Superprotected n-point correlation functions of local operators in N=4 super Yang-Mills

TL;DR

This work identifies and analyzes two families of local operators in ${ m N}=4$ SYM that share a number of supersymmetries, leading to "superprotected" $n$-point functions whose perturbative corrections vanish and are determined by tree-level contractions. By constructing explicit space-time dependent operators, the authors reveal a twisted conformal symmetry structure, where the twisted generators render correlators position-independent (on $\mathbb{R}^4$) or governed by 2D holomorphic data (on $\mathbb{R}^2$), with Ward identities enforcing exact non-renormalization. For the first construction on $\mathbb{R}^4$, the correlation functions reduce to Gaussian matrix-model contractions and receive no perturbative corrections due to ${\mathcal Q}^\pm$-exactness of the action in the zero-instanton sector and a vanishing universal four-point prefactor ${\mathcal R}$; in the second construction on $\mathbb{R}^2$, four-point functions are likewise unrenormalized, and explicit one-loop checks for higher-point cases also show vanishing corrections, supported by a robust twisted-symmetry framework. Together, these results suggest a broader principle that families of operators sharing supersymmetries can yield exactly computable correlators and motivate exploration of holographic and generalizations to other submanifolds and operator classes.

Abstract

In this paper we study the n-point correlation functions of two different families of local gauge invariant operators in N=4 supersymmetric Yang-Mills theory. The main idea is to consider the correlation functions of operators which all share a number of supersymmetries irrespective of their relative locations. We achieve this by equipping the operators with explicit space-time dependence. We provide evidence by different methods that these n-point correlators do not receive quantum corrections in perturbation theory and are hence given exactly by their tree-level result. The arguments rely on explicit checks for general four-point correlators, some five-point and six-point correlators and a more abstract calculation based on a novel topological twisting of N=4 supersymmetric Yang-Mills theory.