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

TL;DR

This paper extends the understanding of light-like Wilson loops with self-intersections by analyzing their evolution, confirming previous conjectures, and advancing the study of loop space relevant to parton distributions.

Contribution

It develops a framework for the energy evolution of overlapping and self-intersecting Wilson loops, handling complex geometric variations and supporting the study of loop space.

Findings

Evolution consistent with previous conjecture

Handles intricacies of self-intersections

Progress towards understanding complex loop structures

Abstract

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.