Quark confinement , topological susceptibility and all that in 4 dimensional gluodynamics

Abstract

We discuss a few tightly connected problems, such as the $U(1)$ problem, confinement, the $θ$ -dependence within a framework of the dynamical toron approach. We calculate two fundamental characteristics of the theory: the vacuum expectation value (vev) of the Wilson loop and the topological susceptibility. The analogy with well known 2+1 dimensional QED which exhibits confinement phenomenon is also discussed.