Determinant Formulas for Matrix Model Free Energy

TL;DR

This paper presents a new non-perturbative formula for the subleading free energy in multicut hermitian matrix models, extending previous two-cut solutions and providing a direct proof and generalization.

Contribution

It introduces a non-perturbative representation for multicut solutions, generalizing prior two-cut formulas and offering a direct proof.

Findings

Derived a non-perturbative formula for multicut free energy

Extended the Klemm-Marino-Theisen formula to general multicut solutions

Provided a direct proof of the generalized formula

Abstract

The paper contains a new non-perturbative representation for subleading contribution to the free energy of multicut solution for hermitian matrix model. This representation is a generalisation of the formula, proposed by Klemm, Marino and Theisen for two cut solution, which was obtained by comparing the cubic matrix model with the topological B-model on the local Calabi-Yau geometry $\hat {II}$ and was checked perturbatively. In this paper we give a direct proof of their formula and generalise it to the general multicut solution.