Chern-Simons theory with finite gauge group |
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Authors: | Daniel S Freed Frank Quinn |
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Institution: | (1) Department of Mathematics, University of Texas at Austin, 78712 Austin, TX, USA;(2) Department of Mathematics, Virginia Polytechnical Institute, 24061 Blacksburg, VA, USA |
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Abstract: | We construct in detail a 2+1 dimensional gauge field theory with finite gauge group. In this case the path integral reduces to a finite sum, so there are no analytic problems with the quantization. The theory was originally introduced by Dijkgraaf and Witten without details. The point of working it out carefully is to focus on the algebraic structure, and particularly the construction of quantum Hilbert spaces on closed surfaces by cutting and pasting. This includes the Verlinde formula . The careful development may serve as a model for dealing with similar issues in more complicated cases.The first author is supported by NSF grant DMS-8805684, an Alfred P. Sloan Research Fellowship, a Presidential Young Investigators award, and by the O'Donnell Foundation. The second author is supported by NSF grant DMS-9207973 |
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