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

### 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.Comment: 18 page

Topics: High Energy Physics - Theory
Year: 2011
DOI identifier: 10.1142/S0217751X11054668
OAI identifier: oai:arXiv.org:1102.4950