New path description for the M ( k + 1 , 2 k + 3 ) models and the dual Z k graded parafermions
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چکیده
New path description for the M(k + 1, 2k + 3) models and the dual Z k graded parafermions ABSTRACT We present a new path description for the states of the non-unitary M(k + 1, 2k + 3) models. This description differs from the one induced by the Forrester-Baxter solution, in terms of configuration sums, of their restricted-solid-on-solid model. The proposed path representation is actually very similar to the one underlying the unitary minimal models M(k + 1, k + 2), with an analogous Fermi-gas interpretation. This interpretation leads to fermionic expressions for the finitized M(k + 1, 2k + 3) characters, whose infinite-length limit represent new fermionic characters for the irreducible modules. The M(k + 1, 2k + 3) models are also shown to be related to the Z k graded parafermions via a (q ↔ q −1) duality transformation.
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