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Register a new userSymmetry-Protected Topological relationship between $SU(3)$ and $SU(2)times{U(1)}$ in Two Dimension
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Symmetry-protected topological $left(SPTright)$ phases are gapped short-range entangled states with symmetry $G$, which can be systematically described by group cohomology theory. $SU(3)$ and $SU(2)times{U(1)}$ are considered as the basic groups of Quantum Chromodynamics and Weak-Electromagnetic unification, respectively. In two dimension $(2D)$, nonlinear-sigma models with a quantized topological Theta term can be used to describe nontrivial SPT phases. By coupling the system to a probe field and integrating out the group variables, the Theta term becomes the effective action of Chern-Simons theory which can derive the response current density. As a result, the current shows a spin Hall effect, and the quantized number of the spin Hall conductance of SPT phases $SU(3)$ and $SU(2)times{U(1)}$ are same. In addition, relationships between $SU(3)$ and $SU(2)times{U(1)}$ which maps $SU(3)$ to $SU(2)$ with a rotation $U(1)$ will be given.
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$SO(5) times U(1) times SU(3)$ gauge-Higgs unification model inspired by $SO(11)$ gauge-Higgs grand unification is constructed in the Randall-Sundrum warped space. The 4D Higgs boson is identified with the Aharonov-Bohm phase in the fifth dimension. Fermion multiplets are introduced in the bulk in the spinor, vector and singlet representations of $SO(5)$ such that they are implemented in the spinor and vector representations of $SO(11)$. The mass spectrum of quarks and leptons in three generations is reproduced except for the down quark mass. The small neutrino masses are explained by the gauge-Higgs seesaw mechanism which takes the same form as in the inverse seesaw mechanism in grand unified theories in four dimensions.
The spin-charge-family theory predicts the existence of the fourth family to the observed three. The $4 times 4$ mass matrices --- determined by the nonzero vacuum expectation values of the two triplet scalars, the gauge fields of the two groups of $widetilde{SU}(2)$ determining family quantum numbers, and by the contributions of the dynamical fields of the two scalar triplets and the three scalar singlets with the family members quantum numbers ($tau^{alpha}=(Q, Q,Y)$) --- manifest the symmetry $widetilde{SU}(2) times widetilde{SU}(2) times U(1)$. All scalars carry the weak and the hyper charge of the standard model higgs field ($pm frac{1}{2},mp frac{1}{2}$, respectively). It is demonstrated, using the massless spinor basis, that the symmetry of the $4times4$ mass matrices remains $SU(2) times SU(2) times U(1)$ in all loop corrections, and it is discussed under which conditions this symmetry is kept under all corrections, that is with the corrections induced by the repetition of the nonzero vacuum expectation values included.
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The models with the gauge group $SU(3)_ctimes SU(3)_L times U(1)_X$ (331-models) have been advocated to explain why there are three fermion generations in Nature. As such they can provide partial understanding of the flavour sector. The hierarchy of Yukawa-couplings in the Standard Model is another puzzle which remains without compelling explanation. We propose to use Froggatt-Nielsen -mechanism in a 331-model to explain both fundamental problems. It turns out that no additional representations in the scalar sector are needed to take care of this. The traditional 331-models predict scalar flavour changing neutral currents at tree-level. We show that they are strongly suppressed in our model.
The neutrino and Higgs sectors in the $mbox{SU(2)}_1 times mbox{SU(2)}_2 times mbox{U(1)}_Y $ model with lepton-flavor non-universality are discussed. We show that active neutrinos can get Majorana masses from radiative corrections, after adding only new singly charged Higgs bosons. The mechanism for generation of neutrino masses is the same as in the Zee models. This also gives a hint to solving the dark matter problem based on similar ways discussed recently in many radiative neutrino mass models with dark matter. Except the active neutrinos, the appearance of singly charged Higgs bosons and dark matter does not affect significantly the physical spectrum of all particles in the original model. We indicate this point by investigating the Higgs sector in both cases before and after singly charged scalars are added into it. Many interesting properties of physical Higgs bosons, which were not shown previously, are explored. In particular, the mass matrices of charged and CP-odd Higgs fields are proportional to the coefficient of triple Higgs coupling $mu$. The mass eigenstates and eigenvalues in the CP-even Higgs sector are also presented. All couplings of the SM-like Higgs boson to normal fermions and gauge bosons are different from the SM predictions by a factor $c_h$, which must satisfy the recent global fit of experimental data, namely $0.995<|c_h|<1$. We have analyzed a more general diagonalization of gauge boson mass matrices, then we show that the ratio of the tangents of the $W-W$ and $Z-Z$ mixing angles is exactly the cosine of the Weinberg angle, implying that number of parameters is reduced by 1. Signals of new physics from decays of new heavy fermions and Higgs bosons at LHC and constraints of their masses are also discussed.
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