The contribution of scalars to ${\cal N}=4$ SYM amplitudes II: Young tableaux, asymptotic factorisation and strong coupling

TL;DR

This paper analyzes the scalar contributions to ${ m N}=4$ SYM amplitudes, developing systematic methods using Young tableaux and asymptotic factorization to derive explicit strong coupling expansions and compare with classical string results.

Contribution

It introduces a systematic computation of the $SO(6)$ matrix part using Young tableaux and demonstrates a new factorization property to derive strong coupling expansions.

Findings

Explicit strong coupling expansion of Wilson loops

Leading order dominance over classical $AdS_5$ string contribution

Systematic method using Young tableaux for $SO(6)$ matrix part

Abstract

We disentangle the contribution of scalars to the OPE series of null polygonal Wilson loops/MHV gluon scattering amplitudes in multicolour ${\cal N}=4$ SYM. In specific, we develop a systematic computation of the $SO(6)$ matrix part of the Wilson loop by means of Young tableaux (with several examples too). Then, we use a peculiar factorisation property (when a group of rapidities becomes large) to deduce an explicit polar form. Furthermore, we emphasise the advantages of expanding the logarithm of the Wilson loop in terms of 'connected functions' as we apply this procedure to find an explicit strong coupling expansion (definitively proving that the leading order can prevail on the classical $AdS_5$ string contribution).