Solitonic Integrable Perturbations of Parafermionic Theories

TL;DR

This paper demonstrates the quantum integrability of certain massive perturbations of parafermionic conformal field theories, showing they possess conserved densities and relate to classical soliton solutions, thus advancing understanding of their exact S-matrices.

Contribution

It establishes quantum integrability for a broad class of parafermionic perturbations and links classical soliton solutions to quantum properties, generalizing previous models.

Findings

Quantum conserved densities of scale dimension 2 and 3 identified.

Theories are integrable for any continuous vector coupling.

Classical equations are non-abelian affine Toda equations with soliton solutions.

Abstract

The quantum integrability of a class of massive perturbations of the parafermionic conformal field theories associated to compact Lie groups is established by showing that they have quantum conserved densities of scale dimension 2 and 3. These theories are integrable for any value of a continuous vector coupling constant, and they generalize the perturbation of the minimal parafermionic models by their first thermal operator. The classical equations-of-motion of these perturbed theories are the non-abelian affine Toda equations which admit (charged) soliton solutions whose semi-classical quantization is expected to permit the identification of the exact S-matrix of the theory.