Exact Correlators from Conformal Ward Identities in Momentum Space and the Perturbative $TJJ$ Vertex

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We present a general study of 3-point functions of conformal field theory in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWI' s), introduced in recent works by Bzowski, McFadden and Skenderis (BMS).

• We investigate and detail the structure of the CWI's, their non-perturbative solutions and the transition to momentum space, comparing them to perturbation theory by taking QED as an example.
• We then proceed with an analysis of the $TJJ$ correlator, presenting independent and detailed re-derivations of the conformal equations in the reconstruction method of BMS, originally formulated using a minimal tensor basis in the transverse traceless sector.
• A careful comparison with a second basis introduced in previous studies shows that this correlator is affected by one anomaly pole in the graviton (T) line, induced by renormalization.