Abstract
We review gauge-Higgs unification models based on gauge theories defined on six-dimensional spacetime withS2/Z2topology in the extra spatial dimensions. Nontrivial boundary conditions are imposed on the extraS2/Z2space. 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 E6gauge symmetry without requiring the additional symmetry condition. Both models lead to a standard model-like gauge theory with theSU(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.
Highlights
The Higgs sector of the standard model SM plays an essential role in the spontaneous symmetry breaking SSB from the SU 3 C × SU 2 L × U 1 Y gauge group down to SU 3 C × U 1 EM, thereby giving masses to the SM elementary particles
We have reviewed a gauge theory defined on 6D spacetime with the S2/Z2 topology on the extra space
One scenario based on the SO 12 gauge group requires a symmetry condition for the gauge field
Summary
The Higgs sector of the standard model SM plays an essential role in the spontaneous symmetry breaking SSB from the SU 3 C × SU 2 L × U 1 Y gauge group down to SU 3 C × U 1 EM, thereby giving masses to the SM elementary particles. We have shown interesting properties of one type of gauge-Higgs unification models based on grand unified gauge theories defined on six-dimensional 6D spacetime, with the extradimensional space having the topological structure of two-sphere orbifold S2/Z2 21, 22. A background gauge field is introduced as part of the solution 1 Such a background gauge field is necessary for obtaining chiral fermions in four-dimensional 4D spacetime, even without the symmetry condition. The gauge symmetry, scalar contents, and massless fermions are determined by these boundary conditions and the background gauge field. We note in passing that the mass dimensions of Aμ, Aα, Ψ and g in the 6D model are 1, 0, 5/2 and −1, respectively
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