Hitchin systems at low genera

Hitchin Systems at Low Genera

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 SL2 by exploiting its relation to the classical Neumann integrable systems. 1 Hitchin systems As was realized by Hitchin in [16], a large f...

Hitchin systems on ll-curves

Hitchin systems in N = 2 field theory

This note is a short review of the way Hitchin systems appear in four-dimensional N = 2 supersymmetric field theory. The literature on the Hitchin system and its role in quantum field theory is a vast one. Restricting attention just to the role of Hitchin systems in N = 2 supersymmetric field theory (thus neglecting such fascinating topics as T-duality on the Hitchin fibration and its relation ...

Donagi-markman Cubic for Hitchin Systems

The Donagi-Markman cubic is the differential of the period map for algebraic completely integrable systems. Here we prove a formula for the cubic in the case of Hitchin’s system for arbitrary semisimple g. This was originally stated (without proof) by Pantev for sln.

Hecke-tyurin Parametrization of the Hitchin and Kzb Systems

We study the parametrization of the moduli space Bun2(C)L of rank 2 bundles over a curve C with fixed determinant, provided by Hecke modifications at fixed points of the trivial bundle. This parametrization is closely related to the Tyurin parametrization of vector bundles over curves. We use it to parametrize the Hitchin and KZB systems, as well as lifts of the Beilinson-Drinfeld D-modules. We...