Abstract:
Investigated is a variant of the Wess-Zumino-Witten model called a twisted WZW model, which is associated to a certain Lie group bundle on a family of elliptic curves. The Lie group bundle is a non-trivial bundle with flat connection and related to the classical elliptic r-matrix. (The usual (non-twisted) WZW model is associated to a trivial group bundle with trivial connection on a family of compact Riemann surfaces and a family of its principal bundles.) The twisted WZW model on a fixed elliptic curve at the critical level describes the XYZ Gaudin model. The elliptic Knizhnik-Zamolodchikov equations associated to the classical elliptic r-matrix appear as flat connections on the sheaves of conformal blocks in the twisted WZW model.
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Received: 21 January 1997 / Accepted: 1 April 1997
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Kuroki, G., Takebe, T. Twisted Wess-Zumino-Witten Models on Elliptic Curves . Comm Math Phys 190, 1–56 (1997). https://doi.org/10.1007/s002200050233
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DOI: https://doi.org/10.1007/s002200050233