Study of Unified Theory of Elementary Particles Based on Supergravity

本研究试图在最近理论和实验进展的基础上，通过现象学的一致性，阐明超重力结构作为粒子物理的统一理论。主要的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、它们的分层质量和对非守恒中性电流过程的抑制，可以理解为世代水平对称性的反映，这种对称性在超重力中以特定的方式支配着超势和卡拉尔势的结构。特别是，基于非紧群SU（1,1）的水平对称使我们能够普遍地理解宇称、电荷共轭和时间反转等基本对称的所有违反，作为水平对称的自发破坏。将最小超对称标准模型以向量方式扩展为SU（1,1）的无限维幺正表示，以及夸克和轻子的手性结构，并通过SU（1,1）的自发击穿实现它们的分层汤川相互作用。将该极小模型进一步推广到由SU（1,1）和SU(3)*SU(2)*U(1)组成的非紧化大统一群，给出了低能规范对称、手性无质量谱及其规范量子数之间关系的统一观点。我们还强烈地提出，在类矢量水平对称的自发击穿实现手性世界的背后，存在着由N*2的超引力引起的扩展超对称。由于扩展超对称严重限制了超势和凯勒势的结构，未来沿着这一方向的尝试将使基于超引力的粒子物理统一理论取得巨大进展。

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.