Discrete holomorphic parafermions in the Ashkin-Teller model and SLE

TL;DR

This paper identifies discrete holomorphic parafermions in the Ashkin-Teller model at criticality, linking them to SLE curves, and supports the conjecture that boundary-inserted parafermionic operators generate SLE(4,ρ,ρ) curves.

Contribution

It introduces a mapping of Ashkin-Teller model interfaces to the O(n=1) model and provides evidence for the SLE(4,ρ,ρ) conjecture along the critical line.

Findings

Discrete holomorphic parafermions are found in the Ashkin-Teller model.

The model's interfaces are mapped to the O(n=1) model.

The boundary curve is supported to be SLE(4,ρ,ρ).

Abstract

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 $SLE(4,\rho,\rho)$, where $\rho$ varies along the critical line.