The Topological Charges of the $a_n^{(1)}$ Affine Toda Solitons

Abstract

The topological charges of the \an affine Toda solitons are considered. A general formula is presented for the number of charges associated with each soliton, as well as an expression for the charges themselves. For each soliton the charges are found to lie in the corresponding fundamental representation, though in general these representations are not filled. Each soliton's topological charges are invariant under cyclic permutations of the simple roots plus the extended root or equivalently, under the action of the Coxeter element (with a particular ordering). Multisolitons are considered and are found to have topological charges filling the remainder of the fundamental representations as well as the entire weight lattice. The article concludes with a discussion of some of the other affine Toda theories.

24 pages, LaTeX, DTP-93-35

Cited by in corpus (20)

• Affine Toda field theories with defects
• On purely transmitting defects in affine Toda field theory
• Multi--Soliton Solutions of Affine Toda Models
• Exact S-Matrices for Bound States of $a_2^{(1)}$ Affine Toda Solitons
• Comments on defects in the a_r Toda field theories
• Exact S-matrices for d_{n+1}^{(2)} affine Toda solitons and their bound states
• Quantum mass corrections for affine Toda solitons
• Folding defect affine Toda field theories
• Inverse scattering and solitons in $A_{n-1}$ affine Toda field theories
• Momentum conserving defects in affine Toda field theories
• Toda Soliton Mass Corrections and the Particle--Soliton Duality Conjecture
• Trigonometric S-Matrices, Affine Toda Solitons and Supersymmetry
• Exact quantum S-matrices for solitons in simply-laced affine Toda field theories
• Defect fusing rules in affine Toda field theory
• The R-matrix of the U_q(d_4(3)) algebra and g_2(1) affine Toda field theory
• Integrability of generalised type II defects in affine Toda field theory
• Quantum Affine Symmetry and Scattering Amplitudes of the Imaginary Coupled d_4(3) Affine Toda Field Theory
• Inverse scattering and solitons in $A_{n-1}$ affine Toda field theories II
• Reality of Complex Affine Toda Solitons
• Quantum affine Toda solitons