Abstract
Gauge symmetry breaking through the Hosotani mechanism (the dynamics of nonintegrable phases) in softly broken supersymmetric QCD with ${N}_{F}^{\mathrm{fd}}$ flavors is studied. For $N=\mathrm{even},$ there is a single $\mathrm{SU}(N)$ symmetric vacuum state, while for $N=\mathrm{odd},$ there is a doubly degenerate $\mathrm{SU}(N)$ symmetric vacuum state in the model. We also study generalized supersymmetric QCD by adding ${N}_{F}^{\mathrm{adj}}$ numbers of massless adjoint matter. The gauge symmetry breaking pattern such as $\mathrm{SU}(3)\ensuremath{\rightarrow}\mathrm{SU}(2)\ifmmode\times\else\texttimes\fi{}U(1)$ is possible for appropriate choices of the matter content and values of the supersymmetry breaking parameter. The massless state of the adjoint Higgs scalar is also discussed in the models.
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