Fermions on curved spaces, symmetries, and quantum anomalies

Investigating the Dirac equation in curved backgrounds we point out the role of the Killing‐Yano tensors in the construction of the Dirac‐type operators. The gravitational and axial anomalies are studied for generalized Euclidean Taub‐Newman‐Unti‐Tamburino (Taub‐NUT) metrics, which admit hidden symmetries analogous to the Runge‐Lenz vector of the Kepler‐type problem. The generalized Taub‐NUT metrics exhibit in general gravitational anomalies. Using the Atiyah‐Patodi‐Singer index theorem for manifolds with boundaries, it is shown that these metrics make no contribution to the axial anomaly.