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arXiv · 1209.0822

The Symplectic-Orthogonal Penner Models

Mohammad Dalabeeh·Noureddine Chair
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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 $\chi^r(\mathfrak{M}_{2g,n})$, is identified with a simple formula. It is shown that the free energy in the continuum limit of both the symplectic and the orthogonal Penner models are almost identical, with the structure $F^{SP/SO}(\mu)=1/2F(\mu)\mp F^{NO}(\mu)$, where $F(\mu)$ is the Penner free energy and $F^{NO}(\mu)$ is the free energy contributions from the non-orientable surfaces. Both of these models have the same critical point as the Penner model.

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Mohammad Dalabeeh, Noureddine Chair. 2012-09-04. The Symplectic-Orthogonal Penner Models. https://doi.org/10.1088/1751-8113/43/46/465204

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