Topological Expansion for the Cauchy two-Matrix-Model

TL;DR

This paper derives the complete 1/N^2 topological expansion for a newly introduced two-matrix model with a novel interaction, extending bi-orthogonal polynomial techniques to analyze its correlators and free energies.

Contribution

It provides the first full 1/N^2 expansion for this specific two-matrix model, advancing the understanding of its topological structure.

Findings

Complete 1/N^2 expansion derived

Expansion applies to non-mixed resolvent correlators and free energies

Extends bi-orthogonal polynomial techniques to new model

Abstract

Recently, a two-matrix-model with a new type of interaction [1] has been introduced and analyzed using bi-orthogonal polynomial techniques. Here we present the complete 1/N^2 expansion for the formal version of this model, following the spirit of [2,3], i.e. the full expansion for the non mixed resolvent correlators and for the free energies.