Genus one correlation to multi-cut matrix model solutions

TL;DR

This paper computes genus one corrections for multi-cut Hermitian matrix models using loop equations, confirming previous algebraic geometry results and extending them to arbitrary potentials.

Contribution

It provides a direct loop equation derivation of genus one corrections for multi-cut matrix models, generalizing prior algebraic geometry approaches to arbitrary potentials.

Findings

Confirmed genus one corrections match algebraic geometry results

Extended correction calculations to models with arbitrary potentials

Validated the loop equation method for complex multi-cut solutions

Abstract

We calculate genus one corrections to Hermitian one-matrix model solution with arbitrary number of cuts directly from the loop equation confirming the answer previously obtained from algebro-geometrical considerations and generalizing it to the case of arbitrary potentials.