S-Matrix Identities in Affine Toda Field Theories

TL;DR

This paper extends the understanding of S-matrix and conserved charge identities in affine Toda field theories, providing a systematic framework that applies to both simply-laced and nonsimply-laced Lie algebra cases.

Contribution

It generalizes previous results to nonsimply-laced affine Toda theories and clarifies the role of conserved charges as components of Cartan matrix eigenvectors.

Findings

Extended identities to nonsimply-laced Lie algebras.

Unified framework for S-matrix and conserved charge identities.

Conserved charges correspond to eigenvector components of the Cartan matrix.

Abstract

We note that S-matrix/conserved charge identities in affine Toda field theories of the type recently noted by Khastgir can be put on a more systematic footing. This makes use of a result first found by Ravanini, Tateo and Valleriani for theories based on the simply-laced Lie algebras (A,D and E) which we extend to the nonsimply-laced case. We also present the generalisation to nonsimply-laced cases of the observation - for simply-laced situations - that the conserved charges form components of the eigenvectors of the Cartan matrix.