Twisted WessZuminoWitten Models on Elliptic Curves
Abstract
Investigated is a variant of the WessZuminoWitten 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 nontrivial bundle with flat connection and related to the classical elliptic rmatrix. (The usual (nontwisted) 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 KnizhnikZamolodchikov equations associated to the classical elliptic rmatrix appear as flat connections on the sheaves of conformal blocks in the twisted WZW model.
 Publication:

Communications in Mathematical Physics
 Pub Date:
 1997
 DOI:
 10.1007/s002200050233
 arXiv:
 arXiv:qalg/9612033
 Bibcode:
 1997CMaPh.190....1K
 Keywords:

 Mathematics  Quantum Algebra;
 High Energy Physics  Theory
 EPrint:
 55 pages, LaTeX2e with AMS LaTeX package. (Version 1.4.2t: minor corrections of typographical errors, minor changes of bibliography format, support the old version of amslatex package (not LaTeX2e version).)