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Gauge-Higgs grand unification is formulated. By extending $SO(5) times U(1)_X$ gauge-Higgs electroweak unification, strong interactions are incorporated in $SO(11)$ gauge-Higgs unification in the Randall-Sundrum warped space. Quarks and leptons are contained in spinor and vector multiplets of $SO(11)$. Although the KK scale can be as low as $10 $ TeV, proton decay is forbidden by a conserved fermion number in the absence of Majorana masses of neutrinos.
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$SO(11)$ gauge-Higgs grand unification is formulated in the six-dimensional hybrid warped space in which the fifth and sixth dimensions play as the electroweak and grand-unification dimensions. Fermions are introduced in ${bf 32}$, ${bf 11}$ and ${bf 1}$ of $SO(11)$. Small neutrino masses naturally emerge as a result of a new seesaw mechanism in the gauge-Higgs unification which is characterized by a $3 times 3$ mass matrix.
4D Higgs field is identified with the extra-dimensional component of gauge potentials in the gauge-Higgs unification scenario. $SO(5) times U(1)$ gauge-Higgs EW unification in the Randall-Sundrum warped space is successful at low energies. The Higgs field appears as an Aharonov-Bohm phase $theta_H$ in the fifth dimension. Its mass is generated at the quantum level and is finite. The model yields almost the same phenomenology as the standard model for $theta_H < 0.1$, and predicts $Z$ bosons around 6 - 10 TeV with very broad widths. The scenario is genelarized to $SO(11)$ gauge-Higgs grand unification. Fermions are introduced in the spinor and vector representations of $SO(11)$. Proton decay is naturally forbidden.
We discuss the gauge-Higgs unification in a framework of Lifshitz type gauge theory. We study a higher dimensional gauge theory on R^{D-1}times S^{1} in which the normal second (first) order derivative terms for scalar (fermion) fields in the action are replaced by higher order derivative ones for the direction of the extra dimension. We provide some mathematical tools to evaluate a one-loop effective potential for the zero mode of the extra component of a higher dimensional gauge field and clarify how the higher order derivative terms affect the standard form of the effective potential. Our results show that they can make the Higgs mass heavier and change its vacuum expectation value drastically. Some extensions of our framework are briefly discussed.
Gauge-Higgs unification is the fascinating scenario solving the hierarchy problem without supersymmetry. In this scenario, the Standard Model (SM) Higgs doublet is identified with extra component of the gauge field in higher dimensions and its mass becomes finite and stable under quantum corrections due to the higher dimensional gauge symmetry. On the other hand, Yukawa coupling is provided by the gauge coupling, which seems to mean that the flavor mixing and CP violation do not arise at it stands. In this talk, we discuss that the flavor mixing is originated from simultaneously non-diagonalizable bulk and brane mass matrices. Then, this mechanism is applied to various flavor changing neutral current (FCNC) processes via Kaluza-Klein (KK) gauge boson exchange at tree level and constraints for compactification scale are obtained.
When the extra dimensional space is not simply-connected, dynamics of the AB phase in the extra dimension can induce dynamical gauge symmetry breaking by the Hosotani mechanism. This opens up a new way of achieving unification of gauge forces. It leads to the gauge-Higgs unification. The Hosotani mechanism can be established nonperturbatively by lattice simulations, in which measurements of the Polyakov line give a clue.
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