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

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.