Abstract
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 Σ to G. In particular, Chern–Simons theory on S3, S1×Σ, B3 and the solid torus correspond, respectively, to the WZW model of maps from S2 to G, the G/G model for Σ, 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 \(\), the space of connections modulo those gauge transformations which are the identity at a point n, as itself a principal fiber bundle with affine-linear fiber.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.