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.

18 pages

References in corpus (3)

• Generalised Permutation Branes on a product of cosets $G_{k_1}/H\times G_{k_2}/H$
• Canonical quantization of the WZW model with defects and Chern-Simons theory
• Defects in G/H coset, G/G topological field theory and discrete Fourier-Mukai transform