Domain walls in thermal gauge field theories - myth or reality?

We argue different ZN thermal vacua of hot pure Yang-Mills theory distinguished in the standard approach by different values of Polyakov loop average

T corresponds actually to one and the same physical state. A critical discussion of the argument which are usually put forward in favor of the opposite conclusion (that, in pure continuum Yang-Mills theory, distinct ZN-phases may coexist in the physical space being separated by the domain walls finite surface energy) is given. In particular, we note that the same arguments can be applied with an equal ease to Abelian theories and would lead to the existence of the walls in the high-T 4-dim QED and to appearance of the queer high-T solitons with the mass ∼ T2/e in the Schwinger model. We emphasize that these configurations may be relevant for the Euclidean path integral but whether they correspond to Minkowski space objects is unclear. (author). 16 refs, 2 figs