Free energy topological expansion for the 2-matrix model

TL;DR

This paper develops a comprehensive topological expansion framework for the hermitian two-matrix model, refining diagrammatic rules, formulating a new spectral curve, and deriving explicit formulas for correlation functions and free energy.

Contribution

It introduces a refined diagrammatic approach, a new spectral curve formulation, and closed formulas for all orders of the topological expansion in the two-matrix model.

Findings

Complete topological expansion computed

New spectral curve formulation introduced

Explicit formulas for correlation functions and free energy derived

Abstract

We compute the complete topological expansion of the formal hermitian two-matrix model. For this, we refine the previously formulated diagrammatic rules for computing the 1/ N expansion of the nonmixed correlation functions and give a new formulation of the spectral curve. We extend these rules obtaining a closed formula for correlation functions in all orders of topological expansion. We then integrate it to obtain the free energy in terms of residues on the associated Riemann surface.