Supersymmetric Grand Unified Theory based on Brain World Picture

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The research results of our project for three academic years in 2001 -2003 are as follows:1. Brane world scenario:In order to study the brave world scenario that our world is a three-brave in a higher dimensional space, we consider the simplest case of five dimensional space-time for which the extra one-dimension is compactified to an orbifold S^1/Z_2. We have given the superconformal tensor calculus for such orbifold case and, in particular, clarified the general rule for writing down the superconformal invariant coupling of the matters on the brave to the bulk supergravity and super Yang-Mills multiplets. We also found for the first time that there exist two types of 5D tensor multiplets, gauge and non-gauge ones, in another paper and gave the superconformal tensor calculus for them. We also gave a completely off-shell formulation for "Supersymmetry in Singular Spaces" by Bergshoeff Kallosh-Van Proeyen. With this we have shown that the supersymmetry automatically guarantees the speci … More al relation between the boundary brave tensions and the bulk cosmological term required in the Randall-Sundrum Scenario. In the Altendorfer-Bagger-Nemeschansky approach, on the other hand, we have shown that such a relation does not follow from the supersymmetry but remains to be a fine-tuning.2. Higgs field and quark/lepton mixing in supersymmetric E6 grand unified theory:We examined the pseudo-Nambu-Goldstone boson idea for the Higgs doublet in supersymmetric E6 GUT framework in order to solve the triplet-doublet splitting problem. We found that there necessarily appear extra light pseudo-Nambu-Goldstone bosons other than the desired Higgs doublets; those extra PsNG bosons must uniquely be 10 + 10* representation of SU(5) in order for them not to disturb the gauge coupling unification. Their existence is shown to be barely consistent with the present experimental bound for proton decay. Under the assumptions that 1) the quark/lepton mass matrices take Froggatt-Nielsen's factorized power form with the powers given by anomalous U(1) charges, and 2) the U(1) charges respect the SU(5) GUT structure, we showed that the quark mass data necessarily implies the large 2-3 mixing for neutrinos. If the mass-squared difference ratio data of solar and atmospheric neutrinos is used as an input, then, it implies that the 1-2 mixing must also be large (namely, bi-large mixing). We also add an argument that E6 GUT is favored. Less