Massive torsion modes, chiral gravity, and the Adler-Bell-Jackiw anomaly

TL;DR

This paper explores how axial torsion modes in quantum field theories acquire mass through anomalies, potentially explaining their elusiveness and linking to chiral gravity and CPT violation.

Contribution

It demonstrates from first principles that axial torsion modes become massive due to anomalies, providing insights into their detection challenges and connections to chiral gravity.

Findings

Axial torsion modes have non-transverse vacuum polarization tensors.

Masses of torsion modes are generated at the regulator scale.

The teleparallel limit relates to the Samuel-Jacobson-Smolin action.

Abstract

Regularization of quantum field theories introduces a mass scale which breaks axial rotational and scaling invariances. We demonstrate from first principles that axial torsion and torsion trace modes have non-transverse vacuum polarization tensors, and become massive as a result. The underlying reasons are similar to those responsible for the Adler-Bell-Jackiw (ABJ) and scaling anomalies. Since these are the only torsion components that can couple minimally to spin 1/2 particles, the anomalous generation of masses for these modes, naturally of the order of the regulator scale, may help to explain why torsion and its associated effects, including CPT violation in chiral gravity, have so far escaped detection. As a simpler manifestation of the reasons underpinning the ABJ anomaly than triangle diagrams, the vacuum polarization demonstration is also pedagogically useful. In addition it is shown that the teleparallel limit of a Weyl fermion theory coupled only to the left-handed spin connection leads to a counter term which is the Samuel-Jacobson-Smolin action of chiral gravity in four dimensions.