A finite temperature investigation of dual superconductivity in the modified SO(3) lattice gauge theory

We study the SO(3) lattice gauge theory in 3+1 dimensions with the adjoint Wilson action modified by a Z2 monopole suppression term and by means of the Pisa disorder operator. We find evidence for a finite temperature deconfinement transition driven by the condensation of U(1) magnetic charges. A finite-size scaling test shows consistency with the critical exponents of the 3D Ising model. Lattice SU(N) pure gauge theories in the fundamental representation undergo a finite temperature deconfinement phase transition [1,2] signalled by the spontaneous breaking of the global center symmetry ZN [3,4]. It is an interesting question whether this happens also for the theory in the adjoint representation SU(N)/ZN [5]. In the latter case the center is trivial and naively there is no global symmetry to be broken. Moreover, although both the fundamental and the adjoint SU(N) lattice theories have the same naive continuum limit, Preprint submitted to Elsevier Science 1 February 2008 non-perturbative investigations carried out for Wilson [6,7] as well as for Villain discretizations [8] showed a different behavior. For the adjoint cases no evidence for a finite temperature phase transition was found, whereas a bulk transition separating the strong from the weak coupling regions appeared for both kinds of discretizations. The bulk transition was explained in terms of a condensation of lattice artifacts Z2 monopoles [8]. It was argued that the finite temperature transition could be overshadowed by the bulk one and Z2 monopole suppression terms were thus proposed [9]. More recently the Villain mixed fundamental-adjoint SU(2) model with a monopole (and vortex) suppression has been reinvestigated [10,11,12] and first evidence for a deconfinement transition in the Ising 3D universality class, at least for strong coupling (Nτ = 2), was given. Moreover, in the weak coupling region negative states of the Polyakov loop in the adjoint representation were found [10,13] and later linked to the non-trivial twist sectors of the theory [14], given that on the hypertorus T 4 the partition function of the SO(3) theory in the Villain formulation with complete Z2 monopole suppression was shown to be equivalent to that of the SU(2) theory in the fundamental representation when summed over all twist sectors [15,16,17,18]. In a recent paper we have reinvestigated the SO(3) theory using the Wilson action and a Z2 monopole suppression term with a “chemical potential” λ [19,20,21,22]. The phase diagram in the βA − λ plane was studied at zero and finite temperature monitoring the tunneling between twist sectors and its disappearance for strong enough Z2 monopole suppression. For λ ≥ .85 we have found a strong indication for the existence of a finite temperature deconfinement transition although having restricted the simulation to a fixed