Supersymmetry and unified theories

超对称理论是最有希望的统一理论候选者。在电弱相变中，重子数被破坏。CP破坏是人们对基本粒子物理现象了解最少的一种现象。它只在中性K介子衰变中被观察到。我们计算了中子电偶极矩作为另一种可能的实验上可达到的CP破坏现象。我们发现最小超对称理论可以给出一个可以测量的值，可以将实验精度提高两个数量级，我们发现矩阵模型满足一个非线性重整化群方程。作为量子引力的另一种可能形式，我们研究了2+ 1维量子引力。我们特别感兴趣的是引力与介子的耦合，这个理论可以在二维空间外光滑地解析地继续下去。我们还研究了非线性σ模型和公式化超引力的情形，研究了二维超对称的Yang-Mills理论。利用离散光锥量子化方法计算了质量谱。我们在规范化理论的过程中成功地保持了超对称性。

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.