Spectral curve duality beyond the two-matrix model

TL;DR

This paper introduces an algebraic approach to spectral duality in integrable systems, demonstrating its application to two-matrix models and minimal model conformal field theories coupled to gravity.

Contribution

It presents a unified algebraic framework for spectral dualities, extending beyond the two-matrix model to minimal models coupled with gravity.

Findings

Unified algebraic approach to spectral duality

Application to two-matrix model duality

Application to minimal model conformal field theories

Abstract

We describe a simple algebraic approach to several spectral duality results for integrable systems and illustrate the method for two types of examples: The Bertola-Eynard-Harnad spectral duality of the two-matrix model as well as the various dual descriptions of minimal model conformal field theories coupled to gravity.