Duality in Integrable Systems and Gauge Theories

TL;DR

This paper explores dualities connecting integrable systems and gauge theories, explaining them via Hamiltonian and Poisson reductions, leading to new integrable models including double elliptic systems and applications in supersymmetric gauge theories.

Contribution

It provides a unified framework for understanding dualities in integrable systems through Hamiltonian and Poisson reductions, and introduces new integrable models like double elliptic systems.

Findings

Dualities are explained via Hamiltonian and Poisson reductions.

New integrable systems, including double elliptic models, are constructed.

Applications to supersymmetric gauge theories are discussed.

Abstract

We discuss various dualities, relating integrable systems and show that these dualities are explained in the framework of Hamiltonian and Poisson reductions. The dualities we study shed some light on the known integrable systems as well as allow to construct new ones, double elliptic among them. We also discuss applications to the (supersymmetric) gauge theories in various dimensions.