Hidden geometrical structures in integrable models

Abstract

The bootstrap equations for the ADE series of purely elastic scattering theories have turned out to be intimately connected with the geometry of root systems and the Coxeter element. An informal review of some of this material is given, mentioning also a couple of other contexts -- the Pasquier models, and the simply-laced affine Toda field theories -- where similar structures are encountered. The relevance of twisted Coxeter elements is indicated, and a construction of these elements inspired by the twisted foldings of the affine Toda models is described.

15 pages, preprint NI92018. (one minor elucidation in the last section)

References in corpus (3)

• Duality in Quantum Toda theory and W-algebras
• Partition Functions, Intertwiners and the Coxeter Element
• G_2^1 Affine Toda Field Theory: A Numerical Test of Exact S-Matrix results

Cited by in corpus (8)

• Differential equations and integrable models: the SU(3) case
• On the universal Representation of the Scattering Matrix of Affine Toda Field Theory
• Conserved Charges and Supersymmetry in Principal Chiral Models
• Integrable aspects of the scaling q-state Potts models I: bound states and bootstrap closure
• Tree level integrability in 2d quantum field theories and affine Toda models
• A Collection of Exercises in Two-Dimensional Physics, Part 1
• Lie algebraic structures in integrable models, affine Toda field theory
• Pasquier Models at c=1: Cylinder Partition Functions and the role of the Affine Coxeter Element