Matrix Model for String Unification

1998、1999学年，我们的主要研究重点放在首席研究员和研究生Tokura提出的USP矩阵模型的发展以及伴随而来的时空图景上。在过去的六个月里，我们还努力研究了存在B场的p-p‘系统的性质。在文1，2中给出了USP矩阵模型的基本构造之后，我们首先研究了费米子在理论中所起的作用。非阿贝尔单极子作为伴随着每个时空点的涨落出现。这些单极子是由非阿贝尔Berry相通过对孤子进行积分而得到的，被认为是弦孤子。在文8中，这将我们带到与杨单极子有关的四维时空图。通过Schwinger Dyson方程建立该模型是一个单独且潜在重要的方向。这将不可避免地使矩阵模型被认为是包含多体效应的非微扰弦理论。我们对USP矩阵模型进行了这种表述，并要求对这一方程组进行进一步的分析。

The major emphasis of our research during 1998, 1999 academic year was put on the developments of the USp matric model proposed by the head investigator and the graduate student Tokura as well as on the attendant spacetime picture. In the last six months, we have also put our efforts in examining the properties of p-p' system in the presence of B field.Following the basic construction of the USp matrix model given in paper 1, 2, we first examined the role played by the fermions in the theory. The nonabelian monopoles emerge as fluctuations attendant with each spacetime point. These monopoles are obtained from the nonabelian Berry phase by carrying out the integrations over the famions and are regarded as string soliton. In paper 8, this has led us to the four dimensional spacetime picture associated with Yang monoploles.The fomulation of the model via the Schwinger Dyson equation is a separate and potentially important direction to go. This is inevitable for matrix models to be recognized as nonoperturbative string theory containing manybody effects. We have carried out this formulation for the USp matrix model and further analysis of this system of equations is called for.