Colours associated to non simply-laced Lie algebras and exact S-matrices

TL;DR

This paper introduces new exact S-matrices in 1+1 dimensions linked to non simply-laced Lie algebras, extending previous models and connecting to semi-classical spectra of integrable quantum field theories.

Contribution

It proposes a novel set of exact scattering matrices with a colour structure based on non simply-laced Lie algebras, generalizing earlier models and matching semi-classical spectra.

Findings

New S-matrices associated with non simply-laced Lie algebras.

Recovery of simply-laced HSG models as special cases.

Coupling of different affine Toda models through the new S-matrices.

Abstract

A new set of exact scattering matrices in 1+1 dimensions is proposed by solving the bootstrap equations. Extending earlier constructions of colour valued scattering matrices this new set has its colour structure associated to non simply-laced Lie algebras. This in particular leads to a coupling of different affine Toda models whose fusing structure has to be matched in a suitable manner. The definition of the new S-matrices is motivated by the semi-classical particle spectrum of the non simply-laced Homogeneous Sine-Gordon (HSG) models, which are integrable perturbations of WZNW cosets. In particular, the S-matrices of the simply-laced HSG models are recovered as a special case.