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

TL;DR

This paper demonstrates that the Nieh-Yan form contributes to the ABJ anomaly in spacetimes with torsion using invariant regularization, revealing new effects in the presence of torsion and non-transverse axial torsion.

Contribution

It explicitly shows the Nieh-Yan form's contribution to the ABJ anomaly with invariant regularization, highlighting differences from the torsion-free case.

Findings

Nieh-Yan form contributes to ABJ anomaly with torsion.

Vacuum polarization diagrams replace triangle diagrams in certain torsion cases.

Nieh-Yan contribution is proportional to the square of the regulator mass.

Abstract

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 contributions in the absence of torsion. For dimensional reasons, the Nieh-Yan contribution is proportional to the square of the regulator mass. In spacetimes with flat vierbein but non-trivial 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.