Comment on "Redundancy Channels in the Conformal Bootstrap" by S. R. Kousvos and A. Stergiou

TL;DR

This paper comments on a critique of previous conformal field theory (CFT) computations, clarifying the correct handling of contact terms in correlation functions and defending the original methodology.

Contribution

It clarifies the proper treatment of contact terms in CFT correlation functions and defends the original approach against recent criticisms.

Findings

Contact terms can differ in correlation functions without affecting physical results.

Renormalizing contact terms is unnecessary and can be avoided with a minimal set of quantities.

The original method is correct and preferable for CFT computations.

Abstract

Recent work by Kousvos and Stergiou criticises our work with Zhong Ming Tan [arXiv:1505.00963]. The issue is CFT scaling dimension computations in perturbative Renormalization Group. We identified operators whose correlation functions differ by contact terms. This is allowed because CFT only describes correlation functions away from coincident points. They instead renormalize the contact terms, which are eventually dropped. Our way is not only correct, but preferable as it operates with the minimal set of quantities.