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In this article, we review gauge-Higgs unification models based on gaugetheories defined on six-dimensional spacetime with $S^2/Z_2$ topology in theextra spatial dimensions. On the extra $S^2/Z_2$ space, non-trivial boundaryconditions are imposed. This review considers two scenarios for constructing afour-dimensional theory from the six-dimensional model. One scheme utilizes theSO(12) gauge symmetry with a special symmetry condition imposed on the gaugefield, whereas the other employs the E$_6$ gauge symmetry without requiring theadditional symmetry condition. Both models lead to a Standard Model-like gaugetheory with the SU(3) $\times$ SU(2)$_L$ $\times$ U(1)$_Y$($\times$ U(1)$^2$)symmetry and SM fermions in four dimensions. The Higgs sector of the model isalso analyzed. The electroweak symmetry breaking can be realized, and the weakgauge boson and Higgs boson masses are obtained.

Gauge-Higgs unification models in six dimensions with $S^2/Z_2$ extra space and GUT gauge symmetry