Study of Unified Theory of Elementary Particles Based on Supergravity

本研究试图通过唯象分析，在理论和实验进展的基础上，阐明超引力作为粒子物理统一理论的结构。主要成果是，粒子物理学中实现的特征，如核子的稳定性，夸克和轻子的生成结构，它们的分级质量和对非味道守恒中性流过程的抑制，可以理解为水平对称性的反映，在超引力中，它以特定的方式支配着超势和Kaelar势的结构。特别是，基于非紧群SU（1，1）的水平对称性使我们能够普遍地理解所有宇称、电荷共轭和时间反转等基本对称性的破坏，都是水平对称性的自发破坏。利用SU（1，1）的无限维幺正表示和夸克、轻子的手征结构，对最小超对称标准模型进行了类矢量扩展，并通过SU（1，1）的自发破缺实现了它们的分级Yukawa相互作用.把这个极小模型进一步推广到非紧大统一群，把SU（1，1）和SU（3）*SU（2）*U（1）结合起来，给出了低能规范对称性、手征无质量谱和它们的规范量子数之间关系的统一观点.我们还强烈地认为，在类矢量水平对称性的自发破缺实现手征世界的背后，存在着由N*2的超引力引起的扩展超对称性。由于扩展超对称性严格限制了超势和Kaeler势的结构，今后沿着这一方向的努力将使基于超引力的粒子物理统一理论取得重大进展。

This research attempted to clarify the structure of supergravity as a unified theory of particle physics, based on the recent theoretical and experimental progress, through phenomenological consistencies. The main attainment is that the characteristic features realized in particle physics, such as a stability of nucleons, generation structure of quarks and leptons, their hierarchical masses and the suppression of flavor-nonconserving neutral current processes, can be understood as the reflection of the horizontal symmetry of generations, which governs, in supergravity, the structure of superpotential and Kaelar potential in a specific way. Especially, the horizontal symmetry based on noncompact group SU(1,1) allows us to understand universally all of the violations of the fundamental symmetries of parity, charge conjugation and time reversal, as a spontaneous breakdown of the horizontal symmetry. The minimal supersymmetric standard model is extended in a vectorlike manner with the infinite-dimensional unitary representations of SU(1,1), and chiral structure of quarks and leptons, and their hierarchical Yukawa interactions are realized through the spontaneous breakdown of SU(1,1). The further extension of this minimal model to the noncompact grand unified group, which combines SU(1,1) with SU(3)*SU(2)*U(1), gives unified view on the relation among low energy gauge symmetry, chiral massless spectra and their gauge quantum numbers. It is also strongly suggested that behind the vectorlike horizontal symmetry, whose spontaneous breakdown realizes the chiral world, exists the extended supersymmetry due to supergravity with N*2. Since the extended supersymmetry severely restricts the structure of superpotential and Kaeler potential, future attempts along this direction will give great progress in the unified theory of particle physics based on supergravity.