Integrability of Coupled Conformal Field Theories

TL;DR

This paper investigates the integrability of coupled conformal field theories, focusing on their massive phases and classifying perturbations using Dynkin diagrams, with applications to models like Ising and Heisenberg spin-ladders.

Contribution

It provides a comprehensive classification of integrable perturbations of coupled minimal models using Dynkin diagram analysis.

Findings

Classification of all integrable perturbations achieved

Identification of models interpolating between Ising and Heisenberg systems

Analysis of massive phases via RSOS restrictions

Abstract

The massive phase of two-layer integrable systems is studied by means of RSOS restrictions of affine Toda theories. A general classification of all possible integrable perturbations of coupled minimal models is pursued by an analysis of the (extended) Dynkin diagrams. The models considered in most detail are coupled minimal models which interpolate between magnetically coupled Ising models and Heisenberg spin-ladders along the $c<1$ discrete series.