题目:Correlators for non-semisimple conformal field theories
报告人：Prof. Jürgen Fuchs
(Department of Engineering and Physics, Karlstads University, Sweden)
摘要：Given a factorizable finite ribbon category D, by work of Lyubashenko one can associate to any punctured surface M a functorBl_M from a tensor power of D to the category of finite-dimensional vector spaces. The so obtained vector spaces Bl_M(-) carry representations of the mapping class groups Map(M) and are compatible with sewing, in much the same way as the spaces of conformal blocks of a (semisimple) rational conformal field theory.
I will present a natural construction which, given any object F of D, selects a vector in each of the space Bl_M(F,...,F) (i.e. when every puncture on M is labeled by F). If and only if the object F carries a structure of a 'modular' commutative symmetric Frobenius algebra in D, the vectors obtained by this construction are invariant under the mapping class group actions and are mapped to each other upon sewing. Thereby they are natural candidates for the bulk correlators of a conformal field theory with bulk state space given by F.