%0 Generic %1 stirling2008abelian %A Stirling, Spencer D. %D 2008 %K thesis %T Abelian Chern-Simons theory with toral gauge group, modular tensor categories, and group categories %U http://arxiv.org/abs/0807.2857 %X Classical and quantum Chern-Simons with gauge group $U(1)^N$ were classified by Belov and Moore in belov_moore. 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 frolich_kerler,quinn,joyal_street,eno,dgno. 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.

@misc{stirling2008abelian, abstract = {Classical and quantum Chern-Simons with gauge group $\text{U}(1)^N$ were classified by Belov and Moore in \cite{belov_moore}. 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 \cite{frolich_kerler},\cite{quinn},\cite{joyal_street},\cite{eno},\cite{dgno}. 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.}, added-at = {2016-10-25T12:40:43.000+0200}, author = {Stirling, Spencer D.}, biburl = {https://www.bibsonomy.org/bibtex/2962893a1099c0db2ea96a26a15fc50cd/redlex91}, description = {Abelian Chern-Simons theory with toral gauge group, modular tensor categories, and group categories}, interhash = {2220b3a7d39d38f1c7e3f0e468969474}, intrahash = {962893a1099c0db2ea96a26a15fc50cd}, keywords = {thesis}, note = {cite arxiv:0807.2857Comment: 152 pages}, timestamp = {2016-10-25T12:40:43.000+0200}, title = {Abelian Chern-Simons theory with toral gauge group, modular tensor categories, and group categories}, url = {http://arxiv.org/abs/0807.2857}, year = 2008 }