Mapping class group and U(1) Chern-Simons theory on closed orientable surfaces

Details Mapping class group and U(1) Chern-Simons theory on closed orientable surfaces Mapping class group and U(1) Chern-Simons theory on closed orientable surfaces

2011-03-15

arxiv.org/abs/1103.2820v1

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

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 of form projective representation of the holonomy group and the large gauge transformation group, the mapping class group can be consistently represented, provided the Chern-Simons parameter $k$ satisfies an interesting quantization condition. Also, we find a $k\leftrightarrow1/k$ duality of the representations.

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