Second and Third Order Observables of the Two-Matrix Model

TL;DR

This paper extends the analysis of the two-matrix model by deriving explicit formulas for second and third order observables, including three-loop correlators, using spectral curve structures.

Contribution

It provides explicit formulas for higher-order observables of the two-matrix model based on spectral curve methods, advancing understanding of its complex correlations.

Findings

Explicit formulas for second and third order observables.

Derived three-loop correlator expressions.

Worked out specific examples demonstrating the formulas.

Abstract

In this paper we complement our recent result on the explicit formula for the planar limit of the free energy of the two-matrix model by computing the second and third order observables of the model in terms of canonical structures of the underlying genus g spectral curve. In particular we provide explicit formulas for any three-loop correlator of the model. Some explicit examples are worked out.