Non-renormalisation of extremal correlators in N=4 SYM theory

TL;DR

The paper examines extremal correlators of chiral primary operators in ${\cal N}=4$ SYM with gauge group $SU(N)$ and demonstrates two key non-renormalisation properties: at leading order in perturbation theory, all first-order corrections cancel; and in the non-perturbative, semiclassical regime, instanton contributions vanish due to fermionic zero-mode saturation arguments. The results are derived using the ${\cal N}=1$ superfield formulation and explicit perturbative diagram analysis, followed by a fermionic zero-mode counting in instanton backgrounds. Together, these findings provide strong support for the AdS/SCFT prediction that extremal correlators are tree-level exact and remain uncoupled from quantum corrections across the entire theory. The work further suggests a broader non-renormalisation class and points to future directions, including extension to other gauge groups and multi-trace operators, within the analytic superspace framework.

Abstract

We show that extremal correlators of chiral primary operators in N=4 supersymmetric Yang-Mills theory with SU(N) gauge group are neither renormalised at first order in perturbation theory nor receive contribution from any instanton sector at leading order in the semiclassical expansion. This lends support to the strongest version of a new prediction recently put forward on the basis of the AdS/SCFT correspondence.