Quark Confinement and Deconfinement in QCD from the Viewpoint of Abelian-Projected Effective Gauge Theory

Abstract

We give another derivation of quark confinement in QCD from the viewpoint of the low-energy effective Abelian gauge theory of QCD obtained via Abelian projection. It is based on the recently discovered Berezinskii-Kosterlitz-Thouless phase transition in the four-dimensional Abelian gauge theory. Moreover, we show that there exists a critical gauge coupling constant in QCD, above which confinement set in and below which there is no confinement. In a SU(N) gauge theory with $N_f$ flavored fermions, we argue that this leads to a critical value of fermion flavors $N_f^c$ for the confinement as well as the chiral symmetry breaking, which separates the deconfinement and chiral symmetric phase. A finite-temperature deconfinement transition is also discussed briefly.

14 pages, Latex, version to be published in Phys. Lett. B (two paragraphs are added in pages 10 and 11.)

References in corpus (7)

• The Phase Structure of an SU(N) Gauge Theory with N_f Flavors
• Abelian Magnetic Monopole Dominance in Quark Confinement
• Yang-Mills Theory as a Deformation of Topological Field Theory, Dimensional Reduction and Quark Confinement
• Existence of Confinement Phase in Quantum Electrodynamics
• Abelian-Projected Effective Gauge Theory of QCD with Asymptotic Freedom and Quark Confinement
• Semi-analytical Proof of Abelian Dominance on Confinement in the Maximally Abelian Gauge
• Gluon Propagator in Maximally Abelian Gauge and Abelian Dominance for Long-Range Interaction

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• Strong randomness of off-diagonal gluon phases and off-diagonal gluon mass in the maximally abelian gauge in QCD
• A formulation of the Yang-Mills theory as a deformation of a topological field theory based on background field method and quark confinement problem
• Phase Structure of a Compact U(1) Gauge Theory from the Viewpoint of a Sine-Gordon Model
• A Confining String Theory Derivable from Yang-Mills Theory due to a Novel Vacuum Condensate
• Spontaneous breaking of nilpotent symmetry in boundary BLG theory
• Color Confinement in QCD due to Topological Defects