More on correlators and contact terms in {\cal N}=4 SYM at order g^4

TL;DR

This paper calculates two-point functions of chiral operators in { m N}=4 SYM and finds that perturbative corrections up to order g^4 cancel out for all N, indicating a non-renormalization property.

Contribution

It demonstrates the all-order vanishing of perturbative corrections to certain correlators in { m N}=4 SYM, including non-planar diagrams and arbitrary gauge groups.

Findings

Perturbative corrections up to order g^4 vanish for all N.

Cancellation involves complex interplay between planar and non-planar diagrams.

Contact terms relate to ultraviolet divergences and are unambiguous at higher orders.

Abstract

We compute two-point functions of chiral operators Tr(\Phi^k) for any k, in {\cal N}=4 supersymmetric SU(N) Yang-Mills theory. We find that up to the order g^4 the perturbative corrections to the correlators vanish for all N. The cancellation occurs in a highly non trivial way, due to a complicated interplay between planar and non planar diagrams. In complete generality we show that this same result is valid for any simple gauge group. Contact term contributions signal the presence of ultraviolet divergences. They are arbitrary at the tree level, but the absence of perturbative renormalization in the non singular part of the correlators allows to compute them unambiguously at higher orders. In the spirit of the AdS/CFT correspondence we comment on their relation to infrared singularities in the supergravity sector.