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).