Double-winding Wilson loops and monopole confinement mechanisms

Jeff Greensite; Roman H\"ollwieser

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Double-winding Wilson loops and monopole confinement mechanisms

Jeff Greensite, Roman Höllwieser

High Energy Physics - Lattice · Submitted 19 Nov 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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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.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider "double-winding" Wilson loops in SU(2) gauge theory.	contribution 0.59	0.67	0.01	asserted 0.61
s1	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 $C_2$.	background 0.70	0.14	0.02	asserted 0.96
s2	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.	background 0.67	0.19	0.04	hedged possibility 0.78
s3	In contrast, in a center vortex model of confinement, the behavior is an exponential falloff in the difference of areas $A_2-A_1$.	background 0.93	0.15	0.06	asserted 1.00
s4	We compute such double-winding loops by lattice Monte Carlo simulation, and find that the area law falloff follows a difference-in-areas law.	result 0.94	0.97	0.13	asserted 1.00
s5	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.	interpretation 1.00	0.63	0.97	asserted 0.94

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Original 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.

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17 arXiv papers cite this in 29 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 20 sentences without a confident label

Uses its method or tool 1 paper

For this, the Abelian Stokes theorem can be used to rewrite the spatial Wilson Loop in the so called “Abelian dominance" approximation [ref]

Confinement, Holonomy and Correlated Instanton-Dyon Ensemble I: SU(2) Yang-Mills Theory · The Spatial Wilson Loop · 0.97

Cites it as support 1 paper

A recent study of double-winding Wilson loops [ref] further favors the center vortex degrees of freedom as the dominating fluctuations in the QCD vacuum.

Confining Bond Rearrangement in the Random Center Vortex Model · Introduction · 0.96

Cites it as background 5 papers

The preceding works [ref] investigated the area ($S_1$ and $S_2$) dependence of the expectation value $< W(C_1 ∪C_2) >$ of a double-winding Wilson loop operator $W(C_1 ∪C_2)$ where $S_1$ and $S_2$ are respectively the minimal areas bounded by loops $C_1$ and $C_2$.

Center group dominance in quark confinement · Introduction · 0.97
In the lattice gauge theory, a double-winding Wilson loop operator $W(C_1 ∪C_2)$ has been introduced in [ref] to examine the possible mechanisms for quark confinement.

Investigating quark confinement from the viewpoint of lattice gauge-scalar models · Introduction · 0.98
It has long been known that a centre vortex [ref] model of the QCD vacuum is capable of explaining confinement, and recent work [ref] hints that this is the model of confinement most consistent with lattice results.

Connection between centre vortices and instantons through gauge-field smoothing · Introduction · 0.91

What it cites · 17 sentences without a confident label

Cites as background 13 papers

These dyon configurations should dominate the vacuum at large scales if confinement can be traced to KvBLL (Kraan and van Baal [ref] , Lee and Lu [ref] ) calorons with maximally non-trivial holonomy (hereafter just “calorons”).

SU(2) Calorons and Magnetic Monopoles · Dyon Ensemble · 0.87
These dyon configurations should dominate the vacuum at large scales if confinement can be traced to KvBLL (Kraan and van Baal [ref] , Lee and Lu [ref] ) calorons with maximally non-trivial holonomy (hereafter just “calorons”).

Periodic Instantons with non-trivial Holonomy · Dyon Ensemble · 0.87
The more recent notion that long-range field fluctuations in QCD are dominated by caloron gas ensembles [ref] , [ref] , fits nicely into the framework of the earlier monopole plasma conjectures.

Confining ensemble of dyons · Introduction · 0.93

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