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

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.

2D Integrable systems, 4D Chern–Simons theory and affine Higgs bundles

“…In a recent paper[13], the authors proposed an approach to the affine Gaudin models based on the three-dimensional (3D) BF theory that is very close to the AHB construction.…”

2d Integrable systems, 4d Chern-Simons theory and Affine Higgs bundles

“…In recent paper[21] authors proposed approach to the affine Gaudin models based on the 3d BF theory, which is very close to the AHB construction.…”