3-dimensional mixed BF theory and Hitchin's integrable system

TL;DR

This paper demonstrates how finite Gaudin models and Hitchin systems can be derived from 3-dimensional mixed BF theory through gauge fixing, extending the understanding of their geometric origins.

Contribution

It introduces a novel gauge fixing approach of 3D mixed BF theory to obtain finite Gaudin models and Hitchin systems, connecting these integrable systems to lower-dimensional gauge theories.

Findings

Finite Gaudin models derived from 3D mixed BF theory.

Hitchin systems obtained via similar gauge fixing.

Extension of gauge theory approach to integrable systems.

Abstract

The affine Gaudin model, associated with an untwisted affine Kac-Moody algebra, is known to arise from a certain gauge fixing of 4-dimensional mixed topological-holomorphic Chern-Simons theory in the Hamiltonian framework. We show that the finite Gaudin model, associated with a finite-dimensional semisimple Lie algebra, or more generally the tamely ramified Hitchin system on an arbitrary Riemann surface, can likewise be obtained from a similar gauge fixing of 3-dimensional mixed BF theory in the Hamiltonian framework.