Lie algebras, Fuchsian differential equations and CFT correlation functions

Abstract

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.

15 pages. contribution to the Ramanujan International Symposium on Kac-Moody Lie algebras and Applications (Madras, January 28-31, 2002). For related proceedings contributions see http://tpe.physik.rwth-aachen.de/schweigert/proceedings.html