Double copy structure and the flat space limit of conformal correlators in even dimensions

TL;DR

This paper investigates the flat space limit of conformal field theory correlators in even dimensions, revealing a double copy structure and analyzing the role of divergences, renormalization, and trace anomalies in this limit.

Contribution

It demonstrates the double copy structure in even-dimensional conformal correlators and connects the flat space limit to the leading singularity of a master triangle integral.

Findings

Flat space limit exhibits double copy structure in even dimensions.

Renormalization is necessary due to divergences and branch cuts.

Trace anomaly coefficients control the flat space limit in four dimensions.

Abstract

We analyse the flat space limit of 3-point correlators in momentum space for general conformal field theories in even spacetime dimensions, and show they exhibit a double copy structure similar to that found in odd dimensions. In even dimensions, the situation is more complicated because correlators contain branch cuts and divergences which need to be renormalised. We describe the analytic continuation of momenta required to extract the flat space limit, and show that the flat space limit is encoded in the leading singularity of a 1-loop triangle integral which serves as a master integral for 3-point correlators in even dimensions. We then give a detailed analysis of the renormalised correlators in four dimensions where the flat space limit of stress tensor correlators are controlled by the coefficients in the trace anomaly.