BAER, C. and STROHMAIER, A., 2015. A rigorous geometric derivation of the chiral anomaly in curved backgrounds. arXiv:1508.05345v1 [math-ph], 15pp.
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 $\eta$-invariant of the Cauchy hypersurfaces.
This is a preprint submitted to arXiv on 21 August 2015