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

TL;DR

This paper presents a new derivation of quark confinement in QCD using Abelian projection and phase transition theory, identifying a critical coupling and flavor number for confinement and chiral symmetry breaking.

Contribution

It introduces a novel derivation of quark confinement based on the Berezinskii-Kosterlitz-Thouless transition in Abelian gauge theory and discusses critical parameters for confinement and chiral symmetry breaking.

Findings

Existence of a critical gauge coupling for confinement

Critical number of fermion flavors for phase transition

Brief discussion on finite-temperature deconfinement

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.