Virasoro Characters from Bethe Equations for the Critical Ferromagnetic Three-State Potts Model

Abstract

We obtain new fermionic sum representations for the Virasoro characters of the conformal field theory describing the ferromagnetic three-state Potts spin chain. These arise from the fermionic quasi-particle excitations derived from the Bethe equations for the eigenvalues of the hamiltonian. In the conformal scaling limit, the Bethe equations provide a description of the spectrum in terms of one genuine quasi-particle, and two "ghost" excitations with a limited microscopic momentum range. This description is reflected in the structure of the character formulas, and suggests a connection with the integrable perturbation of dimensions (2/3,2/3)⁺ which breaks the S₃ symmetry of the conformal field theory down to Z₂.

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