Renormalised 3-point functions of stress tensors and conserved currents in CFT

TL;DR

This paper provides a comprehensive momentum-space method for renormalising tensorial 3-point functions in conformal field theories, with explicit results in 3 and 4 dimensions, including anomalies.

Contribution

It introduces a complete prescription for renormalising stress tensor and current correlators in CFTs, revealing the structure of conformal anomalies and their relation to known anomalies.

Findings

Explicit renormalised 3-point correlators in 3 and 4 dimensions

Identification of the tensor structure responsible for the Euler anomaly

Demonstration that the Euler anomaly resembles a double copy of the chiral anomaly

Abstract

We present a complete momentum-space prescription for the renormalisation of tensorial correlators in conformal field theories. Our discussion covers all 3-point functions of stress tensors and conserved currents in arbitrary spacetime dimensions. In dimensions three and four, we give explicit results for the renormalised correlators, the anomalous Ward identities they obey, and the conformal anomalies. For the stress tensor 3-point function in four dimensions, we identify the specific evanescent tensorial structure responsible for the type A Euler anomaly, and show this anomaly has the form of a double copy of the chiral anomaly.