Relativistic Calogero-Moser model as gauged WZW theory

TL;DR

This paper explores the derivation of Calogero-Moser and Sutherland integrable particle systems, including their relativistic versions, through Hamiltonian reduction of advanced algebraic structures, connecting them to 2D gauge theories like the gauged G/G WZW model.

Contribution

It introduces a novel Hamiltonian reduction approach to derive relativistic integrable systems and links them to 2D gauge theories, expanding the understanding of their algebraic and field-theoretic foundations.

Findings

Derived Calogero-Moser and Sutherland systems via Hamiltonian reduction.

Established connection between integrable systems and 2D gauged WZW models.

Extended the framework to include relativistic generalizations.

Abstract

We study quantum intergrable systems of interacting particles from the point of view, proposed in our previous paper. We obtain Calogero-Moser and Sutherland systems as well their Ruijsenaars relativistic generalization by a Hamiltonian reduction of integrable systems on the cotangent bundles over semi-simple Lie algebras, their affine algebras and central extensions of loop groups respectively. The corresponding 2d field theories form a tower of deformations. The top of this tower is gauged G/G WZW model on a cylinder with inserted Wilson line in appropriate representation.