We address the scaling behaviour of contour-shape-dependent ultra-violet singularities of the light-like cusped Wilson loops in Yang-Mills and ${ \cal N} = 4$ 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 Fr\'echet differentials results in the combined geometric and renormalization-group evolution equation, which is applicable beyond the leading order exponentiated Wilson loops.
Categories: hep-th math-ph math.MP