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 to 1/q) duality transformation.

arXiv comment43 pages (minor typo corrected and minor rewording in the introduction)

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• Half-lattice paths and Virasoro characters
• Nonlocal operator basis from the path representation of the M(k+1,k+2) and the M(k+1,2k+3) minimal models
• A quartet of fermionic expressions for $M(k,2k\pm 1)$ Virasoro characters via half-lattice paths
• One-Dimensional Sums and Finitized Characters of $2\times 2$ Fused RSOS Models