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

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

2005-06-23

arxiv.org/abs/hep-th/0506199v4

Phys.Lett. B627 (2005) 224-232

Physics

High Energy Physics

High Energy Physics - Theory

9 pages; minor corrections at the end of section 4; Section 5 removed

Scientific paper

10.1016/j.physletb.2005.09.006

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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