Proving Abelian dominance in the Wilson loop operator

Abstract

We give a gauge-independent definition of Abelian dominance in the Wilson loop operator and a constructive proof of the Abelian dominance through a non-Abelian Stokes theorem via lattice regularization. We obtain a necessary and sufficient condition for the Abelian dominance in the Wilson loop operator in the fundamental representation. In the continuum limit, the gauge field is decomposed such that the Abelian dominance is given as an exact operator relation, leading to the exact (100%) Abelian dominance. On a lattice, we estimate the deviation from the exact Abelian dominance due to non-zero lattice spacing. In order to obtain the best Abelian dominance on a lattice by minimizing the deviation, we discuss how to decompose the gauge field variable into the dominant part and the remaining one to be decoupled on a lattice.

23 pages, no figures

References in corpus (3)

• Compact lattice formulation of Cho-Faddeev-Niemi decomposition: gluon mass generation and infrared Abelian dominance
• Wilson loop and magnetic monopole through a non-Abelian Stokes theorem
• Gauge-independent Abelian mechanism of color confinement in gluodynamics

Cited by in corpus (13)

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• Topological configurations of Yang-Mills field responsible for magnetic-monopole loops as quark confiner
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• Non-Abelian dual superconductivity and Gluon propagators in the deep IR region for SU(3) Yang-Mills theory
• Dual Meissner effect and non-Abelian dual superconductivity in SU(3) Yang-Mills theory
• Discriminating between two reformulations of SU(3) Yang-Mills theory on a lattice
• Non-Abelian dual Meissner effect in SU(3) Yang-Mills theory and confinement/deconfinement phase transition at finite temperature
• Non-Abelian dual Meissner effect and confinement/deconfinement phase transition in SU(3) Yang-Mills theory
• Gluon propagators in the deep IR region and non-Abelian dual superconductivity for SU(3) Yang-Mills
• Reformulations of the Yang-Mills theory toward quark confinement and mass gap