Domain walls, $Z(N)$ charge and $A_0$ condensate: a canonical ensemble study

The deconfinement phase transition is studied in the ensemble canonical with respect to triality. Since this ensemble implies a projection to the zero triality sector of the theory we introduce a quantity which is insensitive to $Z(N_c)$ symmetry but can reveal a critical behaviour in the theory with dynamical quarks. Further, we argue that in the canonical ensemble description of full QCD there exist domains of different $Z(N_c)$ phases which are degenerate and possess normal physical properties. This contradicts the predictions of the grand canonical ensemble. We propose a new order parameter to test the realization of the discrete $Z(N_c)$ symmetry at finite temperature and calculate it for the case of $Z(2)$ gauge fields coupled to fundamental fermions.