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The Z_k^(su(2),3/2) Parafermions

P. Jacob·P. Mathieu
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Abstract

We introduce a novel parafermionic theory for which the conformal dimension of the basic parafermion is 3(1-1/k)/2, with k even. The structure constants and the central charges are obtained from mode-type associativity calculations. The spectrum of the completely reducible representations is also determined. The primary fields turns out to be labeled by two positive integers instead of a single one for the usual parafermionic models. The simplest singular vectors are also displayed. It is argued that these models are equivalent to the non-unitary minimal W_k(k+1,k+3) models. More generally, we expect all W_k(k+1,k+2 beta) models to be identified with generalized parafermionic models whose lowest dimensional parafermion has dimension beta(1-1/k).

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BibTeXRIS

P. Jacob, P. Mathieu. 2005-09-19. The Z_k^(su(2),3/2) Parafermions. https://doi.org/10.1016/j.physletb.2005.09.006

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