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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.

提出并分析了弦理论的一种构造性表述。（1）用解析和数值方法分析了IIB矩阵模型的结构，并检验了该模型是否能正确地产生标准模型的时空维数和场容量。(2)We还分析了如何用矩阵模型表示弯曲时空。我们已经证明了广义相对论的基本对称性，即对称性和局部洛仑兹对称性，作为矩阵的SU（N）对称性的一部分包含在矩阵模型中。我们进一步证明了矩阵模型的路径积分包含所有可能的维数小于或等于10的流形。在这个意义上，矩阵模型不仅描述了给定流形上的涨落度量，而且描述了时空的所有可能拓扑。(3)We将上述分析推广到超引力的情况，提出了一种新的矩阵模型，在这种模型中，超引力的对称性是明显的。我们正在研究这个模型是否等价于原来的IIB矩阵模型。(4)We在改进的平均场近似下进行了高阶计算，证明了四维时空作为IIB矩阵模型的基态是最合理的，结合所得结果，我们试图揭示弦理论的基本对称性和基本原理，并找到万有理论的最终构造性定义。