A Young diagram expansion of the hexagonal Wilson loop (amplitude) in N=4 SYM

We shall interpret the null hexagonal Wilson loop (or, equivalently, six gluon scattering amplitude) in 4D N = 4 Super Yang-Mills, or, precisely, an integral representation of its matrix part, via an ADHM-like instanton construction. In this way, we can apply localisation techniques to obtain combinatorial expressions in terms of Young diagrams. Then, we use our general formula to obtain explicit expressions in several explicit cases. In particular, we discuss those already available in the literature and find exact agreement. Moreover, we are capable to determine explicitly the denominator (poles) of the matrix part, and find some interesting recursion properties for the residues, as well.

Automated summary

In this study, the null hexagonal Wilson loop in 4D N = 4 Super Yang-Mills is interpreted using an ADHM-like instanton construction for the matrix part. Localization techniques are then applied to obtain combinatorial expressions in terms of Young diagrams, leading to explicit expressions in several specific cases with exact agreement to existing literature. Moreover, explicit determinations of the denominator and interesting recursion properties for the residues are found.