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Phase structure of $SU(3)$ gauge-Higgs unification models at finite temperature

Five-dimensional $SU(3)$ gauge-Higgs unification models are studied at finite temperature in the warped extra dimension $S^1/\mathbb{Z}_2$. In order to investigate the phase structure, we developed a technique to compute the one-loop effective potential with the nontrivial Polyakov loop phase and with the nontrivial Wilson line phase along the extra dimension. Effective potentials as functions of two gauge-field condensations are shown for several simple matter contents, including fundamental, sextet, and adjoint representational Dirac fermions. Possible extensions and applications of our formalism are also briefly discussed.