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arXiv 0907.3395hep-th
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含缺陷的WZW模型的正则量子化和Chern-Simons理论

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

Gor Sarkissian

摘要:

我们进行正则量子化的WZW模型的缺陷和置换膜。建立了含$N$缺陷的WZW模型的相空间与含$N$ Wilson线的环乘$R$的Chern-Simons理论的相空间以及含$N$缺陷的WZW模型的相空间与含$N+2$ Wilson线的盘乘$R$的Chern-Simons理论的相空间的辛同胚关系。我们还得到了WZW模型的$N$ -重积在置换膜边界条件下的相空间与球面上具有$N$洞和两条Wilson线的Chern-Simons理论的相空间之间的辛同胚.

英文摘要:

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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