New path description for the M(k+1,2k+3) models and the dual Z_k graded parafermions

TL;DR

This paper introduces a new path description for non-unitary M(k+1,2k+3) models, providing fermionic character formulas and revealing their relation to Z_k graded parafermions through a duality transformation.

Contribution

It proposes a novel path representation for these models, differing from previous solutions, and establishes a duality with Z_k graded parafermions.

Findings

New fermionic character formulas for M(k+1,2k+3) models

Path description similar to unitary minimal models

Relation to Z_k graded parafermions via duality

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.