Finding and solving Calogero-Moser type systems using Yang-Mills gauge theories

TL;DR

This paper demonstrates how Yang-Mills gauge theories on a cylinder can be used to identify and solve Calogero-Moser type integrable systems, including new variants, by exploiting gauge invariance.

Contribution

It establishes a novel connection between Yang-Mills models and Calogero-Moser systems, enabling the derivation and solution of new integrable models through gauge invariance.

Findings

Equivalence between certain Yang-Mills models and Calogero-Moser systems.

Introduction of a generalized ansatz leading to new integrable systems.

Successful solving of these systems using gauge invariance.

Abstract

Yang-Mills gauge theory models on a cylinder coupled to external matter charges provide powerful means to find and solve certain non-linear integrable systems. We show that, depending on the choice of gauge group and matter charges, such a Yang-Mills model is equivalent to trigonometric Calogero-Moser systems and certain known spin generalizations thereof. Choosing a more general ansatz for the matter charges allows us to obtain and solve novel integrable systems. The key property we use to prove integrability and to solve these systems is gauge invariance of the corresponding Yang-Mills model.