Chern-Simons theory with finite gauge group

• DOI: 10.1007/bf02096860
• Publication Date: 2005-09-12T17:34:37Z
• Authors: Daniel S. Freed; Frank Quinn
• Keywords: Chern–Simons theory; Gauge group

44 pages + 1 figure (revised version, this revision fixes some mistakes, changes some notation, clarifies some arguments, redraws the figure, and generally improves the previous version.)<br/>These theories, which are surely some of the simplest possible quantum field theories, were introduced in a paper of Dijkgraaf and Witten. The path integral reduces to a finite sum, so it is quite amenable to direct mathematical study. Although the theory exisits in arbitrary dimensions, it is most interesting in $2+1$~dimensions, where it has a ``modular structure.'' This is related to quantum groups, and the precise details may give clues as to what happens in other contexts. This paper is written using AMSTeX 2.1, which can be obtained via ftp from the American Mathematical Society (instructions included). 1 encapsulated postscript file was submitted separately in uuencoded tar-compressed format.<br/>