  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.
