Oblique confinement at θ≠0 in weakly coupled gauge theories with deformations

Abstract

The main focus of this work is to test the ideas related to the oblique confinement in a theoretically controllable manner using the “deformed QCD” as a toy model. We explicitly show that the oblique confinement in the weakly coupled gauge theories emerges as a result of condensation of N types of monopoles shifted by the phase exp ( i θ + 2 π m N ) in Bloch type construction. It should be contrasted with the conventional and commonly accepted viewpoint that the confinement at θ ≠ 0 is due to the condensation of the electrically charged dyons which indeed normally emerge in the systems with θ ≠ 0 as a result of Witten’s effect. We explain the basic reason why the “dyon” mechanism does not materialize—it is because the Witten’s effect holds for a static magnetic monopole treated as an external source. It should be contrasted with our case when N -types of monopoles are not static, but rather the dynamical degrees of freedom which fluctuate and themselves determine the ground state of the system.