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

TL;DR

This paper investigates special n-point correlation functions in N=4 super Yang-Mills theory that preserve certain supersymmetries and are shown to be protected from quantum corrections, remaining exactly at tree level.

Contribution

It introduces a novel class of supersymmetric, space-time dependent operators and demonstrates their correlation functions are exactly calculable, unaffected by quantum corrections.

Findings

Correlation functions are protected and do not receive quantum corrections.

Explicit checks confirm the non-renormalization for various n-point functions.

A new topological twisting approach supports the non-renormalization results.

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.