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.

17 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

References in corpus (8)

• Flux tubes in the SU(3) vacuum: London penetration depth and coherence length
• Gauge-invariant gluon mass, infrared Abelian dominance and stability of magnetic vacuum
• Compact lattice formulation of Cho-Faddeev-Niemi decomposition: gluon mass generation and infrared Abelian dominance
• Reformulating SU(N) Yang-Mills theory based on change of variables
• Wilson loop and magnetic monopole through a non-Abelian Stokes theorem
• Compact lattice formulation of Cho-Faddeev-Niemi decomposition: string tension from magnetic monopoles
• New descriptions of lattice SU(N) Yang-Mills theory towards quark confinement
• Non-Abelian Dual Superconductor Picture for Quark Confinement

Cited by in corpus (7)

• Quark confinement: dual superconductor picture based on a non-Abelian Stokes theorem and reformulations of Yang-Mills theory
• Magnetic monopole and confinement/deconfinement phase transition in SU(3) Yang-Mills theory
• Decomposition of the static potential in SU(3) gluodynamics
• 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
• Reformulations of the Yang-Mills theory toward quark confinement and mass gap
• Discriminating between two reformulations of SU(3) Yang-Mills theory on a lattice