Abelian Chern-Simons theory with toral gauge group, modular tensor categories, and group categories

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dc.contributor.advisorFreed, Daniel S.en
dc.creatorStirling, Spenceren
dc.date.accessioned2012-09-06T20:03:02Zen
dc.date.accessioned2017-05-11T22:27:18Z
dc.date.available2012-09-06T20:03:02Zen
dc.date.available2017-05-11T22:27:18Z
dc.date.issued2008-08en
dc.descriptiontexten
dc.description.abstractClassical and quantum Chern-Simons with gauge group U(1)N were classified by Belov and Moore in [BM05]. They studied both ordinary topological quantum field theories as well as spin theories. On the other hand a correspondence is well known between ordinary (2 + 1)-dimensional TQFTs and modular tensor categories. We study group categories and extend them slightly to produce modular tensor categories that correspond to toral Chern-Simons. Group categories have been widely studied in other contexts in the literature [FK93],[Qui99],[JS93],[ENO05],[DGNO07]. The main result is a proof that the associated projective representation of the mapping class group is isomorphic to the one from toral Chern-Simons. We also remark on an algebraic theorem of Nikulin that is used in this paper.en
dc.description.departmentMathematicsen
dc.format.mediumelectronicen
dc.identifier.urihttp://hdl.handle.net/2152/17795en
dc.language.isoengen
dc.rightsCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.en
dc.subject.lcshQuantum field theoryen
dc.subject.lcshAbelian categoriesen
dc.subject.lcshTensor productsen
dc.titleAbelian Chern-Simons theory with toral gauge group, modular tensor categories, and group categoriesen

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