A rigorous geometric derivation of the chiral anomaly in curved backgrounds

Autoren: Christian Bär, Alexander Strohmaier (2016)

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.

Zeitschrift:
Comm. Math. Phys.
Verlag:
Springer
Seiten:
703-721
Band:
347, no. 3

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