Gauge theories, Simple Groups and Integrable Systems

TL;DR

This review explores the connections between Hitchin integrable systems, monodromy equations, and topological field theories derived from N=4 supersymmetric Yang-Mills, emphasizing the role of characteristic classes and monopoles.

Contribution

It introduces systems linked to nontrivial characteristic classes and elucidates their relation to monopole configurations in Yang-Mills theory.

Findings

Relations between Hitchin systems and monodromy equations clarified.

Characteristic classes linked to monopole configurations.

Insights into topological field theories from supersymmetric Yang-Mills.

Abstract

In this review we discuss interrelations between classical Hitchin integrable systems, monodromy preserving equations and topological field theories coming from N=4 supersymmetric Yang-Mills theories developed by Gukov, Kapustin and Witten. In particular, we define systems related to bundles with nontrivial characteristic classes and discuss relations of the characteristic classes with monopole configurations in the Yang-Mills theory.