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 to 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.

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