The symplectic-orthogonal Penner models

Abstract

The generating function for the orbifold Euler characteristic of the moduli space of real algebraic curves of genus 2g (locally orientable surfaces) with n marked points is identified with a simple formula. It is shown that the free energies in the continuum limit of both the symplectic and the orthogonal Penner models are almost identical, with the structure , where F(μ) is the Penner free energy and FNO(μ) is the free energy contributions from the non-orientable surfaces. Both of these models have the same critical point as of the Penner model.