5-Dimensional Difficulties of Gauge-Higgs Unifications

We discuss a possibility whether a model of grand gauge-Higgs unification incorporating family unification in higher dimensions can be constructed. We first extend a five dimensional $SU(6)$ grand gauge-Higgs unification model to a five dimensional $SU(7)$ grand gauge-Higgs unification model compactified on an orbifold $S^1/Z_2$ to obtain three generations of quarks and leptons after symmetrybreaking of the larger family unified gauge group. A prescription of constructing a s...

We study grand unified models in the five-dimensional space-time where the extra dimension is compactified on $S^1/Z_2$. The spontaneous breaking of unified gauge symmetries is achieved via vacuum expectation values of the extra-dimensional components of gauge fields. We derive one-loop effective potentials for the zero modes of the gauge fields in SU(7), SU(8), SO(10), and $E_6$ models. In each model, the rank of the residual gauge symmetry that respects the boundary conditi...

We propose a new model of 5D $SU(3)\otimes U(1)_X$ gauge-Higgs unification with a successful electroweak symmetry breaking and a realistic Higgs boson mass. In our model, the representations of the fermions are very simple, the ${\bf 3}, \overline{\bf 3}$ and $\bf \overline{15}$ representations of $SU(3)$ gauge group. Employing the anti-periodic boundary conditions for $\bf \overline{15}$ reduces massless exotic fermions and simplifies the brane localized mass terms. We calcu...

We investigate gauge coupling unification in higher dimensional GUT models with split supersymmetry. We focus on 5d and 6d orbifold GUTs, which permit a simple solution to several problems of 4D GUTs as well as control over GUT scale threshold corrections. In orbifold GUTs, calculable threshold corrections can raise or lower the prediction for $\alpha_s(M_Z)$ in a way that depends on the location of Higgs fields. On the other hand, split supersymmetry lowers the prediction fo...

Lattice simulations of five-dimensional gauge theories on an orbifold revealed that there is spontaneous symmetry breaking. Some of the extra-dimensional components of the gauge field play the role of a Higgs field and some of the four-dimensional components become massive gauge bosons. The effect is confirmed by computing the Coleman-Weinberg potential with a cutoff. We compare the results of this computation with the lattice data.

We study the unitarity bounds of the scattering amplitudes in the extra dimensional gauge theory where the gauge symmetry is broken by the boundary condition. The estimation of the amplitude of the diagram including four massive gauge bosons in the external lines shows that the asymptotic power behavior of the amplitude is canceled. The calculation will be done in the 5 dimensional standard model and the SU(5) grand unified theory, whose 5th dimensional coordinate is compacti...

Electroweak symmetry breaking is explored in a two Higgs doublet model based on a six dimensional $SU(4)$ gauge-Higgs unification compactified on an orbifold $T^2/Z_2$. The remarkable property of this model is a prediction of realistic weak mixing angle $\sin^2 \theta_W = 1/4$ at the compactification scale. We calculate one-loop effective potential of the Standard Model Higgs boson from the contributions of the gauge boson and the fermion in a four-rank totally symmetric tens...

We study Gauge-Higgs Unification in five dimensions on the lattice by means of the mean-field expansion. We formulate it for the case of an SU(2) pure gauge theory and orbifold boundary conditions along the extra dimension, which explicitly break the gauge symmetry to U(1) on the boundaries. Our main result is that the gauge boson mass computed from the static potential along four-dimensional hyperplanes is nonzero implying spontaneous symmetry breaking. This observation supp...

We consider six dimensional gauge models compactified on the orbifold T^2/Z_N (N=2,3,4,6) such that the Standard Model (SM) Higgs doublet arises from the extra-dimensional components of the gauge field. For \Lambda \leq 10^{19} GeV, where \Lambda denotes the compactification scale, we obtain 114.4 GeV \leq m_H \leq 164 GeV for the SM Higgs boson mass. We also consider gauge-Higgs-top and gauge-Higgs-bottom Yukawa unification which respectively yield m_H = 131^{+4}_{-5} GeV an...

Higher dimensional grand unified theories, with gauge symmetry breaking by orbifold compactification, possess SU(5) breaking at fixed points, and do not automatically lead to tree-level gauge coupling unification. A new framework is introduced that guarantees precise unification -- even the leading loop threshold corrections are predicted, although they are model dependent. Precise agreement with the experimental result, \alpha_s^{exp} = 0.117 \pm 0.002, occurs only for a uni...