Magnetic Z N symmetry in hot QCD and the spatial Wilson loop

We discuss the relation between the deconfining phase transition in gauge theories and the realization of the magnetic Z N symmetry. At low temperature the Z N symmetry is spontaneously broken while above the phase transition it is restored. This is intimately related to the change of behaviour of the spatial 't Hooft loop discussed in [1]. We also point out that the realization of the magnetic symmetry has bearing on the behaviour of the spatial Wilson loop. We give a physical argument to the effect that at zero temperature the spatial Wilson loop must have perimeter law behaviour in the symmetric phase but area law behaviour in the spontaneously broken phase. At high temperature the argument does not hold and the restoration of magnetic Z N is consistent with area law for the Wilson loop.