Lie algebras, Fuchsian differential equations and CFT correlation functions [unknown]

Jürgen Fuchs, Ingo Runkel, Christoph Schweigert
2004 Contemporary Mathematics   unpublished
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
more » ... tter on world sheets of arbitrary topology. 2000 Mathematics Subject Classification. 81R10,81T40,33C80,18D10.
doi:10.1090/conm/343/06186 fatcat:za6pz552hvhlpdgitzsembhony