Generalized Loop Space and Evolution of the Light-Like Wilson Loops

TL;DR

This paper investigates the equations governing light-like Wilson loops in quantum chromodynamics within the generalized loop space framework, linking their behavior to geometric properties and renormalization effects.

Contribution

It introduces a formulation of non-local variations of cusped Wilson exponentials on the light-cone using the Fréchet derivative, connecting loop geometry to physical evolution.

Findings

Demonstrates the connection between Wilson loop behavior and geometrical properties in GLS

Links rapidity and renormalization-group behavior to Wilson loop geometry

Provides a new approach to study gauge-invariant quantum correlations

Abstract

Equations of motion for the light-like QCD Wilson loops are studied in the generalized loop space (GLS) setting. To this end, the classically conformal-invariant non-local variations of the cusped Wilson exponentials lying (partially) on the light-cone are formulated in terms of the Fr\'echet derivative. The rapidity and renormalization-group behaviour of the gauge-invariant quantum correlation functions (in particular, the three-dimensional parton densities) are demonstrated to be connected to certain geometrical properties of the Wilson loops defined in the GLS.