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

TL;DR

This paper analyzes 3-point functions in conformal field theories in momentum space, solving conformal Ward identities and comparing non-perturbative solutions with perturbation theory, especially in QED and QCD, revealing the role of conformal anomalies.

Contribution

It provides a comprehensive study of conformal Ward identities for tensor correlators in momentum space, linking non-perturbative solutions to perturbative free field theories in QED and QCD.

Findings

Exact solutions match perturbative free field theories.

Conformal anomalies relate to effective scalar interactions.

Longitudinal operator components are key to anomalies.

Abstract

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