Algebraic-geometrical formulation of two-dimensional quantum gravity

Abstract

We find a volume form on moduli space of double punctured Riemann surfaces whose integral satisfies the Painlevé I recursion relations of the genus expansion of the specific heat of 2D gravity. This allows us to express the asymptotic expansion of the specific heat as an integral on an infinite dimensional moduli space in the spirit of Friedan-Shenker approach. We outline a conjectural derivation of such recursion relations using the Duistermaat-Heckman theorem.

10 pages, Latex file

References in corpus (3)

• Combinatorics of the Modular Group II: the Kontsevich integrals
• Uniformization theory and 2D gravity I. Liouville action and intersection numbers
• Nonperturbative 2D Gravity, Punctured Spheres and $\Theta$-Vacua in String Theories

Cited by in corpus (4)

• The Liouville Geometry of N=2 Instantons and the Moduli of Punctured Spheres
• Nonperturbative Model Of Liouville Gravity
• Zamolodchikov relations and Liouville hierarchy in SL(2,R)_k WZNW model
• The Instanton Universal Moduli Space of N=2 Supersymmetric Yang-Mills Theory