Mathematical Sciences: Geometry of Yang-Mills Moduli Spaces

数学科学：杨米尔斯模空间的几何

• 批准号: 8905211
• 负责人: David Groisser
• 金额: --
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-05-15 至 1992-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8905211&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Yang; Mills

The principal investigator will create a canonical metric for moduli spaces arising in four-dimensional Yang-Mills theory. He will extend the Donaldson program to spaces of 1-instantons over the four sphere and complex projective two-space. Particular attention will be paid to the nature of the boundary of moduli spaces; what is the nature of their strata and how do these strata fit together? The techniques used to approach these questions will be extensions of those used to understand simpler positive-definite manifolds. Four dimensional hypersurfaces have only recently become understandable to geometric topologists. Surprisingly, Donaldson used techniques from the theory of geometric partial differential equations to demonstrate the nonuniqueness of four dimensional space time. The principal investigator will extend this theory to more exotic hypersurfaces in a natural way. Much of this work has considerable impact on the superstring theories of gauge field physics.

首席研究员将创建一个规范度量 在四维杨-米尔斯理论中出现的模空间。 他将把唐纳森计划扩展到1-瞬子空间 复射影二维空间上。 将特别注意边界的性质 模空间;什么是他们的地层的性质，如何做 这些地层合在一起 用于接近的技术 这些问题将是那些用来理解 简单正定流形 四维超曲面直到最近才成为 几何拓扑学家都能理解 出人意料的是，唐纳森 运用几何偏微分理论中的技巧 证明四维非唯一性的方程 空间时间 首席研究员会把这个理论 更奇特的超曲面。 这项工作大部分 对规范的超弦理论产生了重大影响 场物理学。