https://doi.org/10.1140/epjb/e2002-00282-x
On the rational solutions of the 
Knizhnik-Zamolodchikov equation
Theoretical Physics Division,
Institute for Nuclear Research and Nuclear Energy,
Tsarigradsko Chaussee 72, 1784 Sofia, Bulgaria
Corresponding authors: a lhadji@inrne.bas.bg - b tpopov@inrne.bas.bg
Received:
4
October
2001
Published online:
2
October
2002
We present some new results on the rational solutions
of the Knizhnik-Zamolodchikov (KZ) equation for the four-point
conformal blocks of isospin 
primary fields in the 
Wess-Zumino-Novikov-Witten (WZNW) model. The rational solutions
corresponding to integrable representations of the affine algebra
have been classified in [1,2];
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 introduced in [3] and
display a new series of rational solutions for isospins 
corresponding to non-integrable representations of 
PACS: 11.25.Hf – Conformal field theory, algebraic structures / 02.20.Uw – Quantum groups / 11.30.Ly – Other internal and higher symmetries
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002
