Renormalization Group in Gauge Theories

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The research results of our project for two academic years in 1996-1997 are as follows :1.Nonlinear Realization in Supersymmetric Theory : A general method for constructing nonlinear sigma models in supersymmetric theory was reviewed. We noted the fact that Grassmannian nonlinear U(N_f)/U(N_c)*U(N_f-N_c) model can be linearlized into two forms : one form has U(N_c)gauge symmetry and (N_f) global symmetry with matter field belonging to the fundamental representation (N_c, N_f), and the other has U(N_f-N_c) gauge symmetry and U(N_f) global symmetry with matter field belonging to the fundamental representation (N_f-N_c, N_f). We investigated the implication of this exact duality for proving the conjectured duality in N=1 supersymmetric gauge theories.2.Neutrino Mass Texture realizing Large Mixing : Recent SuperKamiokande report suggests a very large mixing between the second and third generation neutrinos nu_<mu> and nu_<gamma>, while the MSW solution for explaining the solar neutrino deficit suggests small nu_e-nu_<mu> mixing. We studied whether these data can be naturally understood consistently with the parallelism between quarks and leptons suggested by GUT theories like SO(10). As a result, we found a natural Majorana mass texture for the right-handed neutrinos which is consistent with all the data and also has several theoretically favorable feutures.3.Unoriented Open-Closed String Field Theory : We constructed a string field theory for the mixed system of open and closed strings, for which even the light-cone gauge formulation has not been given before. We presented the full action for this system and proved its BRS invariance at the tree level. We also analyzed the anomally at the one-loop level recently, and have clarified that the gauge invariance cannot hold unless the system is of unoriented strings and the gauge group is SO(2^<13>=8192).