Non-homogenous disks in the chain of matrices

TL;DR

This paper studies multi-colored discrete disks with non-homogeneous boundaries within a Hermitian multi-matrix model, using spectral curve analysis to solve loop equations and derive recursive formulas for correlation functions in the large matrix limit.

Contribution

It introduces a method to analyze non-homogeneous boundary conditions in multi-matrix models via spectral curves and recursive solutions for correlation functions.

Findings

Derived recursive formulas for mixed trace correlation functions.

Connected spectral curve analysis with boundary condition complexity.

Provided a framework for solving loop equations in multi-matrix models.

Abstract

We investigate the generating functions of multi-colored discrete disks with non-homogenous boundary conditions in the context of the Hermitian multi-matrix model where the matrices are coupled in an open chain. We show that the study of the spectral curve of the matrix model allows one to solve a set of loop equations to get a recursive formula computing mixed trace correlation functions to leading order in the large matrix limit.