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.

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Cited by in corpus (3)

• Lagrangian multiforms on coadjoint orbits for finite-dimensional integrable systems
• 4D Chern-Simons theory with auxiliary fields
• Integrable models from 4d holomorphic BF theory