Vertex operators, semiclassical limit for soliton S-matrices and the number of bound states in Affine Toda Field Theories

TL;DR

This paper calculates soliton time-delays and semiclassical S-matrix limits in non-simply laced Affine Toda Field Theories, providing new formulas for bound states and coupling conditions, and extends vertex operator constructions to these theories.

Contribution

It introduces a vertex operator construction for non-simply laced affine Lie algebras and derives formulas for bound states and S-matrix diagonalization conditions.

Findings

Derived phase shift as sum over bilinears of conserved charges

Provided a general expression for the number of bound states

Identified coupling values where the S-matrix is diagonal

Abstract

Soliton time-delays and the semiclassical limit for soliton S-matrices are calculated for non-simply laced Affine Toda Field Theories. The phase shift is written as a sum over bilinears on the soliton conserved charges. The results apply to any two solitons of any Affine Toda Field Theory. As a by-product, a general expression for the number of bound states and the values of the coupling in which the S-matrix can be diagonal are obtained. In order to arrive at these results, a vertex operator is constructed, in the principal gradation, for non-simply laced affine Lie algebras, extending the previous constructions for simply laced and twisted affine Lie algebras.