Two-point functions of chiral operators in {\cal N}=4 SYM at order g^4

TL;DR

This paper calculates two-point functions of specific chiral operators in { N}=4 SYM theory at order g^4, revealing that perturbative corrections cancel out, supporting the idea of all-order nonrenormalization.

Contribution

It provides a complete perturbative calculation at order g^4 showing cancellations without additional assumptions, extending nonrenormalization results.

Findings

Perturbative corrections vanish at order g^4 for all N.

Cancellations occur in a highly nontrivial manner beyond order g^2.

Supports the conjecture of all-order nonrenormalization of these correlators.

Abstract

We compute two-point functions of chiral operators Tr \Phi^3 in {\cal N}=4 SU(N) supersymmetric Yang-Mills theory to the order g^4 in perturbation theory. We perform explicit calculations using {\cal N}=1 superspace techniques and find that perturbative corrections to the correlators vanish for all N. While at order g^2 the cancellations can be ascribed to the nonrenormalization theorem valid for correlators of operators in the same multiplet as the stress tensor, at order g^4 this argument no longer applies and the actual cancellation occurs in a highly nontrivial way. Our result is obtained in complete generality, without the need of additional conjectures or assumptions. It gives further support to the belief that such correlators are not renormalized to all orders in g and to all orders in N.