Skip to main content
Location of Repository

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

Abstract

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.Comment: 17 pages, 3 figure

Topics: High Energy Physics - Theory
Year: 2012
DOI identifier: 10.1142/S0217732312500873
OAI identifier: oai:arXiv.org:1103.2820
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
• http://arxiv.org/abs/1103.2820 (external link)
• Suggested articles

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.