  Maximal helicity-violating scattering amplitudes in N=4 supersymmetric
Yang-Mills theory are dual to Wilson loops on closed null polygons. We perform
their operator product expansion analysis in two-dimensional kinematics in the
soft-collinear approximation which corresponds to the case when some light-cone
distances vanish. We construct the expansion in terms of multi-particle
"heavy"-light operators, where the "heavy" fields are identified with the
Wilson lines defining the OPE channel and the light fields emerge from the
curvature of the contour. The correlation function of these define the
remainder function. We study the dilatation operator for these operators at one
loop order and find that it corresponds to a non-compact open spin chain. This
provides an alternative view on elementary excitations propagating on the GKP
string at weak coupling, which now correspond to particles traveling along an
open spin chain. The factorized structure of the Wilson loop in the soft limit
allows one to represent the two-loop correction to the octagon Wilson loop as a
convolution formula and find the corresponding remainder function.
