  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.
