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Canonical quantization of the boundary Wess-Zumino-Witten model

Krzysztof Gawedzki·Ivan Todorov·Pascal Tran-Ngoc-Bich
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Abstract

We present an analysis of the canonical structure of the WZW theory with untwisted conformal boundary conditions. The phase space of the boundary theory on a strip is shown to coincide with the phase space of the Chern-Simons theory on a solid cylinder (a disc times a line) with two Wilson lines. This reveals a new aspect of the relation between two-dimensional boundary conformal field theories and three-dimensional topological theories. A decomposition of the Chern-Simons phase space on a punctured disc in terms of the one on a punctured sphere and of coadjoint orbits of the loop group easily lends itself to quantization, providing at the same time a quantization of the boundary WZW model.

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Krzysztof Gawedzki, Ivan Todorov, Pascal Tran-Ngoc-Bich. 2001-01-25. Canonical quantization of the boundary Wess-Zumino-Witten model. https://doi.org/10.1007/s00220-004-1107-6

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