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2008

Lectures on Anomalies

Bilal, Adel

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These lectures on anomalies are relatively self-contained and intended for graduate students who are familiar with the basics of quantum field theory.

We begin with several derivations of the abelian anomaly: anomalous transformation of the measure, explicit computation of the triangle Feynman diagram, relation to the index of the Euclidean Dirac operator.
The chiral (non-abelian) gauge anomaly is derived by evaluating the anomalous triangle diagram with three non-abelian gauge fields coupled to a chiral fermion.
We discuss in detail the relation between anomaly, current non-conservation and non-invariance of the effective action, with special emphasis on the derivation of the anomalous Slavnov-Taylor/Ward identities.

Lectures on Anomalies · Around

Built on

B. Zumino, Chiral anomalies and differential geometry: Lectures given at Les Houches, August 1983
1983
Earlier work this paper cites.
L. Alvarez-Gaumé and E. Witten, Gravitational anomalies
1984
Earlier work this paper cites.
S. Treiman, R. Jackiw, B. Zumino and E. Witten, Current algebra and anomalies
1985
Earlier work this paper cites.
L. Alvarez-Gaumé, An introduction to anomalies
1985
Earlier work this paper cites.
L. Alvarez-Gaumé and P. Ginsparg, The structure of gauge and gravitational anomalies
1986
Earlier work this paper cites.

Similar

M. B. Green, J. H. Schwarz and E. Witten, Superstring theory
1987
Cited alongside, same era.
P. van Nieuwenhuizen, Anomalies in quantum field theory: Cancellation of anomalies in d = 10 d=10 supergravity
1989
Cited alongside, same era.
S. Weinberg, The quantum theory of fields
1996
Cited alongside, same era.
J. Polchinski, String theory
1998
Cited alongside, same era.
M. Nakahara, Geometry, topology and physics
Cited in the paper.

Then

J. A. Harvey, TASI 2003 lectures on anomalies
2003
Later among the works it cites.
A. Bilal and S. Metzger, Anomaly cancellation in M-theory: A critical review
2003
Later among the works it cites.
K. Fujikawa and H. Suzuki, Path integrals and quantum anomalies
2004
Later among the works it cites.
J. Zinn-Justin, Chiral anomalies and topology
2005
Later among the works it cites.

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