Narrow Results

We calculate the effective potential for the vacuum gauge field from the one-loop matter effect in M₃×S³×S¹ spacetime. This background geometry is motivated from the recent studies on gauged supergravities with a positive-definite potential, which admits a generalized Kaluza–Klein reduction. We investigate how symmetry breaking patterns through the Hosotani mechanism are affected by the ratio of the radii of S¹ and S³.

The dynamical fermion mass generation on the 3-brane in the 5D spacetime is discussed in a model with bulk fermions in interaction with fermions on the branes assuming the presence of a constant Abelian gauge field A₅ in the bulk. We calculate the effective potential as a function of the fermion masses and the gauge field A₅. The masses can be found from the stationarity condition for the effective potential (the gap equation). We formulate the equation for the mass spectrum of the 4D-fermions. The phases with finite and vanishing fermion masses are studied and the dependence of the masses on the radius of the fifth dimension is analyzed. The influence of the A₅-gauge field on the symmetry breaking is considered both when this field is a background parameter and a dynamical variable. The critical values of the A₅ field, the coupling constant and the radius are examined.

In the gauge-Higgs unification the 4D Higgs field becomes a part of the extra-dimensional component of the gauge potentials. In the SO(5) × U(1) gauge-Higgs unification in the Randall-Sundrum warped spacetime the electroweak symmetry is dynamically broken through the Hosotani mechanism. The Higgs bosons become absolutely stable, and become the dark matter of the universe. The mass of the Higgs boson is determined from the WMAP data to be about 70 GeV.

Four-dimensional 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 ${𝜃}_H$ 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 ${𝜃}_H<0.1$, and predicts $Z^{\prime }$ bosons around 6–10 TeV with very broad widths. The scenario is generalized to $SO(11)$ gauge-Higgs grand unification. Fermions are introduced in the spinor and vector representations of $SO(11)$. Proton decay is naturally forbidden.

In the gauge-Higgs unification scenario the 4D Higgs field is identified with the zero mode of the extra-dimensional component of gauge potentials. The mass of the Higgs particle in the unification in the Randall-Sundrum warped spacetime is predicted to be in the range 100 GeV - 300 GeV. The WWZ gauge couplings remains almost universal as in the standard model, but substantial deviation results for the Higgs couplings. The WWH and ZZH couplings are suppressed by a factor cos θ_H from the values in the standard model, where θ_H is the Yang-Mills AB phase along the fifth dimension. These can be tested at LHC and ILC.

Four-dimensional Higgs field is identified with the extra-dimensional component of gauge potentials in the gauge-Higgs unifiation scenario. SO(5) × 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 θ_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 θ_H < 0.1, and predicts Z^′ bosons around 6–10 TeV with very broad widths. The scenario is generalized to SO(11) gauge-Higgs grand unification. Fermions are introduced in the spinor and vector representations of SO(11). Proton decay is naturally forbidden.

In the gauge-Higgs unification the 4D Higgs field becomes a part of the extra-dimensional component of the gauge potentials. In the SO(5) × U(1) gauge-Higgs unification in the Randall-Sundrum warped spacetime the electroweak symmetry is dynamically broken through the Hosotani mechanism. The Higgs bosons become absolutely stable, and become the dark matter of the universe. The mass of the Higgs boson is determined from the WMAP data to be about 70 GeV.