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

TL;DR

This work proves a non-renormalization theorem for 3-point functions of chiral primaries in 4d ${\cal N}=4$ SCFTs and for chiral primaries in 2d ${\cal N}=(4,4)$ SCFTs using elementary arguments based on superconformal Ward identities and short multiplet structure, avoiding superspace techniques. The central mechanism is to express marginal deformations as descendants of supercharges, then via carefully chosen Ward identities and null-state relations show that the integrand for coupling variation vanishes, yielding $\nabla C_{IJK}=0$ for the relevant correlators. The authors extend the result to related cases (half-chiral states in 2d, ${\cal N}=(0,4)$ theories, extremal correlators) and discuss possible generalizations to less supersymmetric multiplets, highlighting the non-perturbative independence of these 3-point functions from the coupling across any gauge group. The findings have implications for AdS/CFT comparisons, moduli-space dynamics, and the protection of specific correlators beyond the extremal limit.

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.