Discrete holomorphicity in the chiral Potts model

Author: Ikhlef Yacine   Weston Robert  

Publisher: IOP Publishing

E-ISSN: 1751-8121|48|29|294001-294024

ISSN: 1751-8121

Source: Journal of Physics A: Mathematical and Theoretical, Vol.48, Iss.29, 2015-07, pp. : 294001-294024

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

We construct lattice parafermions for the Z(N) chiral Potts model in terms of quasi-local currents of the underlying quantum group. We show that the conservation of the quantum group currents leads to twisted discrete-holomorphicity (DH) conditions for the parafermions. At the critical Fateev–Zamolodchikov point the parafermions are the usual ones, and the DH conditions coincide with those found previously by Rajabpour and Cardy. Away from the critical point, we show that our twisted DH conditions can be understood as deformed lattice current conservation conditions for an underlying perturbed conformal field theory in both the general &$Ngeqslant 3$; and N = 2 Ising cases.