  We illustrate how the Conformal Ward Identities (CWI) in momentum space for
parity-odd correlators determine the structure of a chiral anomaly interaction,
taking the example of the VVA (vector/vector/axial-vector) and AAA correlators
in momentum space. Only the conservation and the anomalous WIs, together with
the Bose symmetry, are imposed from the outset for the determination of the
correlators. We use a longitudinal/transverse decomposition of tensor
structures and form factors. The longitudinal (L) component is fixed by the
anomaly content and the anomaly pole, while in the transverse (T) sector we
define a new parameterization. We relate the latter both to the Rosenberg
original representation of the VVA and to the longitudinal/transverse (L/T)
one, first introduced in the analysis of $g-2$ of the muon in the investigation
of the diagram in the chiral limit of QCD. The correlators are completely
identified by the conformal constraints whose solutions are fixed only by the
anomaly coefficient, the residue of the anomaly pole. In both cases, our CFT
result matches the one-loop perturbative expression, as expected. The CWIs for
correlators of mixed chirality $J_L J J_R$ generate solutions in agreement with
the all-orders nonrenormalization theorems of perturbative QCD and in the
chiral limit.
