ZN DOMAINS IN GAUGE-THEORIES WITH FERMIONS AT HIGH-TEMPERATURES

At high temperatures, some SU(N) gauge theories with fermions have metastable states related to the Z(N) symmetry of the theory. It has recently been argued that the possible existence of domains of these metastable states may lead to some interesting cosmological consequences. We show that these states, generically, have unacceptable thermodynamic behavior. Their free energy F is-proportional-to T4 with a positive proportionality constant. This leads not only to negative pressure but also to negative specific heat and more seriously, to negative entropy. We argue that although such domains are important in the euclidean theory, they cannot be interpreted as physical domains in Minkowski space. This conclusion remains valid even if sufficient color singlet particles (such as leptons and weak gauge bosons) are added to the system to make the total free energy negative.