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Recently, we proposed a general evolution equation for single quadrilateralWilson loop on the light-cone. In present work, we study the energy evolutionof a combination of two such loops that partially overlap or have aself-intersection. We show that, for a class of geometric variations, thenevolution is consistent with our previous conjecture, and we are able to handlethe intricacies associated with the self-intersections and overlaps. This way,a step forward is made towards the understanding of loop space, with the hopeof studying more complicated structures appearing in phenomenological relevantobjects, such as parton distributions.

Evolution of Light-Like Wilson Loops with a Self-Intersection in Loop Space