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arXiv · 1102.4950

On canonical quantization of the gauged WZW model with permutation branes

Gor Sarkissian
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Abstract

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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Gor Sarkissian. 2011-02-24. On canonical quantization of the gauged WZW model with permutation branes. https://doi.org/10.1142/s0217751x11054668

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