Discrete holomorphic parafermions in the Ashkin-Teller model and SLE

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.

13 pages, 12 figures

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• A Guide to Stochastic Loewner Evolution and its Applications
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• Critical interfaces of the Ashkin-Teller model at the parafermionic point
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Cited by in corpus (7)

• Discrete holomorphicity and integrability in loop models with open boundaries
• Critical interfaces and duality in the Ashkin Teller model
• Integrability and braided tensor categories
• Integrability as a consequence of discrete holomorphicity: the Z_N model
• Spin interfaces in the Ashkin-Teller model and SLE
• Critical domain walls in the Ashkin-Teller model
• Conserved Currents in the Six-Vertex and Trigonometric Solid-On-Solid Models