On the rational solutions of the su(2)_k Knizhnik-Zamolodchikov equation
arXiv:hep-th/0109219 · doi:10.1140/epjb/e2002-00282-x
Abstract
We present some new results on the rational solutions of the Knizhnik-Zamolodchikov equation for the four-point conformal blocks of isospin I primary fields in the SU(2)_k Wess-Zumino-Novikov-Witten model. The rational solutions corresponding to integrable representations of the affine algebra su(2)_k have been classified by Michel, Stanev and Todorov; provided that the conformal dimension is an integer, they are in one-to-one correspondence with the local extensions of the chiral algebra. Here we give another description of these solutions as specific braid-invariant combinations of the so called regular basis and display a new series of rational solutions for isospins I = k+1 corresponding to non-integrable representations of the affine algebra.
EPJ LaTeX Style, amsfonts, 4 pages. A couple of small corrections inserted. Submitted for publication in the Proceedings of the Conference on Geometry, Integrability and Nonlinearity in Condensed Matter and Soft Condensed Matter Physics, 15-20 July 2001, Bansko (Bulgaria)