%0 Journal Article
%T Lie algebras, Fuchsian differential equations and CFT correlation functions
%A Jščrgen Fuchs
%A Ingo Runkel
%A Christoph Schweigert
%J Mathematics
%D 2003
%I arXiv
%X Affine Kac-Moody algebras give rise to interesting systems of differential equations, so-called Knizhnik-Zamolodchikov equations. The monodromy properties of their solutions can be encoded in the structure of a modular tensor category on (a subcategory of) the representation category of the affine Lie algebra. We discuss the relation between these solutions and physical correlation functions in two-dimensional conformal field theory. In particular we report on a proof for the existence of the latter on world sheets of arbitrary topology.
%U http://arxiv.org/abs/hep-th/0301181v1