Confining vacua and Q-state Potts models with Q<1

TL;DR

This paper investigates the relationship between magnetic monopole condensation and center vortex percolation in 3D gauge models related to Q-state Potts models with Q<1, revealing vacua where monopoles do not lead to confinement.

Contribution

It introduces a class of dual 3D gauge models with Q<1, demonstrating that monopole condensation alone does not guarantee confinement, unlike in typical Yang-Mills models.

Findings

Monopole condensation does not always imply confinement.

Existence of vacua with dilute vortex gas and perimeter law Wilson loops.

At stronger coupling, both monopoles and vortices coexist in confining vacua.

Abstract

In most Yang-Mills models the vacuum where magnetic monopoles condense coincides with that where center vortices percolate, thus it is not clear which of these two properties is most directly involved in producing confinement. It is pointed out that there is a class of 3D gauge models, which can be though of as duals of Q-state Potts models with Q < 1, where the magnetic monopole condensation is a necessary but not sufficient condition for percolation of center vortices. A set of numerical tests at Q=1/10 shows that there is a vacuum in which the magnetic monopole condensate does not yield confinement, in the sense that large Wilson loops obey a perimeter law. In such a vacuum the center vortices form a dilute gas of loops. At stronger coupling there is also a truly confining vacuum where both confining mechanisms are present.