Hermitean matrix model free energy: Feynman graph technique for all genera

TL;DR

This paper introduces a diagrammatic Feynman graph technique to compute the free energy of the Hermitian one-matrix model across all genera, accommodating complex eigenvalue distributions over multiple intervals.

Contribution

It develops a novel diagrammatic method for calculating the free energy of the Hermitian matrix model for arbitrary eigenvalue distributions over multiple intervals.

Findings

Provides a systematic Feynman graph approach for all genera

Applicable to eigenvalue distributions spanning multiple intervals

Enhances computational techniques for matrix models

Abstract

We present a diagrammatic technique for calculating the free energy of the Hermitian one-matrix model to all orders of 1/N expansion in the case where the limiting eigenvalue distribution spans arbitrary (but fixed) number of disjoint intervals (curves).