Discretely Holomorphic Parafermions and Integrable Loop Models

Abstract

We define parafermionic observables in various lattice loop models, including examples where no Kramers-Wannier duality holds. For a particular rhombic embedding of the lattice in the plane and a value of the parafermionic spin these variables are discretely holomorphic (they satisfy a lattice version of the Cauchy-Riemann equations) as long as the Boltzmann weights satisfy certain linear constraints. In the cases considered, the weights then also satisfy the critical Yang-Baxter equations, with the spectral parameter being related linearly to the angle of the elementary rhombus.

13 pages, 7 figures Added 2 references, corrected minor typos

References in corpus (2)

• Conformal invariance in random cluster models. I. Holomorphic fermions in the Ising model
• Stochastic Loewner evolution for conformal field theories with Lie-group symmetries