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

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.

5 pages. Proceedings of the Workshop QCD@work 2018, 25-28 June 2018, Matera, Italy

References in corpus (4)

• Renormalised CFT 3-point functions of scalars, currents and stress tensors
• A Nernst current from the conformal anomaly in Dirac and Weyl semimetals
• Exact Correlators from Conformal Ward Identities in Momentum Space and the Perturbative $TJJ$ Vertex
• Renormalization, Conformal Ward Identities and the Origin of a Conformal Anomaly Pole

Cited by in corpus (4)

• Double copy structure of parity-violating CFT correlators
• Higher spin 3-point functions in 3d CFT using spinor-helicity variables
• Momentum space parity-odd CFT 3-point functions
• Constraining momentum space correlators using slightly broken higher spin symmetry