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

TL;DR

The paper probes the enigmatic anomaly poles in anomalous U(1) gauge theories by performing a comprehensive off-shell analysis of the AVV vertex in both the Rosenberg and longitudinal/transverse representations. It shows that anomaly poles can be IR-decoupled yet UV-dominant, implying that a consistent theory requires cancellation of these poles or a nonlocal UV completion; the work also connects the 4D analysis to 5D inflow scenarios and demonstrates how pole-dominated amplitudes threaten unitarity unless the full higher-dimensional structure is included. By deriving explicit massless and massive form factors, and mapping between parameterizations, the authors construct an effective action that isolates the pole contribution and its nonlocal completion, providing a bridge between local effective actions and UV-complete theories. The findings illuminate the UV role of anomaly poles, the need for complete inflow mechanisms in extra dimensions, and set the stage for extending the analysis to conformal anomalies and related nonlocal structures. The results have implications for anomaly cancellation, UV completions, and the consistent formulation of theories with anomalous U(1) symmetries.

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.

Figures (3)

• Figure 1: Triangle diagram with an axial-vector current ($\lambda$) and two vector currents ($\mu$, $\nu$). The momentum parameterization for the direct and the exchange contribution is written here in an explicit form for future reference.
• Figure 2: The scattering process $AA\rightarrow AA$ via a BIM amplitude in the three channels. The subscript $s, t, u$ stands for the channel. The exchanged gauge boson $B$ is different from the external ones and has a mass $M_B$.
• Figure 3: BIM amplitude in the presence of a KK tower of modes exchanged in the s-channel. In a) the external zero modes $A_{(0)}$ are massless while in b) they have a fixed even KK parity $(i)$ and vector couplings with the fermions in the loop.