A common integrable structure in the hermitian matrix model and Hele-Shaw flows

TL;DR

This paper reveals a shared integrable structure between the dispersionless 2-Toda hierarchy in hermitian matrix models and Hele-Shaw flows, linking two seemingly different physical phenomena through mathematical analysis.

Contribution

It demonstrates that the string equations of the dispersionless 2-Toda hierarchy govern both hermitian matrix models and Hele-Shaw flow processes, establishing a unifying integrable framework.

Findings

Identifies the common integrable structure in both models

Shows the relevance of the dispersionless 2-Toda hierarchy in Hele-Shaw flows

Bridges matrix models and fluid dynamics through integrable systems

Abstract

It is proved that the system of string equations of the dispersionless 2-Toda hierarchy which arises in the planar limit of the hermitian matrix model also underlies certain processes in Hele-Shaw flows.