  We discuss, in conformally invariant field theories such as QCD with massless
fermions, a possible link between the perturbative signature of the conformal
anomaly, in the form of anomaly poles of the 1-particle irreducible effective
action, and its description in terms of Wess-Zumino actions with a dilaton. The
two descriptions are expected to capture the UV and IR behaviour of the
conformal anomaly, in terms of fundamental and effective degrees of freedom
respectively, with the dilaton effective state appearing in a nonlinear
realization. As in the chiral case, conformal anomalies seem to be related to
the appearance of these effective interactions in the 1PI action in all the
gauge-invariant sectors of the Standard Model. We show that, as a consequence
of the underlying anomalous symmetry, the infinite hierarchy of recurrence
relations involving self-interactions of the dilaton is entirely determined
only by the first four of them. This relation can be generalized to any even
space-time dimension.
