Instabilities of Coulomb phases and quark confinement in QCD

Abstract

The Gribov picture to quark confinement is based on the Coulomb phase instability due to the very large values that the effective αs coupling constant can reach in the infrared regime. The Gribov instability is driven by a vacuum decay into light quarks beyond a critical value of the coupling constant αs3π(1-2/3)/4 (for SU(3) gauge group). From first principles it has been shown the existence of an instability of the Coulomb phase in pure gauge theories for α≥2, much beyond the Gribov critical value. In this paper we analyze the effect of dynamical quarks in the instability of the Coulomb phase. We find a critical value of the coupling α = 3 where a quark-antiquark pair creation mechanism leads to vacuum instability. However, the new critical value turns out to be larger than the pure gauge critical value α = 2, unlike it is expected in the standard Gribov scenario. The result is analytically derived from first principles and provides further consistency to the picture where quark confinement is mainly driven by gluonic fluctuation instabilities.