Hitchin Systems at Low Genera

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.

20 pages, latex

References in corpus (5)

• Holomorphic Bundles and Many-Body Systems
• Conformal blocks on elliptic curves and the Knizhnik--Zamolodchikov--Bernard equations
• Chern-Simons States at Genus One
• Unitarity of the Knizhnik-Zamolodchikov-Bernard connection and the Bethe Ansatz for the elliptic Hitchin systems
• Self-duality of the SL_2 Hitchin integrable system at genus two

Cited by in corpus (4)

• Chern-Simons theory and BCS superconductivity
• Spectral curves of the hyperelliptic Hitchin systems
• Spinors, Lagrangians and rank 2 Higgs bundles
• Some reductions of rank 2 and genera 2 and 3 Hitchin systems