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The origin of multiplets of chiral fields inSU(2)kat rational level

A Nichols

2004
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Journal of Statistical Mechanics: Theory and Experiment
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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 half integer j there are always a subset of 2j+1 solutions closed under the action of the braid matrices. For integer j these fields have integer conformal dimension and all the 2j+1 solutions are monodromy free. The action of the braid matrices on these
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... 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 πk+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 center.

doi:10.1088/1742-5468/2004/09/p09006
fatcat:o4g7vktfebf2zgke7zrc7yjefm