Gauge Anomaly

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.

Anomalies in gauge symmetries lead to an inconsistency, since a gauge symmetry is required in order to cancel unphysical degrees of freedom with a negative norm (such as a photon polarized in the time direction). Therefore all gauge anomalies must cancel out. This indeed happens in the Standard Model.

The term gauge anomaly is usually used for vector gauge anomalies. Another type of gauge anomaly is the gravitational anomaly, because reparametrization is a gauge symmetry in gravitation.

Read more about Gauge AnomalyCalculation of The Anomaly

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Gauge Anomaly - Calculation of The Anomaly
... In vector gauge anomalies (in gauge symmetries whose gauge boson is a vector), the anomaly is a chiral anomaly, and can be calculated exactly at one loop level, via a Feynman diagram with a chiral fermion running in ... If there is a gauge anomaly, the resulting action will not be gauge invariant ... If we denote by the operator corresponding to an infinitesimal gauge transformation by ε, then the Frobenius consistency condition requires that for any functional, including the (semi)effective ...