Mathematical Sciences: Geometric Structure of Conformal Field Theory

数学科学：共形场论的几何结构

• 批准号: 9301020
• 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: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9301020&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometric; Structure; Conformal

This research is concerned with conformal field theory and specifically with the study of vertex operator algebras. The principal investigator will study the following topics: vertex category theory; reconstruction of vertex operator algebras from vertex tensor categories; modular vertex tensor categories; vertex groups and vertex operator algebras; vertex groups and integrable systems; geometric construction of the Monster; cohomology theory for vertex operator algebras; and vertex manifolds. Conformal field theory is an important physical theory describing both two-dimensional critical phenomena in condensed matter physics and classical motions of strings in string theory. Besides its importance in physics, the beautiful and rich mathematical structure of conformal field theory also has interested many mathematicians. New relations between different branches of mathematics, such as representations of infinite-dimensional Lie algebras and groups, Riemann surfaces and algebraic curves, the Monster sporadic group, modular functions and modular forms, elliptic genera, and knot theory, is revealed in the study of conformal field theory. It is believed that the study of the mathematics involved in conformal field theory will lead to new mathematical structures which will be important both in mathematics and theoretical physics.

这项研究涉及共同场理论，特别是对顶点操作员代数的研究。 主要研究者将研究以下主题：顶点类别理论；来自顶点张量类别的顶点操作员代数的重建；模块化顶点张量类别； 顶点组和顶点操作员代数；顶点组和集成系统；怪物的几何结构； 顶点操作员代数的同时理论；和顶点歧管。 共形场理论是一种重要的物理理论，描述了凝结物理学中的二维临界现象和弦理论中字符串的经典动作。 除了在物理学上的重要性外，共同田地理论的美丽而丰富的数学结构还对许多数学家感兴趣。 数学不同分支之间的新关系，例如无限维谎言代数和群体，riemann表面和代数曲线，怪物零星群，模块化函数和模块化形式，椭圆形属和结理论的新关系。 人们认为，对共形领域理论涉及的数学的研究将导致新的数学结构，这在数学和理论物理学中都将很重要。