Using vacuum domain structure model, trivial static potentials in various representations of F4, E6 and G2 exceptional groups are calculated by means of the unit center element. Due to the absence of the non-trivial center elements, the potential of every representation is screened at far distances. However, the linear part is observed at intermediate quark separations which is investigated by the decomposition of the exceptional group to its maximal subgroups. Comparing the group factor of the super-group with the corresponding one obtained from the non-trivial 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 to the SU (3) subgroup is the same as the potential of the super-group itself. In addition, any regular or singular decomposition to the SU (2) subgroup which produces the Cartan generator with the same elements as h1, 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 h1, are still able to describe the linear potential if the number of SU (2) non-trivial center element which emerge in the decompositions is the same. As a result, it is the center vortices quantized in terms of non-trivial center element of the SU (2) subgroup which give rise to the intermediate confinement in the static potentials.

Abstract. We calculate the potential between static quarks in the fundamental representation of the F 4 exceptional gauge group using domain structures of the thick center vortex model. As non-trivial center elements are absent, the asymptotic string tension is lost while an intermediate linear potential is observed. SU(2) is a subgroup of