On Chern-Simons and WZW partition functions

Direct analysis of the path integral reduces partition functions in Chern-Simons theory on a three-manifold M with group G to partition functions in a WZW model of maps from a Riemann surface Sigma to G. In particular, Chern-Simons theory on S-3, S-1 X Sigma, B-3 and the solid torus correspond, respectively, to the WZW model of maps from S-2 to G, the G/G model for Sigma, and Witten's gauged WZW path integral Ansatz for Chern-Simons states using maps from S2 and from the torus to G. The reduction hinges on the characterization of A/G(n), the space of connections module those gauge transformations which are the identity at a point n, as itself a principal fiber bundle with affine-linear fiber.