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arXiv · 1508.05345

A rigorous geometric derivation of the chiral anomaly in curved backgrounds

Christian Baer·Alexander Strohmaier
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Abstract

We discuss the chiral anomaly for a Weyl field in a curved background and show that a novel index theorem for the Lorentzian Dirac operator can be applied to describe the gravitational chiral anomaly. A formula for the total charge generated by the gravitational and gauge field background is derived in a mathematically rigorous manner. It contains a term identical to the integrand in the Atiyah-Singer index theorem and another term involving the $η$-invariant of the Cauchy hypersurfaces.

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Christian Baer, Alexander Strohmaier. 2016-04-01. A rigorous geometric derivation of the chiral anomaly in curved backgrounds. https://doi.org/10.1007/s00220-016-2664-1

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