Double-winding Wilson loops and monopole confinement mechanisms

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.

12 pages, 12 figures. v2: added references, fixed some misprints

References in corpus (7)

• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
• Confining ensemble of dyons
• An SU(2) KvBLL caloron gas model and confinement
• Duality of gauge field singularities and the structure of the flux tube in Abelian-projected SU(2) gauge theory and the dual Abelian Higgs model
• Cautionary remarks on the moduli space metric for multi-dyon simulations
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• Ensembles of center vortices and chains: Insights from a natural lattice framework
• Double-winding Wilson loops in the $SU(N)$ Yang-Mills theory
• A first analysis of the ensemble of local maxima of maximal center gauge
• Study of the Emergence of a Gluon Mass Scale from Center Vortices Using a Wave-Functional Formalism
• Center group dominance in quark confinement
• Center Vortex vs. Abelian models of the QCD vacuum