Hosotani mechanism in the "color"-singlet plasma.

By projecting the partition function on the "color"-singlet state, we investigate the Hosotani mechanism in the fermion-gauge boson plasma. The present toy-model analysis of the one-loop effective potential at finite temperature shows that the critical temperature of gauge symmetry breaking increases at higher temperature in the smaller volume in the universe. Consequently, it is found that a long-lasting phase transition of the first order may take place in the early universe.