On RSOS models associated to Lie algebras and RCFT

TL;DR

This paper systematically derives RSOS models linked to Lie algebras B_m, C_m, D_m from conformal field theory braiding, describing their Boltzmann weights, crossing properties, and soliton systems related to RCFT perturbations.

Contribution

It provides the first systematic derivation of RSOS models associated with B_m, C_m, D_m Lie algebras from conformal field theory braiding, including Boltzmann weights and soliton system descriptions.

Findings

Derived Boltzmann weights for RSOS models from RCFT

Confirmed crossing properties align with modular transformations

Linked soliton systems to RCFT perturbations

Abstract

RSOS models based on the Lie algebras $B_m$, $C_m$ and $D_m$ are derived from the braiding of conformal field theory. This gives the first systematic derivation of these models earlier described by Jimbo et al. The general two field Boltzmann weights associated to any RCFT are described, giving in particular the off critical thermalized Boltzmann weights. Crossing properties are discussed and are shown to agree with the general theory which connects these with toroidal modular transformations. The soliton systems based on these lattice models are described and are conjectured based on the mass formulae and the spins of the integrals of motions to describe perturbations of the RCFT $G_k\times G_1\over G_{k+1}$, where $G$ is the corresponding Lie algebra.