Loop space and evolution of the light-like Wilson polygons

TL;DR

This paper explores the relationship between the energy evolution of light-like Wilson polygons and their geometric properties in loop space, using a quantum dynamical approach to understand their renormalization and differential area evolution.

Contribution

It introduces a novel connection between Wilson loop geometry and energy evolution, applying Schwinger quantum dynamics to analyze renormalization and differential equations in loop space.

Findings

Wilson polygons' renormalization properties characterized

Differential area evolution equations derived

Implications for parton distribution functions discussed

Abstract

We address a connection between the energy evolution of the polygonal light-like Wilson exponentials and the geometry of the loop space with the gauge invariant Wilson loops of a variety of shapes being the fundamental degrees of freedom. The renormalization properties and the differential area evolution of these Wilson polygons are studied by making use of the universal Schwinger quantum dynamical approach. We discuss the appropriateness of the dynamical differential equations in the loop space to the study of the energy evolution of the collinear and transverse-momentum dependent parton distribution functions.