Research of Grand Unified Theory based on Superstring Model

该项目旨在阐明大统一理论和超弦理论中的各种可能性，探讨两种理论之间的联系点，从而获得大统一理论中尚未解决的基本问题的信息。对于大统一理论的研究，之前提出的两种可能性（一代汤川耦合规范相互作用和实现的希格斯标量作为伪戈德斯通粒子）进行了进一步审查的特殊兴趣的现实模型。结果表明，对于前者，核子的稳定性对模型有严格的约束，而对于后者，模型在辐射修正下是稳定的。该项目的主要工作集中在阐明弦理论的各种可能结构，特别是非阿贝尔轨道的理论。通过构造非阿贝尔轨道折叠上一致描述弦的量子理论，详细研究了封闭弦的1-圈真空振幅的模变换性质，以检验该理论的模不变性对弦论最终的自洽性起着重要作用.在本研究中，需要特别注意弦的零模的处理。它们受理论整体结构，特别是背景场的影响很大，对于非交换轨道褶皱，它们的性质非常复杂。路径积分法被证明是非常强大的这项调查。结果表明，当背景场一致地放置在轨道上时，该理论给出了模不变的真空振幅，对于未来的问题，希望阐明弦理论在非阿贝尔轨道上的唯象意义，这是该项目的最终目的.

The project was intended to clarify the variety of possibilities in grand unified theories and superstring theories, to inquire a point of contact between two theories and thereby to get informations on yet-unsolved fundamental problems in grand unified theories.For the investigation of grand unified theories, two possibilities proposed before (a generation of Yukawa couplings from gauge interactions and a realization of Higgs scalars as pseudo-Goldstone particles) were further examined with the special interest on the reality of the model. It was shown that for the former the stability of nucleon gives severe constraint on the model and for the latter the scenario is stable against radiative corrections.The main effort of the project was focused on the elucidation of the variety of possible structures of string theories, especially on the theories on non-abelian orbifolds. Through the construction of the quantum theory consistently describing strings on non-abelian orbifolds, the modular transformation property of the 1-loop vacuum amplitude of the closed string was investigated in detail, in order to examine the modular invariance of the theory which plays an important role in the final self-consistency of the string theory. In this investigation, the special care is required on the treatment of the zero modes of the string. They are strongly affected by the global structure of the theory, especially by the background fields, and their property is quite complicated for the non-abelian orbifolds. The path-integral method turned out to be very powerful for this investigation. It was shown that, when the background fields are consistently placed on the orbifolds, the theory gives the modular invariant vacuum amplitude.For the future problem, it is desired to clarify the phenomenological implication of the string theory on non-abelian orbifolds, which is the final purpose of the project.