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 deconfining and chiral symmetric phase from the confining and chiral symmetry breaking phase. A finite-temperature deconfinement transition is also discussed briefly.