Petersson measure for surfaces with conical defects

Proposed and validated a matrix integral for volume computation

Connected mathematical results to exact solutions in 2D dilaton gravity

Abstract

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.