# 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.

## See also

## References

- Gothen, Peter B.; García-Prada, Oscar; Bradlow, Steven B. (2007), "What is... a Higgs bundle?" (PDF),
*Notices of the American Mathematical Society*,**54**(8): 980–981, ISSN 0002-9920, MR 2343296 - Hitchin, N. J. (1987), "The self-duality equations on a Riemann surface",
*Proceedings of the London Mathematical Society*, Third Series,**55**(1): 59–126, CiteSeerX 10.1.1.557.2243, doi:10.1112/plms/s3-55.1.59, ISSN 0024-6115, MR 0887284 - Simpson, Carlos T. (1992), "Higgs bundles and local systems",
*Publications Mathématiques de l'IHÉS*,**75**(75): 5–95, doi:10.1007/BF02699491, ISSN 1618-1913, MR 1179076

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