Research of Superstring

如《研究成果报告》所示，该项目从1990年到1992年的3年间的研究成果涉及多个领域。因此，我们在这里仅限于提及其中的主要部分1。关于弦场理论，Hata提出了一种确定同时满足么正不变性和BRS不变性的量子作用量的方法。他还首次证明了几何前弦场论确实具有一般坐标不变性。库戈等人。阐明了作为弦的一种特殊性质的目标空间对偶性实际上包含在弦场理论的规范不变性中。在弦的非微扰方法方面出现了很大的进步，特别是在1维或更少维的弦的矩阵模型方面。Yoneya和他的合作者成功地建立了基于最小作用力原理的二维量子引力。杉本等人。研究了弦场论中的一个演化方程。关于弦理论的结构，Sakamoto做了一个引人注目的发现，环面上的弦理论和奥比福尔德上的弦理论实际上是等价的。从量子引力方面的研究也在积极进行。杉本和他的合作者构建并研究了一个拓扑爱因斯坦引力理论。Nakanishi和Abe发展了一种在算符形式下求解量子引力的新方法，并应用它给出了二维情况的精确解。至于弦理论在基本粒子统一模型中的应用，Matsuoka和他的合作者在Calabi-姚流形上紧致的一些模型中研究了Yukawa耦合常数和小林-Maskawa矩阵。Otubo等人。详细研究了Z_N和Z_N×Z_N中的Yukawa耦合和对称性破缺威尔逊线。

The research results of this project for 3 years from 1990 to 1992 are over many fields as seen in the Report of Research Results. So here we restrict ourselves to mentioning only to the main ones among them.1. Concerning String Field Theory, Hata proposed a method for determining the quantum action satisfying both unitarity and BRS invariance. He also proved for the first time that the pregeometrical string field theory indeed possesses the general coordinate invariance. Kugo et.al. clarified that the target-space duality as a particular property of string is in fact contained in the gauge invariance of the string field theory.2. There appeared a great progress in the non-perturbative approach to strings, in particular in the matrix model for the string in 1 or less dimensions. Yoneya and his collaborator succeeded in formulating 2-dimensional quantum gravity based on the minimal action principle. Sugamoto et.al. studied an evolution equation in the string field theory. As for the structure of string theory, Sakamoto made a remarkable finding that the string theories on a torus and on an orbifold are in fact equivalent.3. Research from the aspect of quantum gravity is also done actively. Sugamoto and his collaborators constructed and studied a topological Einstein gravity theory. Nakanishi and Abe developed a new method for solving quantum gravity in the operator formalism, and gave an exact solution to the 2-dimensional case by applying it.4. As for applications of string theory to unified models of elementary particles, Matsuoka and his collaborators studied Yukawa coupling constants and Kobayashi-Maskawa matrix in some models compactified on Calabi-Yao manifold. Otubo et.al. studied in detail the Yukawa couplings and the symmetry breaking Wilson-lines in Z_N and Z_N X Z_N orbifolds.