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Chiral anomalies

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Recently I have read that there is contraction of chiral anomalies in SM. But people are working on chiral anomalies theory. So I have the question: what is the importance of development of the theory of the chiral anomalies in SM (I see that at least in general it is already at good level) and are there some chiral anomalies in realistic extensions of SM (or, maybe, in some cosmology researches)?

This post imported from StackExchange Physics at 2014-09-20 07:47 (UCT), posted by SE-user Andrew McAddams
asked Sep 19, 2014 in Theoretical Physics by Andrew McAddams (340 points) [ no revision ]
Some general context: In QFTs, anomalies are fairly straight-forward to compute, at the one-loop level. In the case of the standard model, anomaly cancellation works out quite miraculously with unlikely looking cancellations among numbers that depend on the gauge charges -- giving rise to an expectation that there's some simpler UV picture from which these charges come out, and anomaly cancellation in that bigger picture might be easy to understand.

This post imported from StackExchange Physics at 2014-09-20 07:47 (UCT), posted by SE-user Siva
In particular, chiral anomalies are possible when you have "chiral currents" in your theory, i.e. only the Left (or right) handed fermions are charged under some symmetry. Since in the SM, only left-handed fermions are charged under the weak sector, one has to ensure that the gauge symmetry is kosher at the quantum level, and not "anomalous". My comments are very general (hopefully useful to someone) and you might already know all that, and be looking for something specific.

This post imported from StackExchange Physics at 2014-09-20 07:47 (UCT), posted by SE-user Siva

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