Integrable (2k)-Dimensional Hitchin Equations

Abstract

This letter describes a completely-integrable system of Yang-Mills-Higgs equations which generalizes the Hitchin equations on a Riemann surface to arbitrary k-dimensional complex manifolds. The system arises as a dimensional reduction of a set of integrable Yang-Mills equations in 4k real dimensions. Our integrable system implies other generalizations such as the Simpson equations and the non-abelian Seiberg-Witten equations. Some simple solutions in the k=2 case are described.

11 pages, 1 figure

References in corpus (2)

• Octonions, Monopoles, and Knots
• Geometry of Solutions of Hitchin Equations on R^2

Cited by in corpus (3)

• The Kapustin-Witten equations and nonabelian Hodge theory
• On an integrable deformation of Kapustin-Witten systems
• On $2k$-Hitchin's equations and Higgs bundles: a survey