Critical RSOS Models in External Fields

TL;DR

This paper introduces a new class of unitary RSOS scattering models derived from SO(N) critical models in external electric or magnetic fields, connecting them to affine Toda theories and providing explicit S-matrices.

Contribution

It constructs fundamental kink S-matrices for these models and relates special cases to known theories like Sine-Gordon and parafermions, expanding the understanding of RSOS models in external fields.

Findings

Constructed kink S-matrices for the new models

Connected special cases to known integrable theories

Derived RSOS S-matrix for coupled minimal CFTs in SO(4) case

Abstract

We suggest a new family of unitary RSOS scattering models which is obtained by placing the SO(N) critical models in "electric" or "magnetic" field. These fields are associated with two operators from the space of the SO(N) RCFT corresponding to the highest weight of the vector representation of SO(N). A perturbation by the external fields destroys the Weyl group symmetry of an original statistical model. We show that the resulting kinks scattering theories can be viewed as affine imaginary Toda models for non-simply-laced and twisted algebras taken at rational values (roots of unity) of $q$-parameter. We construct the fundamental kink $S$-matrices for these models. At the levels $k=1, 2, \infty$ our answers match the known results for the Sine-Gordon, $Z_{2N}$ - parafermions and free fermions respectively. As a by-product in the SO(4)-case we obtain an RSOS $S$-matrix describing an integrable coupling of two minimal CFT.