English

Twisted Wess-Zumino-Witten models on elliptic curves

q-alg 2009-10-30 v4 High Energy Physics - Theory Quantum Algebra

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.

Keywords

Cite

@article{arxiv.q-alg/9612033,
  title  = {Twisted Wess-Zumino-Witten models on elliptic curves},
  author = {Gen Kuroki and Takashi Takebe},
  journal= {arXiv preprint arXiv:q-alg/9612033},
  year   = {2009}
}

Comments

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).)