Operator Algebras and Algebraic Conformal Field Theories

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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.