Investigations on closed strings and homogeneous spaces in matrix models

人们认识到，时空可以在超弦理论中非微扰自由度的D-膜的微观意义上理解。希望从这个角度对IIB矩阵模型的研究有所帮助。我们认为时空结构是由矩阵特征值的分布决定的。我们可以考虑非交换齐性空间作为具体的例子。我们可以用群论的方法在矩阵模型中构造这样的时空。由于它们像德西特时空一样具有正的宇宙学常数，我们相信它们与理解现实时空的结构有关。我们可以估计在IIB矩阵模型中实现特定时空的概率，评估这种背景下的有效作用。我们已经发现，在大N极限下，这样的概率依赖于时空的维数。此外，我们还发现它在四维时空中表现出最小值。我们相信Wilson线算子在理解矩阵模型中的引力方面起着重要的作用。研究了超重力顶点算子的结构及其相关函数。

It is realized that spacetime may be understood microscopically in terms of D-branes which are nonperturbative degrees of freedom in superstring theory. We hope it is useful to investigate IIB matrix model from such a perspective. It is considered that the spacetime structure is determined from the distributions of the matrix eigenvalues. We may consider noncommutative homogeneous spaces as concrete examples. We can construct such spacetime in matrix models by a group theoretic method. Since they possess the positive cosmological constant just like de Sitter spacetime, we believe they are relevant to understand the structure of realistic spacetime. We can estimate the probability for a particular spacetime to be realized in IIB matrix model y evaluation the effective action for such a background. We have found that such a probability depends on the dimensionality of the spacetime in the large N limit. Furthermore we have found that it exhibits the minimum for the 4 dimensional spacetime. We believe that the Wilson line operators play an important role to understand gravity in matrix models. We have investigated the structure of the spergravity vertex operators and their correlation functions.