Adler-Bell-Jackiw anomaly, the Nieh-Yan form, and vacuum polarization

We show, from first principles, using explicitly invariant Pauli-Villars regularization of chiral fermions, that the Nieh-Yan form does contribute to the Adler-Bell-Jackiw (ABJ) anomaly for spacetimes with generic torsion, and comment on some of the implications. There are a number of interesting and important differences with the usual ABJ contribution in the absence of torsion. For dimensional reasons, the Nieh-Yan term is proportional to the square of the regulator mass. In spacetimes with flat vierbein but nontrivial torsion, the associated diagrams are actually vacuum polarization rather than triangle diagrams and the Nieh-Yan contribution to the ABJ anomaly arises from the fact that the axial torsion “photon” is not transverse.