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Unification Theories Including Gravity and its Mathematical Structure

包括重力及其数学结构在内的统一理论

基本信息

批准号：
02044015
负责人：
OKADA Yasuhiro
金额：
$ 1.28万
依托单位：
Tohoku University
依托单位国家：
日本
项目类别：
Grant-in-Aid for international Scientific Research
财政年份：
1990
资助国家：
日本
起止时间：
1990 至无数据
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-02044015/
关键词：
String theory Gravity P-adic number Unification theory Quark mass matrix Flavor mixing

项目摘要

In this program we studied two subjects, namely the p-adic approach to the string theory and the unified theories of the standard and beyond standard models.Supersrting is the most prominent unified theory including gravity. Although many interesting things have been found, the important questions like what is the vacuum structure of string rely on the ability of non-perturbative calculation in string theory. The p-adic string was initiated to understand new mathematical structure of string in terms of an infinite product formula of the string tree amplitude.This year we reconsidered the p-adic string amplitude based on Bruhat-Tits tree which is a natural analogy to the world sheet of the ordinary string. We can formulate the p-adic loop amplitude using this idea. The remaining problems include to clarify the relationship between the p-adic and ordinarystring theories and to find possible applications of field theories defined over Bruhat-Tits tree.As for unification theories, Frampton and Okada consider the problem of quark masses and flavor mixings. In the standard model with three generations, we have 10 free parameters in the quark sector. Any relations among these parameters suggest physics beyond the standard model. We start a simple ansatz for the quark mass matrices and derive a new relation among two elements of Kobayashi-Maskawa matrix and up-, charm-and top-quark masses. Once the top quark mass is known and more precise measurements of B-meson decay are done we can check the validity of the proposed relation.With T. Yanagida, Frampton also studied the strong CP problem in a model with an extra gauge symmetry and heavy fermions called sark. They pointed out that in the sark model with Peccei-Quinn symmetry a light axion can be avoided.

在这个项目中，我们研究了两个主题，即弦理论的p-adic方法和标准模型和超越标准模型的统一理论。超弦是包括引力在内的最突出的统一理论。尽管人们已经发现了许多有趣的现象，但诸如弦的真空结构等重要问题仍然依赖于弦理论的非微扰计算能力。p-adic弦是为了理解弦的新的数学结构而提出的，它是根据弦树振幅的无限乘积公式。今年我们重新考虑了基于Bruhat-Tits树的p-adic弦振幅，Bruhat-Tits树是普通弦的世界表的自然类比。我们可以用这个思想来表示p-adic环振幅。剩下的问题包括澄清p-adic理论与普通弦理论之间的关系，以及寻找Bruhat-Tits树上定义的场论的可能应用。至于统一理论，Frampton和Okada考虑了夸克质量和味混合问题。在三代标准模型中，夸克扇区有10个自由参数。这些参数之间的任何关系都表明了标准模型之外的物理学。本文对夸克质量矩阵作了一个简单的分析，导出了Kobayashi-Maskawa矩阵的两个元素与上夸克、粲夸克和顶夸克质量之间的一个新的关系。一旦我们知道了顶夸克的质量，并对B介子衰变进行了更精确的测量，我们就可以检验所提出的关系式的正确性。Yanagida，Frampton还研究了一个具有额外规范对称性和称为sark的重费米子的模型中的强CP问题。他们指出，在具有Peccei-Quinn对称性的sark模型中，轻轴子是可以避免的。