Universality of Superstring Matrix Model

我与Ishibashi、Kawai和Tuchiya一起提出了IIB矩阵模型，作为超弦理论的非微扰形式。该模型可通过回路方程与光锥弦场理论联系起来。该模型包含十个厄米特矩阵，它们可以被解释为速度-时间坐标。为了得到真实的四维时空，与其余六个矩阵相比，四个矩阵的本征值分布的尺度必须是无限的。已经指出，IIB矩阵模型包含了一个自然的机制。此外，它还必须包含规范理论，以形成统一的相互作用理论。通过在非对易时空中展开它，我们可以得到非对易规范理论。我们进一步构造了规范不变的可观测量(威尔逊线)。由于威尔逊线将规范场与闭合弦模相耦合，因此在将矩阵模型与引力联系起来时，威尔逊线起着重要作用。我们研究了它们的关联函数的弦行为。

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.