Title: Chiral anomaly in curved backgrounds
Abstract:
Anomalies in quantum field theory stem from the broken symmetry
of the classical theory upon quantization. A prominent example
is the chiral anomaly related to fermionic fields and to the Dirac operator.
The chiral anomaly can be seen arising from the topology of the problem
setting and analyzed by applying the Atiyah-Singer index theorem on
the Dirac operator. This has been well-studied in a locally Euclidean
framework, but rigorous generalizations to curved geometries are lacking.
In this talk I will briefly cover some basics of quantum anomalies
focusing on the chiral anomaly and the Riemannian Dirac operator,
and outline a generalization of the Riemannian case based on the index
theorem on spatially compact Lorentzian manifolds as recently introduced
by Bär & Strohmaier (arXiv:1508.05345).