Exact Correlators from Conformal Ward Identities in Momentum Space and Perturbative Realizations

Understand

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.