We formulate nonperturbative 2D gravity in the framework of Liouville theory. In particular, we express the specific heat Z of pure gravity in terms of an expansion of integrals on moduli spaces of punctured Riemann spheres. We recognize the relevant divisors on moduli spaces and write the integrands in terms of the Liouville action. We evaluate the integrals (rational intersections) and show that Z satisfies the Painlevé I.
NONPERTURBATIVE MODEL OF LIOUVILLE GRAVITY
MATONE, MARCO
1997
Abstract
We formulate nonperturbative 2D gravity in the framework of Liouville theory. In particular, we express the specific heat Z of pure gravity in terms of an expansion of integrals on moduli spaces of punctured Riemann spheres. We recognize the relevant divisors on moduli spaces and write the integrands in terms of the Liouville action. We evaluate the integrals (rational intersections) and show that Z satisfies the Painlevé I.
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