Representation Theory and Quantum Field Theory

表示论和量子场论

• 批准号: 9970499
• 负责人: Feodor Malikov
• 金额: $ 6万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-08-15 至 2002-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9970499&HistoricalAwards=false
• 关键词: Representation; Theory; Quantum; Field

9970499The present proposal is focused on the study of sheaves of vertex algebras over smooth manifolds introduced in a recent work by Schechtman, Vaintrob and the author. The ultimate goal of such a study is the classification of the corresponding cohomology vertex algebras and their modules. This should find interesting applications in quantum cohomology and mirror symmetry.The theory of vertex algebras is a mathematical tool intended for the explanation of conformal field theory. The above-mentioned sheaves of vertex algebras are supposed to explain some recent developments in topological field theory. This line of research has already produced certain results valuable for mathematics itself.

9970499本文主要研究光滑流形上顶点代数层的性质，这是Schechhtman，Vaintrob和作者在最近的工作中提出的. 这种研究的最终目的是对相应的上同调顶点代数及其模进行分类。 这应该在量子上同调和镜像对称中找到有趣的应用。顶点代数理论是用于解释共形场论的数学工具。 顶点代数的上述层被认为可以解释拓扑场论中的一些最新发展。 这条研究路线已经产生了某些对数学本身有价值的结果。