Double-winding Wilson loops and monopole confinement mechanisms

TL;DR

This paper investigates double-winding Wilson loops in SU(2) gauge theory, comparing predictions from abelian confinement models and center vortex models, and finds lattice results support a difference-of-areas law inconsistent with simple abelian models.

Contribution

It demonstrates through lattice simulations that double-winding Wilson loops follow a difference-in-areas law, challenging simple abelian confinement models.

Findings

Double-winding loops follow a difference-in-areas law.

Abelian models predict sum-of-areas falloff, not observed.

Lattice results contradict simple abelian confinement assumptions.

Abstract

We consider "double-winding" Wilson loops in SU(2) gauge theory. These are contours which wind once around a loop $C_1$ and once around a loop $C_2$, where the two co-planar loops share one point in common, and where $C_1$ lies entirely in (or is displaced slightly from) the minimal area of $C_2$. We discuss the expectation value of such double-winding loops in abelian confinement pictures, where the spatial distribution of confining abelian fields is controlled by either a monopole Coulomb gas, a caloron ensemble, or a dual abelian Higgs model, and argue that in such models an exponential falloff in the sum of areas $A_1+A_2$ is expected. In contrast, in a center vortex model of confinement, the behavior is an exponential falloff in the difference of areas $A_2-A_1$. We compute such double-winding loops by lattice Monte Carlo simulation, and find that the area law falloff follows a difference-in-areas law. The conclusion is that even if confining gluonic field fluctuations are, in some gauge, mainly abelian in character, the spatial distribution of those abelian fields cannot be the distribution predicted by the simple monopole gas, caloron ensemble, or dual abelian Higgs actions, which have been used in the past to explain the area law falloff of Wilson loops.