Anomaly Poles as Common Signatures of Chiral and Conformal Anomalies

TL;DR

This paper demonstrates that anomaly poles, initially associated with infrared effects in chiral anomalies, also appear in conformal anomalies affecting gauge fields and gravity, influencing the theories' ultraviolet behavior.

Contribution

It extends the analysis of anomaly poles from chiral anomalies to conformal anomalies, showing their role in the effective action involving gravity and gauge fields.

Findings

Anomaly poles are present in the conformal anomaly effective action.

These poles are decoupled in the infrared but dominate the anomaly.

They influence the non-unitary behavior in the ultraviolet region.

Abstract

One feature of the chiral anomaly, analyzed in a perturbative framework, is the appearance of massless poles which account for it. They are identified by a spectral analysis of the anomaly graph and are usually interpreted as being of an infrared origin. Recent investigations show that their presence is not just confined in the infrared, but that they appear in the effective action under the most general kinematical conditions, even if they decouple in the infrared. Further studies reveal that they are responsible for the non-unitary behaviour of these theories in the ultraviolet (UV) region. We extend this analysis to the case of the conformal anomaly, showing that the effective action describing the interaction of gauge fields with gravity is characterized by anomaly poles that give the entire anomaly and are decoupled in the infrared (IR), in complete analogy with the chiral case. This complements a related analysis by Giannotti and Mottola on the trace anomaly in gravity, in which an anomaly pole has been identified in the corresponding correlator using dispersion theory in the IR. Our extension is based on an exact computation of the off-shell correlation function involving an energy-momentum tensor and two vector currents (the gauge-gauge-graviton vertex) which is responsible for the appearance of the anomaly.