Diffusion of Wilson Loops

TL;DR

This paper models Wilson loop distributions in SU(2) Yang-Mills theory as a diffusion process on the group manifold, revealing conditions for Casimir scaling and screening phenomena, and relating these to underlying symmetries.

Contribution

It introduces a phenomenological diffusion framework for Wilson loops, connecting diffusion dynamics with Casimir scaling and screening, and explores symmetry-based distinctions between fundamental and adjoint loops.

Findings

Diffusion implies Casimir scaling in the absence of forces.

Exact Casimir scaling corresponds to free diffusion.

Screening occurs when diffusion is influenced by a potential.

Abstract

A phenomenological analysis of the distribution of Wilson loops in SU(2) Yang-Mills theory is presented in which Wilson loop distributions are described as the result of a diffusion process on the group manifold. It is shown that, in the absence of forces, diffusion implies Casimir scaling and, conversely, exact Casimir scaling implies free diffusion. Screening processes occur if diffusion takes place in a potential. The crucial distinction between screening of fundamental and adjoint loops is formulated as a symmetry property related to the center symmetry of the underlying gauge theory. The results are expressed in terms of an effective Wilson loop action and compared with various limits of SU(2) Yang-Mills theory.