A Young diagram expansion of the hexagonal Wilson loop (amplitude) in $\mathcal{N}=4$ SYM

Abstract

We shall interpret the null hexagonal Wilson loop (or, equivalently, six gluon scattering amplitude) in 4D $\mathcal{N}=4$ 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.

40 pages, 7 figures

References in corpus (13)

• Gluon scattering amplitudes at strong coupling
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• An Operator Product Expansion for Polygonal null Wilson Loops
• Thermodynamic Bethe Ansatz for planar AdS/CFT: a proposal
• The Quantum Spectral Curve of the ABJM theory
• On the collinear limit of scattering amplitudes at strong coupling
• Evaluating the 6-point Remainder Function Near the Collinear Limit
• The contribution of scalars to $\mathcal{N}=4$ SYM amplitudes
• On the origin of the correspondence between classical and quantum integrable theories
• $QQ$-system and non-linear integral equations for scattering amplitudes at strong coupling
• Vacuum expectation value of twist fields