HOT GAUGE-THEORIES AND ZN PHASES

In this paper several aspects of Z(N) symmetry in gauge theories at hi gh temperatures are discussed. The metastable Z(N) bubbles in SU(N) ga uge theories with fermions may have, generically, unacceptable thermod ynamic behavior. Their free energy F is-proportional-to T4, with a pos itive proportionality constant. This leads not only to negative pressu re but also to negative specific heat and, more seriously, to negative entropy. We argue that although such domains are important in the Euc lidean theory, they cannot be interpreted as physical domains in Minko wski space. A related problem is connected with the analysis of the hi gh-temperature limit of the confining phase. Using two-dimensional QCD with adjoint fermions as a toy model we shall demonstrate that in the light fermion limit there is no breaking of the Z(N) symmetry in the high-temperature limit and thus there are no Z(N) bubbles.