The symplectic-orthogonal Penner models

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 χr(M2g,n) 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, 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.