On holomorphic factorization of WZW and coset models

It is shown how coupling to gauge fields can be used to explain the basic facts concerning holomorphic factorization of the WZW model of two dimensional conformal field theory, which previously have been understood primarily by using conformal field theory Ward identities. We also consider in a similar vein the holomorphic factorization ofG/H coset models. We discuss theG/G model as a topological field theory and comment on a conjecture by Spiegelglas.Research supported in part by NSF Grant PHY86-20266