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Can somebody provide a fairly brief explanation of what the chiral anomaly is? I have been unable to find a concise reference for this. I know QFT at the P&S level so don't be afraid to use math.

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Why don't you just start with Wikipedia for such very general intro questions? See en.wikipedia.org/wiki/Chiral_anomaly –  Luboš Motl Sep 22 '12 at 6:31

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There is a very simple and enlightening explanation due to N.V.Gribov given in his following conference article and also beautifully explained by Dmitri Kharzeev in the following arxiv article(section 1). Gribov's argument doesn't involve the heavy machinery of quantum field theory. He actually proves that in the case of colinear electric and magnetic fields acting on gapless fermions,there is a net flow of chiral charge from the Dirac sea as dictated by the anomaly equation.

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