Gauge anomaly

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In theoretical physics, a gauge anomaly is an example of an anomaly: it is an effect of quantum mechanics - usually a one-loop diagram - that invalidates the gauge symmetry of a quantum field theory i.e. of a gauge theory.

The anomaly usually appears as a Feynman diagram with a chiral fermion running in the loop (a polygon) with n external gauge bosons attached to the loop where [n=1+D/2] where [D] is the spacetime dimension. Anomalies occur only in even spacetime dimensions. For example, the anomalies in the usual 4 spacetime dimensions arise from triangle Feynman diagrams.

Gauge symmetry is a very important symmetry for the consistency of the whole theory, and therefore all gauge anomalies must cancel out. This indeed happens in the Standard Model.

 

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