The partition function of the two-matrix model as an isomonodromic tau-function

TL;DR

This paper demonstrates that the partition function of the two-matrix model can be viewed as an isomonodromic tau-function, extending the concept to systems with less regular leading coefficients.

Contribution

It generalizes the notion of tau-functions for isomonodromic systems beyond the classical ad-regular case, linking matrix models to integrable systems.

Findings

Partition function is an isomonodromic tau-function.

Generalization of tau-function concept to non-ad-regular systems.

Bridges matrix models with isomonodromic deformation theory.

Abstract

We consider the Itzykson-Zuber-Eynard-Mehta two-matrix model and prove that the partition function is an isomonodromic tau function in a sense that generalizes Jimbo-Miwa-Ueno's. In order to achieve the generalization we need to define a notion of tau-function for isomonodromic systems where the ad-regularity of the leading coefficient is not a necessary requirement.