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 only occur 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.