Twisted Wess-Zumino-Witten models on elliptic curves

Gen Kuroki, Takashi Takebe

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1-56
Number of pages56
JournalCommunications in Mathematical Physics
Issue number1
Publication statusPublished - 1997


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