Algebraic-geometrical formulation of two-dimensional quantum gravity

Details Algebraic-geometrical formulation of two-dimensional quantum gravity Algebraic-geometrical formulation of two-dimensional quantum gravity

1995-02-14

arxiv.org/abs/hep-th/9502089v1

Lett.Math.Phys. 36 (1996) 189-196

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, Latex file

Scientific paper

10.1007/BF00714381

We find a volume form on moduli space of double punctured Riemann surfaces whose integral satisfies the Painlev\'e 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.

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