Algebraic-geometrical formulation of two-dimensional quantum gravity
High Energy Physics - Theory
2016-09-06 v1 alg-geom
General Relativity and Quantum Cosmology
Algebraic Geometry
Quantum Algebra
Exactly Solvable and Integrable Systems
q-alg
solv-int
Abstract
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.
Cite
@article{arxiv.hep-th/9502089,
title = {Algebraic-geometrical formulation of two-dimensional quantum gravity},
author = {G. Bonelli and P. A. Marchetti and M. Matone},
journal= {arXiv preprint arXiv:hep-th/9502089},
year = {2016}
}
Comments
10 pages, Latex file