Loop equations for multi-cut matrix models

TL;DR

This paper derives and solves the loop equations for multi-cut matrix models, providing explicit higher genus results and analyzing the double-scaling limit, thereby advancing understanding of complex matrix models in theoretical physics.

Contribution

It introduces a method to solve loop equations for multi-cut matrix models and provides explicit results up to genus two, extending previous single-cut analyses.

Findings

Explicit solutions for multi-cut loop equations up to genus two

Analysis of the double-scaling limit and its relation to one-cut models

Development of an iterative scheme for higher genus contributions

Abstract

The loop equation for the complex one-matrix model with a multi-cut structure is derived and solved in the planar limit. An iterative scheme for higher genus contributions to the free energy and the multi-loop correlators is presented for the two-cut model, where explicit results are given up to and including genus two. The double-scaling limit is analyzed and the relation to the one-cut solution of the hermitian and complex one-matrix model is discussed.