  We discuss the effective action for Polyakov-Wilson loops winding around
compact Euclidean time, which serve as order parameters for the finite
temperature deconfinement transition in $SU(N)$ Yang-Mills gauge theory. We
then apply our results to the study of the high temperature continuation of the
confining phase, and to the analysis of certain $Z_N$ domain walls that have
been argued to play a role in cosmology. We argue that the free energy of these
walls is much larger than previously thought.
