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Institute for the Physics and Mathematics of the UniverseWPI

IPMU Mathematics and Physics seminar in Kashiwa

Date: July 31, 2008, 15:30 - 17:00
Place: Seminar Room at IPMU Prefab. B, Kashiwa Campus of the University of Tokyo
Speaker: Akihiro Tsuchiya (IPMU)
Title: Vertex Operator Algebra with C2-finite conditions and Logarithmic Conformal Field Theory
Abstract: Recently Logarithmic Conformal Field Theory is getting some interesting progress. In this talk I'll explain my recent works about mathematical foundation of the theory. In so called rational conformal field theory, the abelian category of the representations of chiral algebra (or V.O.A.) is semi-simple, so all representations are direct sum of simple modules. We construct conformal field theory based on representation theory of V.O.A. with C2-finite conditions. The abelian category of representation of this V.O.A. is Artin and Noither and the number of simple modules is finite, but it is not semi-simple. We define the sheaf of conformal blocks, and show how the factorization properties are works. Then we can define fusion tensor category over the abelian category of representations of this V.O.A. Finally I'll talk some example called W(p).