Mixed anomaly

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.

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. Anomalies occur only in even spacetime dimensions. For example, the anomalies in the usual 4 spacetime dimensions arise from triangle Feynman diagrams.

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.

String theory	Bosonic string theory M-theory Supergravity Superstring theory

Canonical quantum gravity	Loop quantum gravity Wheeler–DeWitt equation

Euclidean quantum gravity	Hartle–Hawking state

Others	Causal dynamical triangulation Causal sets Noncommutative geometry Spin foam Group field theory Superfluid vacuum theory Twistor theory

Applications

Quantum cosmology

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Mixed anomaly

See also