Analysis of superstrings by matvix models

本研究的目的是从矩阵模型的角度分析弦理论的非微扰方面，并推导出我们世界的基本性质。在前两年的研究中，我们研究了矩阵模型中作为时空延拓的特征值的动力学。在单圈计算中，我们证明了本征值的统计系统受Haussdorf维数为4的支化聚合物系统的支配。虽然分布是分形的，但分形维数与我们世界的维数的一致性表明了我们方法的正确性。在后半部分的研究中，我们证明了矩阵模型与时空的非对易性质，特别是数学家们所研究的非对易几何有着密切的关系。这表明我们的模型可以描述重力。我们还试图证明矩阵模型的背景独立性。这项研究仍在调查中。

The purpose of this research is to analyze the nonperturbative aspects of string theory from the matrix model point of view and derive fundamental properties of our world. In the first two years of the research, we have investigated the dynamics of eigenvalues which are considered as the extent of space-time in matrix models. In one loop calculation, we have shown that the statistical system of eigenvalues is governed by the system of branched polymer whose Haussdorf dimension is four. Although the distribution is fractal, the coincidence of the fractal dimension with the dimension of our world suggests the correctness of our approach. In the latter half of the research, we have shown that the matrix model has close relationship with the noncommutaative nature of space-time, in particular, noncommutative geometry which had been investigated by mathematicians. It is an indication that our model can describe gravity. We have also tried to show the background independence of matrix models. This research is still under investigations.