MS Seminar (Mathematics - String Theory)

Speaker: Akihiro Tsuchiya (IPMU)
Title: Tensor structure on module category of W_p Vertex Operator Algebras
Date: Tue, Jan 31, 2012, 15:30 - 17:00
Place: Seminar Room A
Abstract: The theory of Vertex Operator Algebra (VOA) is an algebraic counter parts of Conformal Field Theories (CFT). In order to develop CFT on Rieman surfaces, corresponding VOA must satisfies some strong conditions. The known examples of VOA with these conditions are VOA associated to integrable representations of affine Lie algebras and VOA associated to minimal series representations of Virasoro Lie algebras. In these cases, the representation category is semi-simple, and the number of simple object is finite.
Quite recently it has been interested in VOA with these finiteness conditions, and representation categoric is not semi-simple. In this case associated CFT is called Logarithmic CFT. But the known examples of these VOA are very few. In this lecture I'll talk about so called W_p triplet algebras.
Main results are:
(1) Structures of abelian category W_p-mod,
(2) Structures of braided monodal structures on W_p-mod defined by associated CFT.
Details are in "math QA 09024607" and "math QA 12010419."