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arXiv · 1604.07247

Integrable (2k)-Dimensional Hitchin Equations

R. S. Ward
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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.

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R. S. Ward. 2016-04-25. Integrable (2k)-Dimensional Hitchin Equations. https://doi.org/10.1007/s11005-016-0849-3

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