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

TL;DR

This paper derives new fermionic sum representations for Virasoro characters in the critical ferromagnetic three-state Potts model, linking Bethe equations to conformal field theory spectra and symmetry breaking.

Contribution

It introduces novel fermionic sum formulas for Virasoro characters based on Bethe equations, revealing a connection to integrable perturbations and symmetry reduction.

Findings

New fermionic sum representations for Virasoro characters.

Spectrum description involving one genuine and two ghost quasi-particles.

Connection to integrable perturbations breaking $S_3$ symmetry.

Abstract

We obtain new fermionic sum representations for the Virasoro characters of the confromal 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 $S_3$ symmetry of the conformal field theory down to $Z_2$.