Large Gauge Hierarchy in Gauge-Higgs Unification

We study a five dimensional SU(3) nonsupersymmetric gauge theory compactified on $M^4\times S^1/Z_2$ and discuss the gauge hierarchy in the scenario of the gauge-Higgs unification. Making use of calculability of the Higgs potential and a curious feature that coefficients in the potential are given by discrete values, we find two models, in which the large gauge hierarchy is realized, that is, the weak scale is naturally obtained from an unique large scale such as a grand unified theory scale or the Planck scale. The size of the Higgs mass is also discussed in each model. One of the models we find realizes both large gauge hierarchy and consistent Higgs mass, and shows that the Higgs mass becomes heavier as the compactified scale becomes smaller.Comment: 21 pages, no figures, version to appear in PR

Effect of Bare Mass on the Hosotani Mechanism

It is pointed out that the existence of bare mass terms for matter fields changes gauge symmetry patterns through the Hosotani mechanism. As a demonstration, we study an SU(2) gauge model with massive adjoint fermions defined on $M^4\otimes S^1$. It turns out that the vacuum structure changes at certain critical values of $mL$, where $m~(L)$ stands for the bare mass (the circumference of $S^1$). The gauge symmetry breaking patterns are different from models with massless adjoint fermions. We also consider a supersymmmetric SU(2) gauge model with adjoint hypermultiplets, in which the supersymmetry is broken by bare mass terms for the gaugino and squark fields instead of the Scherk-Schwarz mechanism.Comment: 10 pages, version to appear in Phys. Lett.

On Gauge Symmetry Breaking via Euclidean Time Component of Gauge Fields

We study gauge theories with/without an extra dimension at finite temperature, in which there are two kinds of order parameters of gauge symmetry breaking. The one is the zero mode of the gauge field for the Euclidean time direction and the other is that for the direction of the extra dimension. We evaluate the effective potential for the zero modes in one-loop approximation and investigate the vacuum configuration in detail. Our analyses show that gauge symmetry can be broken only through the zero mode for the direction of the extra dimension and no nontrivial vacuum configuration of the zero mode for the Euclidean time direction is found.Comment: 22 pages, 6 figures, references and typos corrected, version to appear in PR

Spontaneous Supersymmetry Breaking from Extra Dimensions

We propose a new spontaneous supersymmetry breaking mechanism, in which extra compact dimensions play an important role. To illustrate our mechanism, we study a simple model consisting of two chiral superfields, where one spatial dimension is compactified on a circle $S^1$. It is shown that supersymmetry is spontaneously broken irrespective of the radius of the circle, and also that the translational invariance for the $S^1$-direction and a global symmetry are spontaneously broken when the radius becomes larger than a critical radius. These results are expected to be general features of our mechanism. We further discuss that our mechanism may be observed as the O'Raifeartaigh type of supersymmetry breaking at low energies.Comment: 10 pages, No figur

Bulk Mass Effects in Gauge-Higgs Unification at Finite Temperature

We study the bulk mass effects on the electroweak phase transition at finite temperature in a five dimensional SU(3) gauge-Higgs unification model on an orbifold. We investigate whether the Higgs mass satisfying the experimental lower bound can be compatible with the strong first order phase transition necessary for a successful electroweak baryogenesis. Our numerical results show that the above statement can be realized by matter with bulk mass yielding a viable Higgs mass. We also find an interesting case where the heavier Higgs gives the stronger first order phase transition.Comment: 17 pages, 1 figur

Dynamical Gauge-Higgs Unification in the Electroweak Theory

$SU(2)_L$ doublet Higgs fields are unified with gauge fields in the $U(3)_s \times U(3)_w$ model of Antoniadis, Benakli and Quir\'{o}s' on the orbifold $M^4 \times (T^2/Z_2)$. The effective potential for the Higgs fields (the Wilson line phases) is evaluated. The electroweak symmetry is dynamically broken to $U(1)_{EM}$ by the Hosotani mechanism. There appear light Higgs particles. There is a phase transition as the moduli parameter of the complex structure of $T^2$ is varied.Comment: 14 pages, 3 figures, v.

Multi-Higgs Mass Spectrum in Gauge-Higgs Unification

We study an SU(2) supersymmetric gauge model in a framework of gauge-Higgs unification. Multi-Higgs spectrum appears in the model at low energy. We develop a useful perturbative approximation scheme for evaluating effective potential to study the multi-Higgs mass spectrum. We find that both tree-massless and massive Higgs scalars obtain mass corrections of similar size from finite parts of the loop effects. The corrections modify multi-Higgs mass spectrum, and hence, the loop effects are significant in view of future verifications of the gauge-Higgs unification scenario in high-energy experiments.Comment: 32 pages; typos corrected and a few comments added, published versio

Effects of Bulk Mass in Gauge-Higgs Unification

We study effects of bulk mass on electroweak symmetry breaking and Higgs mass in the scenario of five dimensional SU(3) gauge-Higgs unification defined on M^4\times S^1/Z_2. The asymptotic form of effective potential for the Higgs field is obtained, from which a transparent and useful expression for the Higgs mass is found. The small vacuum expectation values (VEV) for Higgs field can be realized by choosing bulk mass parameters approriately for a fixed set of matter content. The bulk mass for periodic fermion field, in general, has effects to make the Higgs mass less heavy. On the other hand, the bulk mass for antiperiodic field does not directly affect the Higgs mass, but it contributes to increase or decrease the Higgs mass, depending on how small the VEV is induced due to the antiperiodic field. We give numerical examples to confirm these effects, in which the role of the bulk mass is also definitely clear.Comment: 14 pages, no figures, (v2)typos and errors corrected, (v3)the final version to appear in PL

Aspects of Phase Transition in Gauge-Higgs Unification at Finite Temperature

We study the phase transition in gauge-Higgs unification at finite temperature. In particular, we obtain the strong first order electroweak phase transition for a simple matter content yielding the correct order of Higgs mass at zero temperature. Two stage phase transition is found for a particular matter content, which is the strong first order at each stage. We further study supersymmetric gauge models with the Scherk-Schwarz supersymmetry breaking. We again observe the first order electroweak phase transition and multi stage phase transition.Comment: 18 pages, 7 figures, references corrected, minor correctio