Higgs bundle
In mathematics, a Higgs bundle is a pair consisting of a holomorphic vector bundle E and a Higgs field φ, a holomorphic 1-form taking values in End such that φ ∧ φ = 0.
Such pairs were introduced by, who named the field φ after Peter Higgs because of an analogy with Higgs bosons. The term 'Higgs bundle', and the condition φ ∧ φ = 0 was introduced later by Simpson.
A Higgs bundle can be thought of as a "simplified version" of a flat holomorphic connection on a holomorphic vector bundle, where the derivative is scaled to zero. The nonabelian Hodge correspondence says that, under suitable stability conditions, the categories of flat holomorphic connections and Higgs bundles are actually equivalent, so one can learn a lot about gauge theory by working with the simplified objects, Higgs bundles.
