Universality of Superstring Matrix Model

我与Ishibashi， Kawai和Tsuchiya一起提出了IIB矩阵模型作为超弦理论的非微扰公式。该模型可以通过环方程与光锥弦场理论联系起来。这个模型包含十个厄米矩阵，它们可以被解释为速度-时间坐标。为了推导出真实的四维时空，四个矩阵的特征值分布的尺度与其他六个矩阵相比必须变得无穷大。本文指出，IIB矩阵模型包含了一种自然机制。此外，它必须包含相互作用统一理论的规范理论。通过在非对易时空周围展开，我们可以推导出非对易规范理论。我们进一步构造了规范不变可观测值（威尔逊线）。由于威尔逊线将规范场耦合到闭弦模式，因此在矩阵模型与引力的关系中起着重要的作用。我们研究了它们的相关函数的弦行为。

I have proposed IIB matrix model as a nonperturbative formulation of superstring theory with Ishibashi, Kawai and Tsuchiya. This model may be related to light-cone string field theory through loop equations. This model contains ten Hermitian matrices which may be interpreted as pace-time coordinates. In order to derive realistic four dimensional space-time, the scale of eigen value distributions of four matrices must become infinite in comparison to the remaining six matrices. It has been pointed out that IIB matrix model contains a natural mechanism for it. Furthermore it must contain gauge theories for a unified theory of interactions. By expanding it around a noncommutative space-time, we can derive noncommutative gauge theory. We have further constructed gauge invariant observables (Wilson lines). Since Wilson lines couple gauge fields to closed string modes, they play an important role in relating matrix models to gravitation. We have studied stringy behavior of their correlation functions.