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Abelian Chern-Simons theory with toral gauge group, modular tensor categories, and group categories by Stirling, Spencer D. is a scholarly article available to read on EtoBox.

What is Abelian Chern-Simons theory with toral gauge group, modular tensor categories, and group categories about?

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.

Author

Stirling, Spencer D.

Published

2008

Language

EN