Research of Superstring

该项目1990 - 1992年3年的研究成果涵盖多个领域，详见《研究成果报告》。因此，我们在这里只谈其中主要的几种。在弦场论中，Hata提出了一种确定同时满足统一性和BRS不变性的量子作用的方法。他还首次证明了几何前弦场论确实具有一般的坐标不变性。Kugo出版社。澄清了目标空间对偶性作为弦的一种特殊性质实际上包含在弦场理论的规范不变性中。弦的非摄动方法有了很大的进展，特别是一维或更小维弦的矩阵模型。Yoneya和他的合作者成功地建立了基于最小作用原理的二维量子引力。Sugamoto出版社。研究了弦场理论中的演化方程。关于弦论的结构，坂本作了一个显著的发现，即环面上的弦论和轨道上的弦论实际上是等价的。量子引力方面的研究也在积极进行。Sugamoto和他的合作者构建并研究了拓扑爱因斯坦引力理论。Nakanishi和Abe开发了一种在算子形式下求解量子引力的新方法，并应用它给出了二维情况下的精确解。关于弦理论在基本粒子统一模型中的应用，Matsuoka等研究了Calabi-Yao流形上紧化模型中的Yukawa耦合常数和Kobayashi-Maskawa矩阵。Otubo出版社。详细研究了Z_N和Z_N X Z_N轨道中的汤川耦合和对称破缺威尔逊线。

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.