Solitons and Vertex Operators in Twisted Affine Toda Field Theories

Abstract

Affine Toda field theories in two dimensions constitute families of integrable, relativistically invariant field theories in correspondence with the affine Kac-Moody algebras. The particles which are the quantum excitations of the fields display interesting patterns in their masses and coupling and which have recently been shown to extend to the classical soliton solutions arising when the couplings are imaginary. Here these results are extended from the untwisted to the twisted algebras. The new soliton solutions and their masses are found by a folding procedure which can be applied to the affine Kac-Moody algebras themselves to provide new insights into their structures. The relevant foldings are related to inner automorphisms of the associated finite dimensional Lie group which are calculated explicitly and related to what is known as the twisted Coxeter element. The fact that the twisted affine Kac-Moody algebras possess vertex operator constructions emerges naturally and is relevant to the soliton solutions.

27 pages (harvmac) + 3 figures (LaTex) at the end of the file, Swansea SWAT/93-94/19

References in corpus (9)

• Quantum Solitons in Affine Toda Field Theories
• Exact S-Matrices for Nonsimply-Laced Affine Toda Theories
• Affine Toda Solitons and Vertex Operators
• Root Systems and Purely Elastic S-Matrices II
• On a generalised bootstrap principle
• Hirota's Solitons in the Affine and the Conformal Affine Toda Models
• Affine Toda Solitons and Automorphisms of Dynkin Diagrams
• A remark on the coupling-dependence in affine Toda field theories
• Crossing and Antisolitons in Affine Toda Theories

Cited by in corpus (9)

• Tau-functions and Dressing Transformations for Zero-Curvature Affine Integrable Equations
• Semi-classical spectrum of the Homogeneous sine-Gordon theories
• On the universal Representation of the Scattering Matrix of Affine Toda Field Theory
• Non-unitarity in quantum affine Toda theory and perturbed conformal field theory
• $A_n^{(1)}$ Toda solitons and the dressing symmetry
• More non-Abelian loop Toda solitons
• Vertex operators, semiclassical limit for soliton S-matrices and the number of bound states in Affine Toda Field Theories
• New Z(3) strings
• Vertex Operator Representation of the Soliton Tau Functions in the $A_n^{(1)}$ Toda Models by Dressing Transformations