25.04.2024, 16:15
– Raum 1.10
Forschungsseminar Differentialgeometrie
Atiyah-Singer-Indexsatz
Lennart Ronge (UP)
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.