Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mapping class group and U(1) Chern-Simons theory on closed orientable
  surfaces   U(1) Chern-Simons theory is quantized canonically on manifolds of the form
$M=\mathbb{R}\times\Sigma$, where $\Sigma$ is a closed orientable surface. In
particular, we investigate the role of mapping class group of $\Sigma$ in the
process of quantization. We show that, by requiring the quantum states to form
representation of the holonomy group and the large gauge transformation group,
both of which are deformed by quantum effect, the mapping class group can be
consistently represented, provided the Chern-Simons parameter $k$ satisfies an
interesting quantization condition. The representations of all the discrete
groups are unique, up to an arbitrary sub-representation of the mapping class
group. Also, we find a $k\leftrightarrow1/k$ duality of the representations.

12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph