On canonical quantization of the gauged WZW model with permutation branes

Details On canonical quantization of the gauged WZW model with permutation branes On canonical quantization of the gauged WZW model with permutation branes

2011-02-24

arxiv.org/abs/1102.4950v1

Physics

High Energy Physics

High Energy Physics - Theory

18 pages

Scientific paper

In this paper we perform canonical quantization of the product of the gauged WZW models on a strip with boundary conditions specified by permutation branes. We show that the phase space of the $N$-fold product of the gauged WZW model $G/H$ on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of the double Chern-Simons theory on a sphere with $N$ holes times the time-line with $G$ and $H$ gauge fields both coupled to two Wilson lines. For the special case of the topological coset $G/G$ we arrive at the conclusion that the phase space of the $N$-fold product of the topological coset $G/G$ on a strip with boundary conditions given by permutation branes is symplectomorphic to the phase space of Chern-Simons theory on a Riemann surface of the genus $N-1$ times the time-line with four Wilson lines.

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