Higgs bundle

In mathematics, a Higgs bundle is a pair (E,φ) consisting of a holomorphic vector bundle E and a Higgs field φ, a holomorphic 1-form taking values in End(E) such that φ ∧ φ = 0. Such pairs were introduced by Hitchin (1987), 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 (which is vacuous in Hitchin's original set-up on Riemann surfaces) was introduced later by Simpson.

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