We study the dynamical symmetry breaking in the gauge-Higgs unification of the five-dimensional theory compactified on an orbifold, S 1 /Z 2 . This theory identifies Wilson line degrees of freedom as ''Higgs doublets.'' We consider SU(3) c ϫSU(3) W and SU(6) models with the compactification scale of order of a few TeV. The gauge symmetries are reduced to SU(3) c ϫSU(2) L ϫU(1) Y and SU(3) c ϫSU(2) L ϫU(1) Y ϫU(1), respectively, through the orbifolding boundary conditions. We estimate the one loop effective potential of ''Higgs doublets,'' and find that the electroweak breaking is realized through the radiative corrections when there are suitable numbers of bulk fields possessing the suitable representations. The masses of ''Higgs doublets'' are O͑100͒ GeV in this scenario.

We propose a natural Higgs sector in E 6 grand unified theory (GUT) with anomalous U (1) A gauge symmetry. In this scenario, the doublettriplet splitting can be realized, while proton decay via dimension 5 operators is suppressed. Gauge coupling unification is also realized without fine-tuning. The GUT scale obtained in this scenario is generally lower than the usual GUT scale, 2 × 10 16 GeV, and therefore it should be possible to observe proton decay via dimension 6 operators in near future experiments. The lifetime of a nucleon in this model is roughly estimated as τ p (p → e + π 0 ) ∼ 3 × 10 33 years. It is shown that the Higgs sector is compatible with the matter sector proposed by one of the present authors, which reproduces realistic quark and lepton mass matrices, including a bilarge neutrino mixing angle. Combining the Higgs sector and the matter sector, we can obtain a completely consistent E 6 GUT. The input parameters for this model are only eight integer anomalous U (1) A charges (+3 for singlet Higgs) for the Higgs sector and three (half) integer charges for the matter sector.of the standard gauge group. If all these PNG modes have only tiny masses around the weak scale, then not only is coupling unification destroyed but also the gauge couplings diverge below the GUT scale. Therefore, we have to give these PNG fields superheavy masses. However, in order to do so, we have to introduce some interactions between Higgs fields, and this requirement is in opposition to that needed to stabilize the DW-type of VEV. This conflict is similar to that existing in the SO(10) case.This paper aims at obtaining a unified description of the Higgs sector in E 6 model, in which the above stated problem and the DT splitting problem are solved. It may seem that SO(10) unified models are promising for this purpose. However, if we proceed to E 6 , there are more advantages in addition to the natural FCNC suppression. In particular, we have the following:1. The FN field naturally emarges as the composite operator Φ Φ , where Φ andΦ are needed to break E 6 down to SO(10).2. The usual doublet Higgs field H is already included in the field Φ.3. In the Higgs sector, the condition for the unification of gauge coupling constants automatically provides "R parity" in terms of anomalous U(1) A naturally, and therefore we do not have to introduce additional R parity.Moreover, we can construct a completely consistent and realistic E 6 GUT scenario by combining this Higgs sector and the matter sector. After explaining how the vacuum in the Higgs sector is determined by anomalous U(1) A charges ( §2) and giving a quick review of the SO(10) model ( §3), we explain how the above desirable features in the Higgs sector are naturally obtained in the E 6 unification ( §4) and a completely consistent E 6 GUT scenario ( §5). Vacuum determinationHere we explore some general structures of VEVs that are determined from the superpotential of the Higgs sector. The Higgs sector is the most poorly part, and usually the VEVs of Higgs fields are introd...

We propose a novel way to break grand unified gauge symmetries via the Hosotani mechanism in models that can accommodate chiral fermions. Adjoint scalar fields are realized through the so-called diagonal embedding method which is often used in the heterotic string theory. We calculate the one-loop effective potential of the adjoint scalar field in a five dimensional model compactified on an S 1 =Z 2 orbifold, as an illustration. It turns out that the potential is basically the same as the one in an S 1 model, and thus the results in literatures, in addition to the chiral fermions, can be realized easily.

We derive the low energy effective theory of Gauge-Higgs unification (GHU) models in the usual four dimensional framework. We find that the theories are described by only the zero-modes with a particular renormalization condition in which essential informations about GHU models are included. We call this condition "Gauge-Higgs condition" in this letter. In other wards, we can describe the low energy theory as the SM with this condition if GHU is a model as the UV completion of the Standard Model. This approach will be a powerful tool to construct realistic models for GHU and to investigate their low energy phenomena.

We calculate the quantum corrections to the mass of the zero mode of the fifth component of the gauge field at two-loop level in a five dimensional massless QED compactified on S 1 . We discuss in detail how the divergences are exactly canceled and the mass becomes finite. The key ingredients to obtain the result are the shift symmetry and the Ward-Takahashi identity. We also evaluate the finite part of corrections.