F4, E6 and G2 exceptional gauge groups in the vacuum domain structure model

Using a vacuum domain structure model, we calculate trivial static potentials in various representations of F-4, E-6, and G(2) exceptional groups by means of the unit center element. Due to the absence of the nontrivial center elements, the potential of every representation is screened at far distances. However, the linear part is observed at intermediate quark separations and is investigated by the decomposition of the exceptional group to its maximal subgroups. Comparing the group factor of the supergroup with the corresponding one obtained from the nontrivial center elements of SU(3) subgroup shows that SU(3) is not the direct cause of temporary confinement in any of the exceptional groups. However, the trivial potential obtained from the group decomposition into the SU(3) subgroup is the same as the potential of the supergroup itself. In addition, any regular or singular decomposition into the SU(2) subgroup that produces the Cartan generator with the same elements as h(1), in any exceptional group, leads to the linear intermediate potential of the exceptional gauge groups. The other SU(2) decompositions with the Cartan generator different from h(1) are still able to describe the linear potential if the number of SU(2) nontrivial center elements that emerge in the decompositions is the same. As a result, it is the center vortices quantized in terms of nontrivial center elements of the SU(2) subgroup that give rise to the intermediate confinement in the static potentials.