Research of Grand Unified Theory based on Superstring Model

这个项目的目的是阐明大统一理论和超弦理论中的各种可能性，寻找两个理论之间的接触点，从而获得关于大统一理论中尚未解决的基本问题的信息。为了研究大统一理论，进一步考察了之前提出的两种可能性(规范相互作用产生的一代汤川耦合和将希格斯标量实现为伪Goldstone粒子)，并对模型的真实性特别感兴趣。结果表明，对于前者，核子的稳定性给出了严格的约束条件，而对于后者，情形对于辐射修正是稳定的。该项目的主要工作集中在阐明弦理论的各种可能的结构，特别是关于非阿贝尔奥比诺德的理论。通过构造描述非阿贝尔轨道上弦的量子理论，详细研究了闭弦单圈真空振幅的模变换性质，以检验该理论的模不变性，该理论对弦理论的最终自洽起着重要作用。在这项研究中，需要特别注意弦的零模的处理。它们受到理论整体结构的强烈影响，特别是受背景场的影响，并且对于非阿贝尔结构，它们的性质是相当复杂的。路径积分方法被证明对这一调查非常有效。结果表明，当背景场一致地放置在奥氏流形上时，该理论给出了模不变式真空振幅。对于未来的问题，希望澄清弦理论在非阿贝尔奥氏流形上的唯象意义，这也是本项目的最终目的。

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.