On geometric scaling of light-like Wilson polygons: Higher orders in αsαs

We address the scaling behaviour of contour-shape-dependent ultraviolet singularities of the light-like cusped Wilson loops in Yang–Mills and N=4N=4 super-Yang–Mills theories in the higher orders of the perturbative expansion. We give the simple arguments to support the idea that identifying of a special type of non-local infinitesimal shape variations of the light-like Wilson polygons with the Fréchet differentials results in the combined geometric and renormalization-group evolution equation, which is applicable beyond the leading order exponentiated Wilson loops.