Mixed anomaly

{{short description|Gauge anomaly from multiple gauge groups}}

In theoretical physics, a mixed anomaly is an example of an anomaly: it is an effect of quantum mechanics — usually a one-loop diagram — that implies that the classically valid general covariance and gauge symmetry of a theory of general relativity combined with gauge fields and fermionic fields cannot be preserved simultaneously in the quantum theory.

The adjective "mixed" usually refers to a mixture of a gravitational anomaly and gauge anomaly, but may also refer to a mixture of two different gauge groups tensored together, like the SU(2) and the U(1) of the Standard Model.

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

Image:Triangle diagram.svg

General covariance and gauge symmetries are very important symmetries for the consistency of the whole theory, and therefore all gravitational, gauge, and mixed anomalies must cancel out.