Z2 monopoles, vortices and the universality of the SU(2) deconfinement transition

We investigate the effect of Z2 magnetic monopoles and vortices on the finite temperature deconfinement phase transition in the fundamental - adjoint SU(2) lattice gauge theory. In the limit of complete suppression of the Z2 monopoles, the mixed action for the SU(2) theory in its Villain form is shown to be self-dual under the exchange of the fundamental and adjoint couplings. By further suppressing the Z2 vortices we show that the extended model reduces to the Wilson action with a modified coupling. The universality of the SU(2) deconfinement phase transition with the Ising model is therefore expected to remain intact in the entire plane of the fundamental-adjoint couplings in the continuum limit. The self-duality arguments related to the suppression of Z2 monopoles are also applicable to the Villain form of mixed action for the SU(N) theory with ZN magnetic monopoles.