Remarks on the Confinement in the $G(2)$ Gauge Theory Using the Thick Center Vortex Model

TL;DR

This paper explores how the thick center vortex model, applied to the $SU(3)$ subgroups of the $G(2)$ gauge theory, can explain confinement properties at various distances without domain modification.

Contribution

It demonstrates that $SU(3)$ subgroups within $G(2)$) can account for confinement phenomena using the vortex model without additional modifications.

Findings

$SU(3)$ subgroups influence $G(2)$ confinement properties.

Two $SU(3)$ vortices with opposite fluxes explain confinement.

The model applies at both intermediate and large distances.

Abstract

The confinement problem is studied using the thick center vortex model. It is shown that the $SU(3)$ Cartan sub algebra of the decomposed $G(2)$ gauge theory can play an important role in the confinement. The Casimir eigenvalues and ratios of the $G(2)$ representations are obtained using its decomposition to the $SU(3)$ subgroups. This leads to the conjecture that the $SU(3)$ subgroups also can explain the $G(2)$ properties of the confinement. The thick center vortex model for the $SU(3)$ subgroups of the $G(2)$ gauge theory is applied without the domain modification. Instead, the presence of two $SU(3)$ vortices with opposite fluxes due to the possibility of decomposition of the $G(2)$ Cartan sub algebra to the $SU(3)$ groups can explain the properties of the confinement of the $G(2)$ group both at intermediate and asymptotic distances which is studied here.