On Geometric Scaling of Light-Like Wilson Polygons: Higher Orders in $α_s$

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 Fréchet differentials results in the combined geometric and renormalization-group evolution equation, which is applicable beyond the leading order exponentiated Wilson loops.

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