Hexagonal Wilson Loops in Planar $\mathcal{N}=4$ SYM Theory at Finite Coupling

Abstract

We report on the complete OPE series for the 6-gluon MHV and NMHV amplitudes in planar $\mathcal{N}=4$ SYM theory. Namely, we provide a finite coupling prediction for all the terms in the expansion of these amplitudes around the collinear limit. These furnish a non-perturbative representation of the full amplitudes.

Figures (1)

• Figure 1: The pattern of auxiliary rapidities entering the matrix part has a simple group theoretical interpretation. The three sets of rapidities $w^{1,2,3}$ can be identified with the three nodes of the $SU(4)$ Dynkin diagram. The occupation numbers $K_{1,2,3}$ are fixed such that the overall state with $N_\phi$ scalars, $N_\psi$ fermions and $N_{\bar{\psi}}$ anti-fermions belongs to the $SU(4)$ representation $\{{\bf 1},{\bf\bar{4}},{\bf 6},{\bf4},{\bf 1}\}$ for $r_b=\{0,1,2,3,4\}$ respectively. The cartoon depicted here is related to (\ref{['matrixpart']}) by identifying the solid lines with $f$'s and the dashed lines with $g$'s.