Genus one contribution to free energy in hermitian two-matrix model

TL;DR

This paper calculates the genus 1 correction to the free energy in the Hermitian two-matrix model using theta-functions, linking it to various advanced mathematical structures like tau-functions and spectral curves.

Contribution

It provides a novel explicit expression for the genus 1 free energy correction in terms of theta-functions associated with spectral curves.

Findings

Expressed genus 1 correction via theta-functions

Connected free energy correction to isomonodromic tau-function

Linked spectral curve analysis to Bergmann tau-function and Laplacian determinants

Abstract

We compute an the genus 1 correction to free energy of Hermitian two-matrix model in terms of theta-functions associated to spectral curve arising in large N limit. We discuss the relationship of this expression to isomonodromic tau-function, Bergmann tau-function on Hurwitz spaces, G-function of Frobenius manifolds and determinant of Laplacian in a singular metric over spectral curve.