{{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 <math>n=1+D/2</math> where <math>D</math> 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.
==References== * {{cite book |last1=Cheng |first1=T.P.|last2=Li |first2=L.F. |date=1984 |title=Gauge Theory of Elementary Particle Physics|publisher=Oxford Science Publications }}
== See also ==
* Gravitational anomaly * Green–Schwarz mechanism
{{quantum gravity}}
{{DEFAULTSORT:Mixed Anomaly}} Category:Anomalies (physics) Category:Quantum gravity
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