Constructive Definition of String Theory and Unified Theory of Elementary Particles

提出并分析了弦理论的一种构造性表述。更具体地说，(1)我们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恰当地生成了标准模型的时空维度和场内容。(2)我们还分析了弯曲时空如何用矩阵模型来表示。我们证明了广义相对论的基本对称性，即微分同胚和局部Lorentz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维度小于或等于10的可能流形。在这个意义上，矩阵模型不仅描述了给定流形上的起伏度规，而且描述了时空的所有可能的拓扑。(3)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，其中超引力的对称性是明显的。我们正在研究这个模型是否与原IIB矩阵模型等价。(4)我们对改进的平均场近似进行了高阶计算，证明了四维时空最有可能作为IIB矩阵模型的基态。通过结合所获得的结果，我们试图揭示弦理论的基本对称性和原理，并找到万物理论的终极建设性定义。

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.