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Physics Letters B

Duality relations between SU (N)k and SU (k)N WZW models and their braid matrices

Stephen G. Naculich, Howard J. Schnitzer

Published Jul 1, 1990• 45 citations
Publisher
DOI
10.1016/0370-2693(90)90061-a

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We study solutions of the Knizhnik–Zamolodchikov equation for discrete representations of SU (2) k at rational level k +2 = p / q using a regular basis in which the braid matrices are well defined for all spins. We show that at spin J = ( j +1) p −1 for there are always a subset of 2 j +1 solutions closed under the action of the braid matrices. For these fields have integer conformal dimension and all the 2 j +1 solutions are monodromy free. The action of the braid matrices on these can be consistently accounted for by the existence of a multiplet of chiral fields with extra SU (2) quantum numbers ( m = − j ,..., j ). In the quantum group SU q (2), with q = e −i π/( k +2) , there is an analogous structure and the related representations are trivial with respect to the standard generators but transform in a spin j representation of SU (2) under the extended centre.