Operator Algebras and Algebraic Conformal Field Theories

算子代数和代数共形场论

• 批准号: 0457651
• 负责人: Feng Xu
• 金额: $ 10.8万
• 依托单位: University of California-Riverside
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-05-15 至 2008-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0457651&HistoricalAwards=false
• 关键词: Operator; Algebras; Algebraic; Conformal; Field

The PI will study interactions between operator algebras and conformal field theories which have proved to be very fruitful lately. The main emphasis of this research is placed on the study of certain representation theory questions such as Kac-Wakimoto conjecture, orbifolds and boundary states in conformal field theories using operator algebraic techniques. The applications of these operator algebraic techniques will lead to proofs of representation theory questions and shed lights on exotic subfactors such as those coming from conformal inclusions. The theory of operator algebras was introduced by John von Neumann in order to provide a proper mathematical framework for Quantum Mechanics. Conformal field theory was a theory describing critical phenomena in condensed matter physics, and it also plays an important role in string theory. The remarkable interactions between operator algebras and conformal field theory has led to many interesting mathematical issues. The aim of this research is to find solutions to some of the important mathematical issues that surface in this context which have a wide range of applications.

PI将研究运算符代数和共形场理论之间的相互作用，这些理论最近被证明是非常富有成果的。这项研究的主要重点放在对某些表示理论问题的研究上，例如使用操作员代数技术中的共形领域理论中的Kac-Wakimoto猜想，Orbifolds和边界状态。 这些操作员代数技术的应用将导致代表理论问题的证明，并在外来子因子（例如来自保形夹杂物的）上发出灯光。约翰·冯·诺伊曼（John von Neumann）引入了操作者代数理论，以便为量子力学提供适当的数学框架。共形场理论是一种描述凝结物理学中关键现象的理论，它在弦理论中也起着重要作用。操作方代数与保形场理论之间的显着互动导致了许多有趣的数学问题。 这项研究的目的是为在这种情况下浮出水面的一些重要数学问题找到解决方案。