Integrable (2k)-Dimensional Hitchin Equations

TL;DR

This paper introduces a new integrable system of Yang-Mills-Higgs equations extending Hitchin equations to higher-dimensional complex manifolds, derived from higher-dimensional Yang-Mills equations, with implications for other generalized equations.

Contribution

It presents a novel integrable system generalizing Hitchin equations to arbitrary complex dimensions, derived from higher-dimensional Yang-Mills equations, and connects to other important equations.

Findings

Derived simple solutions for the case k=2

Established connections to Simpson and non-abelian Seiberg-Witten equations

Generalized Hitchin equations to higher dimensions

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.