Renormalizable minimal SO(10) GUT in 4D and 5D

This report is a review of the present status of GUT, especially renormalizable minimal SO(10) GUT, and its future prospect. It consists of two parts. In part I, I review how the minimal renormalizable supersymmetric SO(10) GUT, an SO(10) framework with only one ${\bf 10}$ and one $\bar{\bf 126}$ Higgs multiplets in the Yukawa sector, is attractive because of its high predictivity. Indeed it not only gave a consistent predictions on neutrino oscillation data but also did reasonable and interesting values for Leptogenesis, LFV, muon g-2, neutrinoless double beta decay etc. However, this model suffers from problems, apart from the small deviations from the observed values, related to running of gauge couplings and proton decay. The gauge coupling unification may be spoiled due to the presence of intermediate scales much lighter than the grand unification (GUT) scale. In addition, the gauge couplings blow up around the GUT scale because of the presence of Higgs multiplets of large representations. In order to remedy these pathologies, in part II, we extend GUT into 5D. We propose two approaches: one is to consider the warped extra dimension, using the bulk Higgs profile to explain the intermediate energy scales. Another is to use the orbifold GUT. Both approaches are complementary to each other.Comment: A talk in the workshop on GUT held at Ritsumeikan Univ. on Dec.17-19 200

The current problems of the minimal SO(10) GUT and their solutions

This talk consists of two parts. In part I we review how the minimal renormalizable supersymmetric SO(10) model, an SO(10) framework with only one 10 and one 126 Higgs multiplets in the Yukawa sector, is attractive because of its highly predictive power. Indeed it not only gives a consistent predictions on neutrino oscillation data but also gives reasonable and interesting values for leptogenesis, LFV, muon g-2, neutrinoless double beta decay etc. However, this model suffers from problems related to running of gauge couplings. The gauge coupling unification may be spoiled due to the presence of Higgs multiplets much lighter than the grand unification (GUT) scale. In addition, the gauge couplings blow up around the GUT scale because of the presence of Higgs multiplets of large representations. In part II we consider the minimal SO(10) model in the warped extra dimension and show a possibility to solve these problems.Comment: 15 pages, 7 figures, Talk given at the International Workshop on Neutrino Masses and Mixings Toward Unified Understanding of Quarks and Lepton Mass Matrices, held at University of Shizuoka on December 17-19, 200

Massive Analogue of Ashtekar-CJD Action

The action of Ashtekar gravity have been found by Cappovilla, Jacobson and Dell. It does not depend on the metric nor the signature of the space-time. The action has a similar structure as that of a massless relativistic particle. The former is naturally generalized by adding a term analogous to a mass term of the relativistic particle. The new action possesses a constant parameter regarded as a kind of a cosmological constant. It is interesting to find a covariant Einstein equation from the action. In order to do it we will examine how the geometrical quantities are determined from the non-metric action and how the Einstein equation follows from it.Comment: 6p. Te

Strongly Correlated Electrons and Neutron Scattering

Various aspects of close and interesting relationship between antiferromagnetism and singlet ground states are introduced for which neutron scattering have been playing vital roles. The special emphasis is on the disorder-induced antiferromagnetism in spin-Peierls systems, which can be viewed as a nucleation process of classical magnetic order in the background of singlet state whose origin is purely quantum-mechanical. It is then pointed out that similar features will be found in Ce_xCu_2Si_2 and high T_c cuprates. Finally the possible charge ordering process in NaV_2O_5 is discussed which leads to the quenching of localized spins.Comment: 8 pages, 3 figures, Proceedings of 7th ISSP International Symposium "Frontiers in Neutron Scattering Research" (To appear in J. Phys. Chem. Solids (1999)