Matrix eigenvalue model: Feynman graph technique for all genera

TL;DR

This paper introduces a diagrammatic Feynman graph technique to compute the free energy of matrix eigenvalue models across all genera, accommodating arbitrary eigenvalue distributions over multiple intervals.

Contribution

It develops a novel diagrammatic method for calculating the free energy of matrix eigenvalue models for arbitrary eigenvalue distributions and all orders of 1/N expansion.

Findings

Provides a diagrammatic technique applicable to models with multiple eigenvalue intervals

Enables calculation of free energy to all orders of 1/N expansion

Applicable to models with arbitrary power β in the Vandermonde determinant

Abstract

We present the diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with arbitrary power $\beta$ by the Vandermonde determinant) to all orders of 1/N expansion in the case where the limiting eigenvalue distribution spans arbitrary (but fixed) number of disjoint intervals (curves).