Root Systems and Purely Elastic S-Matrices II

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.

21 pages

Cited by in corpus (47)

• Classically integrable boundary conditions for affine Toda field theories
• Affine Toda field theory on a half line
• Factorized Scattering in the Presence of Reflecting Boundaries
• Affine Toda Field Theory in the Presence of Reflecting Boundaries
• On a generalised bootstrap principle
• Differential equations and integrable models: the SU(3) case
• On the universal Representation of the Scattering Matrix of Affine Toda Field Theory
• Vertex Operators and Soliton Time Delays in Affine Toda Field Theory
• The ultraviolet Behaviour of Integrable Quantum Field Theories, Affine Toda Field Theory
• Massive and massless phases in self-dual $Z_N$ spin models: some exact results from the thermodynamic Bethe ansatz
• Generalising the staircase models
• A remark on the coupling-dependence in affine Toda field theories
• Affine Toda Solitons and Systems of Calogero-Moser Type
• Particle Reflection Amplitudes in a_n^(1) Toda Field Theories
• D-Branes on ALE Spaces and the ADE Classification of Conformal Field Theories
• Reflection factors and exact g-functions for purely elastic scattering theories
• Exact S-matrices for d_{n+1}^{(2)} affine Toda solitons and their bound states
• Quantum mass corrections for affine Toda solitons
• The Quantum Spectrum of the Conserved Charges in Affine Toda Theories
• Massive Corrections to Entanglement in Minimal E8 Toda Field Theory
• Functional Equations of Form Factors for Diagonal Scattering Theories
• Integrable aspects of the scaling q-state Potts models II: finite-size effects
• Integrable aspects of the scaling q-state Potts models I: bound states and bootstrap closure
• Toda Soliton Mass Corrections and the Particle--Soliton Duality Conjecture
• Integrable Field Theories and Their CCFT Duals
• Solitons and Vertex Operators in Twisted Affine Toda Field Theories
• Non-Hermitian multi-particle systems from complex root spaces
• A Moyal Quantization of the Continuous Toda Field
• Affine Toda field theories related to Coxeter groups of non-crystallographic type
• Anyonic Interpretation of Virasoro Characters and the Thermodynamic Bethe Ansatz
• Exact quantum S-matrices for solitons in simply-laced affine Toda field theories
• An Algebraic Approach to Form Factors
• On sums of tensor and fusion multiplicities
• Fusion, mass, and representation theory of the Yangian algebra
• Tree level integrability in 2d quantum field theories and affine Toda models
• Defect fusing rules in affine Toda field theory
• From tree- to loop-simplicity in affine Toda theories I: Landau singularities and their subleading coefficients
• Exact two-particle Matrix Elements in S-Matrix Preserving Deformation of Integrable QFTs
• Universal amplitude ratios and Coxeter geometry in the dilute A model
• Restricted Quantum Theory of Affine Toda Solitons
• Form Factors in $D_n^{(1)}$ Affine Toda Field Theories
• Dorey's Rule and the q-Characters of Simply-Laced Quantum Affine Algebras
• Y-Systems for Generalised Gibbs Ensembles in Integrable Quantum Field Theory
• Quantum anomalies in A^{(1)}_r Toda theories with defects
• One-loop inelastic amplitudes from tree-level elasticity in 2d
• Vertex operators, semiclassical limit for soliton S-matrices and the number of bound states in Affine Toda Field Theories
• Pasquier Models at c=1: Cylinder Partition Functions and the role of the Affine Coxeter Element