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 directly in Lorentzian signature and in a mathematically rigorous manner. It contains a term identical to the integrand in the Atiyah–Singer index theorem and another term involving the \({\eta}\)-invariant of the Cauchy hypersurfaces.
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Communicated by Y. Kawahigashi
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Bär, C., Strohmaier, A. A Rigorous Geometric Derivation of the Chiral Anomaly in Curved Backgrounds. Commun. Math. Phys. 347, 703–721 (2016). https://doi.org/10.1007/s00220-016-2664-1
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DOI: https://doi.org/10.1007/s00220-016-2664-1