The Trace Anomaly and the Gravitational Coupling of an Anomalous U(1)

TL;DR

This paper investigates the structure of the trace anomaly in abelian gauge theories with mixed axial-vector and vector currents, revealing the role of massless scalar degrees of freedom in gravitational couplings.

Contribution

It extends previous work on the TJJ correlator to mixed axial-vector/vector currents and analyzes the anomalous Ward identities and their implications for gauge and conformal anomalies.

Findings

Mixed massive correlators of the form TJ_V J_A vanish due to Ward identities and C-invariance.

Massless scalar degrees of freedom appear in the coupling of chiral and vector theories to gravity.

Results align with prior studies on gauge and conformal anomalies in QED and QCD.

Abstract

We extend a previous computation of the TJJ correlator, involving the energy-momentum tensor of an abelian gauge theory and two vector currents, to the case of mixed axial-vector/vector currents. The study is performed in analogy to the case of the $AVV$ vertex for the chiral anomaly. We derive the general structure of the anomalous Ward identities and provide explicit tests of their consistency using Dimensional Reduction. Mixed massive correlators of the form $TJ_V J_A$ are shown to vanish both by Ward identities and by C-invariance. The result is characterized by the appearance of massless scalar degrees of freedom in the coupling of chiral and vector theories to gravity, affecting both the soft and the ultraviolet region of the vertex. This is in agreement with previous studies of the effective action of gauge and conformal anomalies in QED and QCD.