Confinement and the center of the gauge group

The role of the center of the gauge group in the phenomenon of confinement in Yan-Mills theory is investigated. Starting from the most general perspective of considering all possible choices for the gauge symmetry group, we then focus on G(2) Yang-Mills theory: the simplest pure gauge theory with a trivial center and without 't Hooft flux vortices. Numerical simulations show the presence of a first order finite temperature deconfinement phase transition in G(2) Yang-Mills theory in (3+1) dimensions. Interestingly, the C(2) gauge symmetry can be broken to an SU(3) subgroup by the Higgs mechanism. We investigate the relation between the deconfinement phase transition in G(2) and SU(3) Yang-Mills theories by numerical simulations in the G(2) gauge-Higgs system.