Geometry of spinors in 14 dimensions

14 维旋量的几何

• 批准号: 2438136
• 金额: --
• 依托单位: University of Nottingham
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2438136
• 关键词: Geometry; spinors; 14; dimensions

Spinors in 14 dimensions are exceptional because they are intimately linked to the octonions. There are two signatures when Majorana-Weyl spinors in this dimension exist, namely (7,7) and (11,3). The former case has been studied with motivations coming from generalised geometry, and Spin(7,7) orbits in the space of Majorana-Weyl spinors to an extent understood. The latter case is to a very large degree an open question. This project will aim to complete the questions left unanswered in the (7,7) case and provide a classification of the orbits in the (11,3) case. The motivations for this project are in the fact that in both cases the full content of one generation of the SM fermions can be encoded by such a Majorana-Weyl spinor. The main question of interest is whether the rich geometric structures that such spinors define has anything to do with the structures one finds in the SM of particle physics.

14维中的旋量是例外，因为它们与八元数密切相关。在这个维中存在Majorana-Weyl旋量时有两个签名，即（7，7）和（11，3）。前一种情况已被研究的动机来自广义几何，和自旋（7，7）轨道在空间中的马约拉纳-外尔旋量的理解程度。后一种情况在很大程度上是一个悬而未决的问题。该项目旨在完成（7，7）情况下未回答的问题，并提供（11，3）情况下的轨道分类。这个项目的动机是，在这两种情况下，一代SM费米子的全部内容都可以由这样的马约拉纳-外尔旋量编码。感兴趣的主要问题是，此类旋量定义的丰富几何结构是否与粒子物理学SM中发现的结构有关。