Axion anomalies

TL;DR

This paper investigates how axion-like fields induce anomalies in fermionic axial currents, exploring their origins, effects in gravitational backgrounds, and implications during inflation, combining quantum field theory and gravitational effects.

Contribution

It provides a detailed analysis of fermion-axion couplings, demonstrating the origin of anomalies and the role of counterterms in the presence of gravity and during inflation.

Findings

Axion fields induce non-conservation of axial currents in massless fermions.

Counterterms can remove anomaly contributions in the effective action.

Anomalies are confirmed during pseudoscalar-driven inflation in de Sitter space.

Abstract

We study fermions derivatively coupled to axion-like or pseudoscalar fields, and show that the axial vector current of the fermions is not conserved in the limit where the fermion is massless. This apparent violation of the classical chiral symmetry is due to the background axion field. We compute the contributions to this anomalous Ward identity due to the pseudoscalar field alone, which arise in Minkowski space, as well as the effects due to an interaction with an external gravitational field. For the case of massless fermions, these interactions induce terms in the axion effective action that can be removed by the addition of local counterterms. We demonstrate that these counterterms are generated by the transformation of the path integral measure when transforming the theory from a form where the chiral symmetry is manifest to one where the symmetry is only apparent after using the classical equations of motion. We work perturbatively in Minkowski space and include the effects of interactions with a linearized gravitational field. Using the heat kernel method, we study the transformation properties of the path integral measure, and include the effects of non-linear gravity as well as interactions with gauge fields. Finally, we verify our relation by considering derivatively coupled fermions during pseudoscalar-driven inflation and computing the divergence of the axial current in de Sitter spacetime.