Mathematical Sciences: Generalized Theta Functions, Hypergeometric and Conformal Field Theory

数学科学：广义 Theta 函数、超几何和共形场论

• 批准号: 9504884
• 负责人: Roberto Silvotti
• 金额: $ 5.1万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1998-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9504884&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Generalized; Theta; Functions

9504884 Silvotti The proposed research lies in the interface of algebraic geometry and quantum field theory. The investigator proposes to give a complete and direct topological description of the models of conformal field theory corresponding to generalized theta functions in terms of cohomology spaces. The cohomology to be used is the cohomology of multivalued holomorphic differential forms on the affine complement of hypersurfaces in complex algebraic varieties. The proposed research brings together very classical problems in function theory with the latest development in mathematical physics (quantum field theory). The underlying physical theory was originally introduced to describe the critical behavior of a class of statistical systems on planar lattices.

9504884 Silvotti 拟议的研究在于代数几何和量子场论的接口。研究者建议对与上同调空间中的广义theta函数相对应的共形场论模型给出完整而直接的拓扑描述。要使用的上同调是复代数簇中超曲面的仿射补上的多值全纯微分形式的上同调。 拟议的研究将函数论中的非常经典的问题与数学物理（量子场论）的最新发展结合在一起。底层物理理论最初是为了描述平面晶格上一类统计系统的临界行为而引入的。