Anomaly (physics) - Gauge Anomalies

Gauge Anomalies

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). An attempt to cancel them—i.e., to build theories consistent with the gauge symmetries—often leads to extra constraints on the theories (such is the case of the gauge anomaly in the Standard Model of particle physics). Anomalies in gauge theories have important connections to the topology and geometry of the gauge group.

Anomalies in gauge symmetries can be calculated exactly at the one-loop level. At tree level (zero loops), one reproduces the classical theory. Feynman diagrams with more than one loop always contain internal boson propagators. As bosons may always be given a mass without breaking gauge invariance, a Pauli–Villars regularization of such diagrams is possible while preserving the symmetry. Whenever the regularization of a diagram is consistent with a given symmetry, that diagram does not generate an anomaly with respect to the symmetry.

Vector gauge anomalies are always chiral anomalies. Another type of gauge anomaly is gravitational anomaly.