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

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