Diffusion of Wilson Loops

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.

9 pages, 3 figures, revtex; v2: 3 references added

References in corpus (1)

• Brownian Motion, Chern-Simons Theory, and 2d Yang-Mills

Cited by in corpus (16)

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• Surface-Invariants in 2D Classical Yang-Mills Theory
• Two dimensional fermions in four dimensional YM
• Random walks of Wilson loops in the screening regime
• Confining gauge fields
• Kramers-Moyall cumulant expansion for the probability distribution of parallel transporters in quantum gauge fields
• Matching of Wilson loop eigenvalue densities in 1+1, 2+1 and 3+1 dimensions