Subfactors and conformal field theories

PI将研究算子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。本研究的重点是利用算子代数技术研究共形场论中的一些表征理论问题，如Kac-Wakimoto猜想、轨道和边界态。这些算子代数技术的应用将导致表征理论问题的证明，并阐明来自保角包含的奇异子因子。为了给量子力学提供一个合适的数学框架，约翰·冯·诺伊曼引入了算子代数理论。共形场论是描述凝聚态物理中临界现象的理论，在弦理论中也占有重要地位。算子代数与共形场论之间显著的相互作用导致了许多有趣的数学问题。本研究的目的是为在这一背景下出现的一些具有广泛应用的重要数学问题找到解决方案。

The PI will study interactions between operator algebras and conformalfield theories which have proved to be very fruitful lately. The mainemphasis 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 techniqueswill lead to proofs of representation theory questionsand 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 incondensed matter physics, and it also plays an important role in string theory. The remarkable interactions between operator algebrasand conformal field theory has led to many interesting mathematicalissues. The aim of this researchis to find solutions to some of the important mathematical issues that surface in this context which have a wide range of applications.