Constructive Formulation of String Theory

提出并分析了弦理论的一种构造性表述。我们用一种称为IIB矩阵模型（有时也称为IKKT模型）的矩阵模型来表示弦理论，并考察了标准模型的时空维数和场内容是否由这个模型适当地产生。分析了IIB矩阵模型与非对易几何的关系，找到了在该模型中实现弯曲时空和广义坐标不变性的机制。虽然我们需要一个密集的数值模拟或一些新的分析方法来证明我们的形式的有效性，我们希望这个模型将解释各种物理量，如夸克和轻子的质量，并作为一切的理论。

A constructive formulation of string theory is proposed and analyzed. We have expressed string theory in terms of a matrix model called IIB matrix model (or sometimes called IKKT model), and examined whether the dimension of the space-time and the field contents of the standard model are properly generated by this model. We also have analyzed the relation between IIB matrix model and the non-commutative geometry, and found a mechanism of realizing curved space-time and the general coordinate invariance in this model. Although we need an intensive numerical simulation or some new analytic method to prove the validity of our formalism, we expect that this model will explain various physical quantities such as masses of quarks and leptons, and serves as the theory of everything.