Conserved charges and soliton solutions in affine Toda theory

TL;DR

This paper investigates conserved charges in affine Toda field theories using conformal extensions, computes their values for solitons, and relates these to Lie algebra structures, enhancing understanding of integrable models.

Contribution

It introduces a method to compute conserved charges in affine Toda theories via conformal extensions and links these charges to Lie algebra eigenvectors, providing new insights.

Findings

Conserved charges are computed explicitly for single soliton solutions.

Charges are related to eigenvectors of the Cartan matrix.

The approach connects integrable field theories with Lie algebra structures.

Abstract

We study the conserved charges of affine Toda field theories by making use of the conformally invariant extension of these theories. We compute the values of all charges for the single soliton solutions, and show that these are related to eigenvectors of the Cartan matrix of the finite-dimensional Lie algebra underlying the theory.