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Phase Structures of SU(N) Gauge-Higgs Models on Multiply Connected Spaces

We study an SU(N) gauge-Higgs model with N_F massless fundamental fermions on M^3 \otimes S^1. The model has two kinds of order parameters for gauge symmetry breaking: the component gauge field for the S^1 direction (Hosotani mechanism) and the Higgs field (Higgs mechanism). We find that the model possesses three phases called Hosotani, Higgs and coexisting phases for N=odd, while for N=even, the model has only two phases, the Hosotani and coexisting phases. The phase structure depends on a parameter of the model and the size of the extra dimension. The critical radius and the order of the phase transition are determined. We also consider the case that the representation of matter fields under the gauge group is changed. We find some models, in which there is only one phase, independent of parameters of the models as well as the size of the extra dimension.