Three-point functions in planar N=4 super Yang-Mills Theory for scalar operators up to length five at the one-loop order

TL;DR

This paper systematically computes one-loop three-point functions of scalar operators up to length five in planar N=4 super Yang-Mills theory, including operator mixing effects, providing new detailed structure constants.

Contribution

It introduces a combinatorial dressing technique for one-loop corrections and resolves operator mixing up to order g_YM^2 for scalar operators.

Findings

Computed 40 structure constants involving scalar operators up to length five.

Developed a method to promote tree-level correlators to one-loop level.

Resolved operator mixing including bi-fermions and derivatives at one-loop.

Abstract

We report on a systematic perturbative study of three-point functions in planar SU(N) N=4 super Yang-Mills theory at the one-loop level involving scalar field operators up to length five. For this we have computed a sample of 40 structure constants involving primary operators of up to and including length five which are built entirely from scalar fields. A combinatorial dressing technique has been developed to promote tree-level correlators to one-loop level. In addition we have resolved the mixing up to the order (g_YM)^2 level of the operators involved, which amounts to mixings with bi-fermions, with bi-derivative insertions as well as self-mixing contributions in the scalar sector. This work supersedes a preprint by two of the authors from 2010 which had neglected the mixing contributions.