Supersymmetric Grand Unified Theory based on Brain World Picture

我们在2001年至2003年三个学年的研究成果如下：1.膜世界情景：为了研究我们的世界是高维空间中的三勇士的勇敢世界情景，我们考虑了五维时空中额外的一维被压缩成一个超对称S^1/Z_2的最简单的情形。我们给出了这种情形的超共形张量演算，特别是阐明了写下勇敢者的物质与体超引力和超杨-Mills多重态的超共形不变耦合的一般规则。在另一篇论文中，我们还首次发现存在规范和非规范两种类型的5D张量多重态，并给出了它们的超共形张量演算。我们还给出了Berghoff Kallosh-Van Proeyen的“奇异空间中的超对称性”的一个完全脱离壳层的公式。有了这一点，我们已经证明了超对称性自动保证了特殊的…边界勇敢的张力和兰德尔-桑德鲁姆方案中所要求的大宇宙项之间有更多的联系。另一方面，在Altendorfer-Bagger-Nemeschansky方法中，我们已经证明了这种关系不是从超对称性而来的，而是一种微调。超对称E6大统一理论中的希格斯场和夸克/轻子混合：为了解决三重态分裂问题，我们研究了超对称E6GUT框架中希格斯双态的伪Nambu-Goldstone玻色子理论。我们发现，除了希格斯双重态之外，必然会出现额外的轻伪Nambu-Goldstone玻色子；这些额外的PsNG玻色子必须唯一地是SU(5)的10+10*表示，才不会干扰规范耦合的统一。它们的存在被证明与目前质子衰变的实验界限几乎不一致。在1)夸克/轻子质量矩阵具有由反常U(1)电荷给出的幂的Froggatt-Nielsen分解形式，以及2)U(1)电荷遵循SU(5)肠道结构的假设下，我们证明了夸克质量数据必然意味着中微子的大2-3混合。如果以太阳中微子和大气中微子的质量平方差比数据作为输入，则意味着1-2混合也必须是大的(即双大混合)。我们还添加了一个论点，即E6 Gut是受青睐的。较少

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