Higher genus correlators for the hermitian matrix model with multiple cuts

TL;DR

This paper develops an iterative method to solve the loop equations of the hermitian matrix model with multiple cuts, providing explicit genus-one results and revealing new universality classes, especially in the two-cut case.

Contribution

It introduces a novel iterative scheme for multi-cut hermitian matrix models and derives explicit genus-one correlators, highlighting new universality classes and differences in the two-cut double-scaling limit.

Findings

Explicit genus-one correlators for arbitrary multi-cut models

Elliptic integrals appear in boundary conditions

Two-cut solutions can differ from known continuum models

Abstract

An iterative scheme is set up for solving the loop equation of the hermitian one-matrix model with a multi-cut structure. Explicit results are presented for genus one for an arbitrary but finite number of cuts. Due to the complicated form of the boundary conditions, the loop correlators now contain elliptic integrals. This demonstrates the existence of new universality classes for the hermitian matrix model. The two-cut solution is investigated in more detail, including the double-scaling limit. It is shown, that in special cases it differs from the known continuum solution with one cut.