ar X iv : h ep - l at / 0 20 90 93 v 1 9 S ep 2 00 2 1 Confinement without a center : the exceptional group G ( 2 )

We discuss theories with the exceptional centerless gauge group G(2), paying attention to confinement and the pattern of chiral symmetry breaking. Exploiting the Higgs mechanism to break the symmetry down to SU (3), we also present how the familiar features of confinement and chiral symmetry breaking of SU (3) gauge theories reemerge. G(2) gauge theories show up as an unusual theoretical framework to study SU (3) gauge theories without the " luxury " of a center. 1. Introduction and motivations In the last few years, accumulating numerical evidence of the relevance of center vortices in the effective mechanism of confinement in non– Abelian gauge theories has been collected. Center vortices and twist sectors [1] are present in a pure gauge theory with symmetry group G if Π 1 (G/center(G)) = 0, Π 1 being the first homo-topy group. The exceptional group G(2) is the simplest group without center vortices and twist sectors. Thus, it is interesting to investigate how confinement can show up in a theory with such a gauge group. Moreover, a property making G(2) particularly interesting is that it has SU (3) as a subgroup. In our study we have focused our attention on the way confinement and the pattern of chiral symmetry breaking show up in G(2) gauge theories and how they change into the more familiar SU (3) case as the symmetry gets broken.