Nonperturbative Model Of Liouville Gravity

TL;DR

This paper derives nonperturbative results in Liouville gravity, expressing the specific heat through integrals on moduli spaces and linking it to Painlevé I, advancing understanding of quantum gravity models.

Contribution

It introduces a nonperturbative approach to Liouville gravity, connecting the specific heat to integrals on moduli spaces and Painlevé I equations.

Findings

Expressed the specific heat in terms of moduli space integrals

Linked the specific heat to Painlevé I equation

Provided nonperturbative insights into Liouville gravity

Abstract

We obtain nonperturbative results in the framework of continuous Liouville theory. In particular, we express the specific heat ${\cal Z}$ of pure gravity in terms of an expansion of integrals on moduli spaces of punctured Riemann spheres. The integrands are written in terms of the Liouville action. We show that ${\cal Z}$ satisfies the Painlev\'e I.