nLab anomaly cancellation

Idea

Given an action functional with a quantum anomaly, an anomaly cancellation is a modification of this such that the anomaly disappears. Usually this is specifically understood to be the modification given by adding another action functional which is also anomalous, such that the total anomaly vanishes, hence that both contributions cancel each other.

For more see at quantum anomaly.

Related concepts

• tadpole cancellation

References

General

With an eye towards application in mathematical physics:

• Mikio Nakahara, Chapter 13 of: Geometry, Topology and Physics, IOP 2003 (doi:10.1201/9781315275826, pdf)

Discussions of spin structures as anomaly cancellation for the spinning particle (see also the references hereuantum mechanics#ReferencesRelationToMorseTheory) at supersymmetric quantum mechanics):

• Edward Witten, p. 65-68 in: Global anomalies in string theory, in: W. Bardeen and A. White (eds.) Symposium on Anomalies, Geometry, Topology, World Scientific (1985) 61-99 [pdf, spire:214913]

• Luis Alvarez-Gaumé, p. 165 of: Supersymmetry and the Atiyah-Singer index theorem, Comm. Math. Phys. 90 2 (1983) 161-173 [doi:10.1007/BF01205500, euclid]

• Daniel Friedan, P. Windey, Supersymmetric derivation of the Atiyah-Singer index and the chiral anomaly, Nucl. Phys. B 235 (1984) 395 [doi:10.1016/0550-3213(84)90506-6]

In the standard model of particle physics

Discussion of anomaly cancellation in the standard model of particle physics:

• Nakarin Lohitsiri, David Tong, Hypercharge Quantisation and Fermat’s Last Theorem (arXiv:1907.00514)

  (relating to Fermat's last theorem)

In string theory

Review in string theory:

• John H. Schwarz, Anomaly Cancellation: A Retrospective From a Modern Perspective (2001) [doi:10.1142/9789812778185_0014, pdf]