Twisted Wess-Zumino-Witten Models on Elliptic Curves |
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Authors: | Gen Kuroki Takashi Takebe |
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Institution: | Mathematical Institute, Tohoku University, Sendai 980, Japan, JP Department of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153, Japan.?E-mail: takebe@ms.u-tokyo.ac.jp, JP
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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.
Received: 21 January 1997 / Accepted: 1 April 1997 |
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