Discrete holomorphic parafermions in the Ashkin-Teller model and SLE

We find discrete holomorphic parafermions of the Ashkin–Teller model on the critical line, by mapping appropriate interfaces of the model onto the O(n = 1) model. We give support to the conjecture that the curve created by the insertion of parafermionic operators at two points on the boundary is SLE(4, ρ, ρ), where ρ varies along the critical line