A non-renormalization theorem for chiral primary 3-point functions

TL;DR

This paper proves a non-renormalization theorem for 3-point functions of BPS primaries in certain supersymmetric theories, using elementary Ward identities and superconformal algebra structures.

Contribution

It provides a simple, elementary proof of non-renormalization for specific 3-point functions in supersymmetric conformal field theories, avoiding superspace methods.

Findings

Non-renormalization of 3-point functions established

Elementary proof based on Ward identities

Potential generalizations to less supersymmetric cases

Abstract

In this note we prove a non-renormalization theorem for the 3-point functions of 1/2 BPS primaries in the four-dimensional N = 4 SYM and chiral primaries in two dimensional N =(4,4) SCFTs. Our proof is rather elementary: it is based on Ward identities and the structure of the short multiplets of the superconformal algebra and it does not rely on superspace techniques. We also discuss some possible generalizations to less supersymmetric multiplets.