Conserved charges in the chiral 3-state Potts model

TL;DR

This paper identifies new conserved currents in the chiral 3-state Potts model, suggesting an infinite set of such currents which deepen understanding of its integrable structure.

Contribution

It generalizes Zamolodchikov's counting argument and explicitly constructs inhomogeneous conserved currents, proposing an infinite hierarchy in the chiral 3-state Potts model.

Findings

Discovery of new inhomogeneous conserved currents

Conjecture of an infinite set of conserved currents

Implications for integrability of the chiral Potts model

Abstract

We consider the perturbations of the 3-state Potts conformal field theory introduced by Cardy as a description of the chiral 3-state Potts model. By generalising Zamolodchikov's counting argument and by explicit calculation we find new inhomogeneous conserved currents for this theory. We conjecture the existence of an infinite set of conserved currents of this form and discuss their relevance to the description of the chiral Potts models.