CANONICAL QUANTIZATION OF THE WZW MODEL WITH DEFECTS AND CHERN-SIMONS THEORY

We perform canonical quantization of the WZW model with defects and permutation branes. We establish symplectomorphism between phase space of WZW model with N defects on cylinder and phase space of Chern-Simons theory on annulus times R with N Wilson lines, and between phase space of WZW model with N defects on strip and Chern-Simons theory on disk times R with N + 2 Wilson lines. We obtained also symplectomorphism between phase space of the N-fold product of the WZW model on strip with boundary conditions specified by permutation branes, and phase space of Chern-Simons theory on sphere times R with N holes and two Wilson lines.