Gauge-Higgs Unification Models in Six Dimensions withS2/Z2Extra Space and GUT Gauge Symmetry

We review gauge-Higgs unification models based on gauge theories defined on six-dimensional spacetime with S2/Z2 topology in the extra spatial dimensions. Nontrivial boundary conditions are imposed on the extra S2/Z2 space. This review considers two scenarios for constructing a four-dimensional theory from the six-dimensional model. One scheme utilizes the SO(12) gauge symmetry with a special symmetry condition imposed on the gauge field, whereas the other employs the E6 gauge symmetry without requiring the additional symmetry condition. Both models lead to a standard model-like gauge theory with the SU(3)×SU(2)L×U(1)Y(×U(1)2) symmetry and SM fermions in four dimensions. The Higgs sector of the model is also analyzed. The electroweak symmetry breaking can be realized, and the weak gauge boson and Higgs boson masses are obtained