Abstract
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.
Users
Please
log in to take part in the discussion (add own reviews or comments).