Gauge-independent "Abelian" and magnetic-monopole dominance, and the dual Meissner effect in lattice $SU(2)$ Yang-Mills theory

Abstract

In the $SU(2)$ Yang-Mills theory on the four-dimensional Euclidean lattice, we confirm the gauge-independent "Abelian" dominance (or the restricted field dominance) and gauge-independent magnetic-monopole dominance in the string tension of the linear potential extracted from the Wilson loop in the fundamental representation. The dual Meissner effect is observed by demonstrating the squeezing of the chromoelectric field flux connecting a pair of quark and antiquark. In addition, the circular magnetic-monopole current is induced around the chromoelectric flux. The type of the dual superconductivity is also determined by fitting the result with the dual Ginzburg-Landau model. Thus the dual superconductor picture for quark confinement is supported in a gauge-independent manner. These results are obtained based on a reformulation of the lattice Yang-Mills theory based on the change of variables a la Cho-Duan-Ge-Faddeev-Niemi combined with a non-Abelian Stokes theorem for the Wilson loop operator. We give a new procedure (called the reduction) for obtaining the color direction field which plays the central role in this reformulation.

arXiv comment17 pages, 7 figures, 4 tables, The completely revised version according to the new data: Fig.1, Fig.3, Fig.4, Fig.5, Fig.6, Fig.7; Table I, Table II, Table III, Table IV; eq.(35),(36),(37),(38),(60),(61),(62) are improved. The ref.[33][34][35][41:2nd ref.][43][44] are added. The conclusion is also modified

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• Quark confinement: dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory
• Flux tubes in the QCD vacuum
• Three-quark potential and Abelian dominance of confinement in SU(3) QCD
• Gauge-invariant description of Higgs phenomenon and quark confinement
• Type of dual superconductivity for the $SU(2)$ Yang--Mills theory
• Decomposition of the static potential in SU(3) gluodynamics
• Magnetic monopole and confinement/deconfinement phase transition in SU(3) Yang-Mills theory
• Double-winding Wilson loops in SU(N) lattice Yang-Mills gauge theory
• How to extract the dominant part of the Wilson loop average in higher representations
• Discriminating between two reformulations of SU(3) Yang-Mills theory on a lattice
• Reformulations of the Yang-Mills theory toward quark confinement and mass gap