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

Understand

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.