Spatial ʹt Hooft loop, hot QCD and ZN domain walls

We show that the deconfinement phase transition in the pure Yang-Mills theory can be characterized by the change of behaviour the spatial ʹt Hooft loop, V(C). In the confining phase V has a perimeter law behaviour V(C)∝exp{−mP(C)}, while in the deconfined phase it has the area law behaviour V(C)∝exp{−αS(C)}. We show that the area law behaviour of the ʹt Hooft loop is intimately related to the plasma-like distribution of the color charges in the hot QCD vacuum. We also show that the “dual string tension” α is equal to the “wall tension” of the ZN domain walls previously calculated by Bhattacharya, Goksch, Korthals-Altes and Pisarski [Phys. Rev. Lett. 66 (1991) 998; Nucl. Phys. B 383 (1992) 497]. All these properties generalize immediately to other nonabelian theories without fundamental charges, such as supersymmetric Yang Mills. In theories with fundamental charges the ʹt Hooft loop presumably has the area law behaviour already at zero temperature and therefore is not a good order parameter in the strict sense.