Narrow Results

The instability of protons is a crucial prediction of supersymmetric GUTs. We review the decay in minimal supersymmetric SU(5), which is dominated by dimension-five operators, and discuss the implications of the failure of Yukawa unification for the decay rate. In a consistent SU(5) model, where SU(5) relations among Yukawa couplings hold, the proton decay rate can be several orders of magnitude smaller than the present experimental bound. Finally, we discuss orbifold GUTs, where proton decay via dimension-five operators is absent. The branching ratios of dimension-six decay can significantly differ from those in four dimensions.

We review the gauge symmetry breaking mechanism due to orbifold projections in orbifold model building. We explicitly show the existence of a scale of breaking if such a symmetry breaking is due to freely-acting orbifold operators only, i.e. in case the breaking is realized nonlocally in the internal space. We show that such a scale is related to the compactification moduli only, and that there are no extra continuous parameters, at least in semirealistic models with SUSY in four dimensions. In this sense, the mechanism is peculiarly different from the standard Higgs (or Hosotani) symmetry breaking mechanism. We show that the mechanism also differs from that present in standard orbifold models where, even in the presence of discrete Wilson lines, a scale of breaking is generically missing, since the breaking is localized in specific points in the internal space.

We review a set of background geometries where the described nonlocal breaking is realized, both in the case of two and six extra dimensions. In the latter case, relevant in string model building, we consider both heterotic and open string compactifications.

Unlike all the previous studies on proton decay which worked only in the Minimal Supersymmetric Standard Model, we study the effects of the dimension-5 operators in the Supersymmetric Unification Models with left–right symmetry at low energy. The full chargino sector is used for the analysis. Dressing of the RRRR operators by the SU(2)_R wino makes important or even dominant contributions to the proton decay modes into charged leptons.

In third quantization the origin of fermion families is easy to understand: the electron field, the muon field and the tau field are identical fields in precisely the same sense as three electrons are identical and indistinguishable particles of a theory of second quantization. In both cases, the permutation of these fields or particles leaves the Lagrangian invariant. One can also extend the concept of family to gauge bosons. This can be obtained through the semidirect product of the gauge group with the group of permutations of n objects. In this paper we have studied the group . We explain why we have chosen E₆ as fundamental gauge group factor and why we start with a model with four gauge boson/fermion families to accommodate and to fit the Standard Model with only three fermion families. We suggest a possible symmetry breaking pattern of that could explain quark, lepton and neutrino masses and mixings.

We investigate the gauge-Higgs unification models within the scheme of the coset space dimensional reduction, beginning with two types of set up; fourteen-dimensional gauge theory with simple gauge groups and ten-dimensional gauge theory with direct product gauge groups. We found some phenomenologically acceptable models through an exhaustive search for the candidates of the coset spaces, the gauge group in higher dimension, and fermion representation.

We classify the standard model fermions, which originate from bulk fields of the 27 or representation after orbifold breaking, in E₆ grand unified theories on five- or six-dimensional space–time, under the condition that q, e^c and u^c survive as zero modes for each 27 or . We study features of supersymmetric SU(5) ×U(1)₁ ×U(1)₂ model.

Cosmological Collider Physics gives us the opportunity to probe high-energy physics from observing the space–time fluctuations generated during inflation imprinted on the cosmic microwave background. In other words, it is a method to investigate physics on energy scales that cannot be reached by terrestrial accelerators by means of precise observations of the universe. In this paper, we focus on the case where the GUT scale is close to the energy scale of inflation, and calculate three-point function of inflaton by exchanging the Higgs boson in GUT at tree level. The results are found to be consistent with the current observed restrictions on non-Gaussianity without a drastic fine-tuning of parameters, and it might be possible to detect the signature of the Higgs boson in GUT by 21 cm spectrum, future LSS and future CMB depending on our model parameters.

We study on the origin of the Kobayashi-Maskawa phase¹ in the E₆ GUT with SU(2)_F family symmetry by spontaneous CP violation. We show that the spontaneous CP violation in the GUT model not only understands the origin of the Kobayashi-Maskawa phase but also solves new and old SUSY CP problems. We also comment on the neutrino sector that large neutrino mixings and large CP phases are predicted as in usual E₆ GUT models. This talk is base on the papers.