Illusory ZN Metastable States in Hot Gauge Theories

Abstract

where β = 1 T is the inverse temperature, and P denotes path ordering. The theories are in a confined phase specified by 〈L〉 = 0 under Tc, and they are in a deconfined phase specified by 〈L〉 = 0 above Tc. 1) When fermions in the fundamental representation are absent, there is a ZN symmetry, which is a center symmetry of SU(N). Above Tc, it is expected that 〈L〉 takes one of the values of ZN , i.e. 〈L〉 ∝ e 2πin N . (n = 0, 1, · · · , N − 1) N -fold degenerate vacua are specified by these ZN values. 2), 3) It is interesting to consider cosmological processes in which the domains of these degenerate ZN vacua exist. Their interface tension has been calculated. 4) (However, there is a claim that there is one unique vacuum and that physical ZN domains do not exist, because the true symmetry is not SU(N) but SU(N)/ZN . 5)) If fermions in the fundamental representation are added, the ZN symmetry is broken. The reason for this is that, although the Lagrangian density