Color confinement and screening in the $\mathbf{\theta}$ -vacuum

Abstract

QCD perturbation theory ignores the compact nature of $SU(3)$ gauge group that gives rise to the periodic $\theta$-vacuum of the theory. We propose to modify the gluon propagator to reconcile perturbation theory with the anomalous Ward identities for the topological current in the $\theta$-vacuum. As a result, the gluon couples to the Veneziano ghost describing the tunneling transitions between different Chern-Simons sectors of the vacuum; we call the emerging gluon dressed by ghost loops a "glost". We evaluate the glost propagator and find that it has the form $G(p) = (p^2 + \chi_{top}/p^2)^{-1}$ where $\chi_{top}$ is the Yang-Mills topological susceptibility related to the $\eta'$ mass by Witten-Veneziano relation; this propagator describes confinement of gluons at distances $\sim \chi_{top}^{-1/4} \simeq 1$ fm. The same functional form of the propagator was originally proposed by Gribov as a solution to the gauge copies problem that plagues perturbation theory. The resulting running coupling coincides with the perturbative one at $p^2 \gg \sqrt{\chi_{top}}$, but in the infrared region either freezes (in pure Yang-Mills theory) or vanishes (in full QCD with light quarks), in accord with experimental evidence. Our scenario makes explicit the connection between confinement and topology of the QCD vacuum; we discuss the implications for spin physics, high energy scattering, and the physics of quark-gluon plasma.