Root Systems and Purely Elastic S-Matrices II

TL;DR

This paper explores the properties of ADE series purely elastic S-matrices using root system theory, deriving relationships between pole structures, bootstrap equations, and three-point couplings, with implications for Thermodynamic Bethe Ansatz.

Contribution

It provides a universal derivation of properties of ADE S-matrices and links root systems to bootstrap equations and coupling signs in affine Toda theories.

Findings

Relationship between pole structure and bootstrap equations derived from root system properties

Formula for signs of three-point couplings in affine Toda theories

Simplified proof of Klassen and Melzer's result relevant to Thermodynamic Bethe Ansatz

Abstract

Starting from a recently-proposed general formula, various properties of the ADE series of purely elastic S-matrices are rederived in a universal way. In particular, the relationship between the pole structure and the bootstrap equations is shown to follow from properties of root systems. The discussion leads to a formula for the signs of the three-point couplings in the simply-laced affine Toda theories, and a simple proof of a result due to Klassen and Melzer of relevance to Thermodynamic Bethe Ansatz calculations.