Fréchet derivative for light-like Wilson Loops
arXiv:1401.2721 · doi:10.1016/j.physletb.2014.12.029
Abstract
We address the equations of motion for the light-like QCD Wilson exponentials defined in the generalized loop space. We attribute an important class of the infinitesimal shape variations of the rectangular light-like Wilson loops to the Fréchet derivative associated to a diffeomorphism in loop space what enables the derivation of the law of the classically conformal-invariant shape variations. We show explicitly that the Fréchet derivative coincides (at least in the leading perturbative or- der) with the area differential operator introduced in the previous works. We discuss interesting implications of this result which will allow one to relate the rapidity evolution and ultra-violet evolution of phenomenologically important quantum correlation functions (such as 3-dimensional parton distribution functions) and geometrical properties of the light-like cusped Wilson loops.
13 pages, 6 figures (revised some typos and misprints)
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