Nonperturbative Model Of Liouville Gravity

Abstract

We obtain nonperturbative results in the framework of continuous Liouville theory. In particular, we express the specific heat $\mathcal{Z}$ 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 $\mathcal{Z}$ satisfies the Painlevé I.

11 pages, LaTex file

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