Research of Grand Unified Theory based on Superstring Model

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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.