The Chiral Anomaly in QFT and Gravity

Nich Harshman

Chiral symmetry (where we project particles into right- and left-handed components) is deeply important in the standard model, and nature doesn't treat both hands in the same way. Most notably, the Z boson couples to each hand in a different way, and the W bosons do not couple to right-handed particles at all! However, when we quantize a theory of fermions (more specifically, Dirac spinors), we find that this classical symmetry breaks down at the quantum level. This is the chiral anomaly, and it explains why the neutral pion decay's into two photons.

Gravitation is very similar in structure to the theory of gauge fields that describe the vector bosons. Naturally, we are able to derive an analogous anomaly for a fermion coupled to curved spacetime. Both of these cases of the chiral anomaly will be presented and discussed.

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