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arXiv · 0907.3395

Canonical quantization of the WZW model with defects and Chern-Simons theory

Gor Sarkissian
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Abstract

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 disc times $R$ with $N+2$ Wilson lines. We obtained also symplectomorphism between phase space of the $N$-fold product of the WZW model with boundary conditions specified by permutation branes, and phase space of Chern-Simons theory on sphere with $N$ holes and two Wilson lines.

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Gor Sarkissian. 2009-07-20. Canonical quantization of the WZW model with defects and Chern-Simons theory. https://doi.org/10.1142/s0217751x10048305

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