A rigorous geometric derivation of the chiral anomaly in curved backgrounds

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 $\eta$-invariant of the Cauchy hypersurfaces.

references added, introduction rewritten, examples added, published version

References in corpus (2)

• An explicit quantum weak energy inequality for Dirac fields in curved spacetimes
• Locally covariant chiral fermions and anomalies

Cited by in corpus (6)

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• A Mathematical Analysis of the Axial Anomaly
• Energy methods for Dirac-type equations in two-dimensional Minkowski space
• Bogolyubov invariant via relative spectral invariants on manifolds
• Hadamard states for bosonic quantum field theory on globally hyperbolic spacetimes