Dualities in integrable systems and N=2 theories

TL;DR

This paper explores dualities in integrable systems linked to N=2 supersymmetric Yang-Mills theories, revealing connections to string theory T duality, S duality, and 3d mirror symmetry, and their implications for low-energy dynamics.

Contribution

It establishes novel correspondences between string dualities and integrable system transformations in the context of N=2 theories.

Findings

T duality relates to separation of variables in integrable systems

Analogues of S duality and 3d mirror symmetry are identified in many-body Hitchin systems

Insights into low-energy effective actions of N=2 theories

Abstract

We discuss dualities of the integrable dynamics behind the exact solution to the N=2 SUSY YM theory. It is shown that T duality in the string theory is related to the separation of variables procedure in dynamical system. We argue that there are analogues of S duality as well as 3d mirror symmetry in the many-body systems of Hitchin type governing low-energy effective actions.