Mathematical Sciences: Geometric Structure of Conformal Field Theories

数学科学：共形场论的几何结构

• 批准号: 9104519
• 负责人: Yi-Zhi Huang
• 金额: --
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9104519&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Structure; Conformal; Mathematical; Sciences; Geometric; Structure; Conformal

This research is concerned with the geometric structure of conformal field theory. The principal investigator will study the following topics: (1) binary trees and the Lie bracket; (2) determinant line bundles and vertex operator algebras; (3) a geometric proof of duality for more than two twisted elements; (4) an abstract form of the geometric definitions of finite dimensional Lie algebras, vertex operator algebras and higher dimensional quantum field theory; (5) exponentiating vertex operator algebras; (6) exponentiations of vertex operator algebras and elliptic cohomology. The research supported concerns an important focus of current mathematical activity, where group representation theory, quantum field theory, and algebraic geometry all come together. This work has important implications for theoretical physics, as well as several areas of mathematics.

这项研究与保形场理论的几何结构有关。 首席研究人员将研究以下主题：（1）二元树和谎言括号； （2）行列线束和顶点操作员代数； （3）二元性的几何证明，用于两个以上的扭曲元素； （4）有限维谎言代数，顶点操作员代数和更高维量子场理论的几何定义的抽象形式； （5）凸起顶点操作员代数； （6）顶点操作员代数和椭圆形的共同体的凸起。 这项研究支持当前数学活动的重要重点，在该活动中，小组表示理论，量子场理论和代数几何都融合在一起。 这项工作对理论物理以及数学的几个领域具有重要意义。