A remark on the coupling-dependence in affine Toda field theories

TL;DR

This paper analyzes the coupling dependence in affine Toda field theories based on non simply-laced Lie algebras, providing a universal S-matrix form and illustrating it with specific algebra pairs.

Contribution

It introduces a universal form for the coupling-constant dependence in affine Toda models, relating quantum S-matrix properties to classical couplings.

Findings

Derived a universal S-matrix coupling dependence formula

Connected quantum properties to classical couplings in affine Toda theories

Illustrated results with the dual pair $f_4^{(1)}$ and $e_6^{(2)}$

Abstract

The affine Toda field theories based on the non simply-laced Lie algebras are discussed. By rewriting the S-matrix formulae found by Delius et al, a universal form for the coupling-constant dependence of these models is obtained, and related to various general properties of the classical couplings. This is illustrated via the S-matrix associated with the dual pair of algebras $f_4^{(1)}$ and $e_6^{(2)}$.