Anomalous U(1) Models in Four and Five Dimensions and their Anomaly Poles

TL;DR

This paper investigates the role of anomaly poles in anomalous gauge theories, analyzing their signatures, origins, and implications for unitarity and model consistency in four and five dimensions.

Contribution

It provides a comprehensive perturbative analysis of anomaly vertices using two representations, clarifies the UV significance of anomaly poles, and discusses their impact on unitarity and model formulation.

Findings

Anomaly poles do not couple in the infrared for generic vertices.

Poles are responsible for unitarity violations in the UV.

Consistent models require cancellation of polar contributions.

Abstract

We analyze the role played by anomaly poles in an anomalous gauge theory by discussing their signature in the corresponding off-shell effective action. The origin of these contributions, in the most general kinematical case, is elucidated by performing a complete analysis of the anomaly vertex at perturbative level. We use two independent (but equivalent) representations: the Rosenberg representation and the longitudinal/transverse (L/T) parameterization, used in recent studies of $g-2$ of the muon and in the proof of non-renormalization theorems of the anomaly vertex. The poles extracted from the L/T parameterization do not couple in the infrared for generic anomalous vertices, as in Rosenberg, but we show that they are responsible for the violations of unitarity in the UV region, using a class of pole-dominated amplitudes. We conclude that consistent formulations of anomalous models require necessarily the cancellation of these polar contributions. Establishing the UV significance of these terms provides a natural bridge between the anomalous effective action and its completion by a nonlocal theory. Some additional difficulties with unitarity of the mechanism of inflow in extra dimensional models with an anomalous theory on the brane, due to the presence of anomaly poles, are also pointed out.