Oblique Confinement at $\theta\neq 0$ in weakly coupled gauge theories with deformations

TL;DR

This paper investigates oblique confinement in weakly coupled gauge theories using deformed QCD, showing it arises from monopole condensation with phase shifts, contrasting with the dyon condensation mechanism traditionally assumed.

Contribution

It demonstrates that oblique confinement at non-zero theta angles results from monopole condensation with phase shifts, challenging the conventional dyon-based explanation.

Findings

Oblique confinement emerges from monopole condensation with phase shifts.

The dyon mechanism does not apply to dynamical monopoles in this context.

Monopoles are dynamical, not static, influencing the ground state and confinement.

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 $\exp(i\frac{\theta+2\pi m}{N})$ in Bloch type construction. It should be contrasted with conventional and commonly accepted viewpoint that the confinement at $\theta\neq 0$ is due to the condensation of the electrically charged dyons which indeed normally emerge in the systems with $\theta\neq 0$ 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.