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We present a general study of 3-point functions of conformal field theory(CFT) in momentum space, following a reconstruction method for tensorcorrelators, based on the solution of the conformal Ward identities (CWIs),introduced in recent works. We investigate and detail the structure of the CWIsand their non-perturbative solutions, and compare them to perturbation theory,taking QED and QCD as examples. Exact solutions of CFT's in the flat backgroundlimit in momentum space are matched by the perturbative realizations in freefield theories, showing that the origin the conformal anomaly is related toefffective scalar interactions, generated by the renormalization of thelongitudinal components of the corresponding operators.

Conformal Ward Identities and the Coupling of QED and QCD to Gravity