Axial gravity: a non-perturbative approach to split anomalies

TL;DR

This paper develops a non-perturbative method to compute split anomalies in a Dirac fermion theory coupled to a metric-axial-tensor background, confirming previous findings on odd parity trace anomalies.

Contribution

It introduces a non-perturbative approach using heat kernel techniques to compute split anomalies in a novel fermion-gravity coupling model.

Findings

Computed two odd parity trace anomalies non-perturbatively.

Verified anomalies converge to known odd parity trace anomaly in a specific limit.

Confirmed previous results on the coefficient and form of the odd parity trace anomaly.

Abstract

In a theory of a Dirac fermion field coupled to a metric-axial-tensor (MAT) background, using a Schwinger-DeWitt heat kernel technique, we compute non-perturbatively the two (odd parity) trace anomalies. A suitable collapsing limit of this model corresponds to a theory of chiral fermions coupled to (ordinary) gravity. Taking this limit on the two computed trace anomalies we verify that they tend to the same expression, which coincides with the already found odd parity trace anomaly, with the identical coefficient. This confirms our previous results on this issue.