Operator Algebras and Algebraic Conformal Field Theories

PI将研究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有成果的。本研究的重点是利用算符代数技术研究共形场论中的某些表象理论问题，如Kac-Wakimoto猜想、ORBORIBORD和边界态等。这些算子代数技巧的应用将导致对表示理论问题的证明，并有助于揭示奇异的子因素，例如来自保形包含的那些。算符代数理论是由约翰·冯·诺伊曼提出的，目的是为量子力学提供一个适当的数学框架。共形场理论是描述凝聚态物理中临界现象的理论，它在弦理论中也扮演着重要的角色。算符代数与保形场理论之间的显著相互作用导致了许多有趣的数学问题。这项研究的目的是为在这一背景下出现的一些重要的数学问题找到解决方案，这些问题具有广泛的应用。

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.