| 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).
|
