Matrix Model for String Unification

我们在1998 - 1999学年的主要研究重点是由首席研究员和研究生Tokura提出的USp矩阵模型的发展以及随之而来的时空图像。在过去的六个月里，我们也致力于研究B场存在下p-p'系统的性质，在文献1、2给出的USp矩阵模型的基本结构之后，我们首先考察了费米子在理论中的作用。非交换单极子是伴随着每一个时空点的涨落而出现的。这些磁单极子是由非交换Berry相位通过对Famion积分得到的，被认为是弦孤子。在文献8中，这一结果将我们引向了与Yang单极子相关的四维时空图象，而通过Schwinger Dyson方程建立该模型是一个独立的、潜在的重要方向。这是矩阵模型被认为是包含多体效应的非微扰弦理论的必然结果。我们已经进行了这个配方的USP矩阵模型和进一步的分析，这个系统的方程是必要的。

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.