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

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

2009-07-20

arxiv.org/abs/0907.3395v2

Physics

High Energy Physics

High Energy Physics - Theory

26 pages, minor corrections done

Scientific paper

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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