Supersymmetry and unified theories

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Supersymmetric Theories are the most promissing candidate for unified theories. At the electroweak phase transition, baryon number is violated. With this mechanism, we computed baryon number of the universe in the minimal supersymmetric theory.CP violation is the least understood physical phenomena of elementary particles. It is observed only in neutral Kaon decays. We have computed neutron electric dipole moment as another possible experimentally accessible CP violating phenomena. We found that the minimal supersymmetric thoery can give a value which cna be measured by improving the experimental precision of two orders of magnitude.We have found that matrix model satisfied a nonlinear renormalization group equation. We have found various critical exponents by this method.As another possible formulation of quantum gravity, we studied quantum gravity in 2+epsilon dimensions. We have especially interested in gravity coupled to dilaton.This theory can be smoothly continued analytically beyond 2 dimensions. We have studied also the case with nonlinear sigma models and fomulated supergravity.We have studied supersymmetric Yang-Mills thoeries in 2 dimensions. By means of discretized light-cone quantization, we have evaluated massive spectra. We have succeeded to preserve supersymmetry in regularizing the theory.