Constructive Definition of String Theory and Unified Theory of Elementary Particles

弦理论和基本粒子统一论的构造性定义

基本信息

批准号：
14540254
负责人：
KAWAI Hikaru
金额：
$ 2.18万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2005
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540254/
关键词：
string theory constructive definition IIB matrix model nonperturbative effects generation of space-time improved mean field approximation unified theory theory of everything 超弦理論非摂動的定式化曲がった時空一般座標変換不変性局所ローレンツ不変性行列模型量子重力

项目摘要

A constructive formulation of string theory is proposed and analyzed. More concretely,(1)We have analyzed the structure of IIB matrix model both in analytic and numerical methods, and examined whether the dimension of the space-time and the field contents of the standard model are properly generated by this model.(2)We also have analyzed how curved space-time can be represented by the matrix model. We have shown that the fundamental symmetries of the general relativity, diffeomorphisms and local Lorentz symmetry, are included in the matrix model as a part of the SU(N) symmetry of the matrices. We have further shown that the path integral of the matrix model contains all possible manifolds with dimensions less than or equal to ten. In this sense, the matrix model describes not only the fluctuating metric on a given manifold but also all possible topologies of space-time.(3)We have generalized the above analysis to the case of supergravity, and proposed a new type of matrix model in which the symmetry of supergravity is manifest. We are investigating whether this model is equivalent to the original IIB matrix model or not.(4)We have performed a higher order calculation of the improved mean field approximation, and shown that the four dimensional space-time is most plausible as the ground state of IIB matrix model.By combining the obtained results, we are trying to reveal the fundamental symmetry and principles of string theory, and find the ultimate constructive definition of the theory of everything.

提出和分析了弦理论的建设性表述。更具体地说，（1）我们已经在分析和数值方法中分析了IIB矩阵模型的结构，并检查了该模型是否正确生成了时空的维度和标准模型的现场内容。（2）。（2）我们还分析了矩阵模型如何表示曲线时空。我们已经表明，作为矩阵的SU（N）对称性的一部分，将一般相对性，差异性和局部Lorentz对称性的基本对称性包括在矩阵模型中。我们进一步表明，矩阵模型的路径积分包含所有可能的歧管，其尺寸小于或等于十。从这个意义上讲，矩阵模型不仅描述了给定歧管上的波动度量，而且还描述了时空的所有可能拓扑。（3）我们已将上述分析概括为超级强烈的情况，并提出了一种新型的矩阵模型其中超级对称性的体现。我们正在研究该模型是否等同于原始IIB矩阵模型。（4）我们对改进的平均场近似进行了更高的阶段计算，并表明四维时空是最合理的，作为基态通过结合获得的结果，我们试图揭示弦理论的基本对称性和原理，并找到一切事物理论的最终建设性定义。