Twisted Wess-Zumino-Witten models on elliptic curves

Details Twisted Wess-Zumino-Witten models on elliptic curves Twisted Wess-Zumino-Witten models on elliptic curves

1996-12-28

arxiv.org/abs/q-alg/9612033v4

Commun.Math.Phys. 190 (1997) 1-56

Physics

High Energy Physics

High Energy Physics - Theory

55 pages, LaTeX2e with AMS LaTeX package. (Version 1.4.2t: minor corrections of typographical errors, minor changes of bibliog

Scientific paper

10.1007/s002200050233

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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