The large-N limits of the chiral Potts model

In this paper we study the large-N limits of the integrable N-state chiral Potts model. Three chiral solutions of the star-triangle equations are derived, with states taken from all integers, or from a finite or infinite real interval. These solutions are expected to be chiral-field lattice deformations of parafermionic conformal field theories. A new two-sided hypergeometric identity is derived as a corollary.