Hitchin Systems at Low Genera

TL;DR

This paper explores low-genus Hitchin integrable systems and the Knizhnik-Zamolodchikov-Bernard connection, focusing on explicit constructions and relations to classical integrable models at genera 0, 1, and 2.

Contribution

It provides explicit descriptions of Hitchin systems at low genera and constructs action-angle variables for the genus 2 SL(2) case using its connection to the Neumann system.

Findings

Explicit action-angle variables for genus 2 Hitchin system with SL(2)

Relations established between Hitchin systems and classical integrable models

Descriptions of Hitchin systems at low genera (0, 1, 2)

Abstract

The paper gives a quick account of the simplest cases of the Hitchin integrable systems and of the Knizhnik-Zamolodchikov-Bernard connection at genus 0, 1 and 2. In particular, we construct the action-angle variables of the genus 2 Hitchin system with group SL(2) by exploiting its relation to the classical Neumann integrable systems.