Gauge-invariant gluon mass, infrared Abelian dominance and stability of magnetic vacuum

Abstract

We give an argument for deriving analytically the infrared ``Abelian'' dominance in a gauge invariant way for the Wilson loop average in SU(2) Yang--Mills theory. In other words, we propose a possible mechanism for realizing the dynamical Abelian projection in the SU(2) gauge-invariant manner without breaking color symmetry. This supports validity of the dual superconductivity picture for quark confinement. We also discuss the stability of the vacuum with magnetic condensation as a by-product of this result.

25 pages, 3 figures (4 eps files); version accepted for publication in Phys.Rev.D; One paragraph is added at each end of sections 3,4 and 5 for comparing the analytical result with the lattice results of my group based on the new formulation, together with the results in the conventional MAG if available. footnote 4 is added, and a reference is added. A number of sentences and phrases are improved

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• New descriptions of lattice SU(N) Yang-Mills theory towards quark confinement
• Center vortices as sources of Abelian dominance in pure SU(2) Yang-Mills theory
• Magnetic monopoles and center vortices as gauge-invariant topological defects simultaneously responsible for confinement
• Resolving the instability of the Savvidy vacuum by dynamical gluon mass
• Magnetic Monopole Loops supported by a Meron pair as the Quark Confiner