Massive torsion modes from Adler-Bell-Jackiw and scaling anomalies

TL;DR

This paper shows that axial torsion and torsion trace modes acquire mass due to anomalies in quantum field theories, potentially explaining their elusiveness and related CPT violation effects.

Contribution

It demonstrates from first principles that certain torsion modes become massive due to anomalies, linking quantum regularization to torsion phenomenology.

Findings

Axial torsion modes are non-transverse and massive due to anomalies.

Torsion mass scale is naturally of the order of the regulator scale.

Provides a pedagogical demonstration of anomaly effects on torsion modes.

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.