Colour valued Scattering Matrices

TL;DR

This paper introduces a new class of colour-valued scattering matrices that generalize affine Toda models, relate to Lie algebras, and exhibit parity violation, with implications for integrable quantum field theories.

Contribution

It presents a novel construction of colour-valued S-matrices linked to Lie algebras, extending affine Toda models and analyzing their thermodynamic properties.

Findings

New S-matrix generalizing affine Toda models

Parity violation in the constructed S-matrix

Identification of ultraviolet central charges

Abstract

We describe a general construction principle which allows to add colour values to a coupling constant dependent scattering matrix. As a concrete realization of this mechanism we provide a new type of S-matrix which generalizes the one of affine Toda field theory, being related to a pair of Lie algebras. A characteristic feature of this S-matrix is that in general it violates parity invariance. For particular choices of the two Lie algebras involved this scattering matrix coincides with the one related to the scaling models described by the minimal affine Toda S-matrices and for other choices with the one of the Homogeneous sine-Gordon models with vanishing resonance parameters. We carry out the thermodynamic Bethe ansatz and identify the corresponding ultraviolet effective central charges.