  The general solution of the conformal Ward identities (CWI's) in momentum
space, and their matching to perturbation theory, allows to uncover some
specific characteristics of the breaking of conformal symmetry, induced by the
anomaly. It allows to compare perturbative features of the 1-particle
irreducible (1PI, nonlocal) anomaly action with the prediction of a similar
(but exact) nonlocal action identified by the CWI's. The two predictions can be
exactly matched at the level of 3-point functions. The analysis of the $TJJ$
and $TTT$ shows that both approaches - based either on 1PI or on the exact
solutions of the CWI's - predict massless (dynamical) scalar exchanges in
3-point functions as the signature of the conformal anomaly. In a local
formulation such 1PI actions exhibit a ghost in the spectrum which may induce
ghost condensation. We also discuss alternative approaches, which take to
Wess-Zumino forms of the action with an asymptotic dilaton, which should be
considered phenomenological alternatives to the exact nonlocal action. If
derived by a Weyl gauging, they also include a ghost in the spectrum. The two
formulations, nonlocal and of WZ type, can be unified under the assumption that
they describe the same anomaly phenomenon at two separate (UV/IR) ends of the
renormalization group flow, possibly separated by a vacuum rearrangement at an
intermediate scale. A similar analysis is presented for an $\mathcal{N}=1$
supersymmetric Yang-Mills theory. We comment on the possibile cosmological
implications of such quasi Nambu-Goldstone modes as ultralight dilatons and
axions.
