Exact S-Matrices for Bound States of $a_2^{(1)}$ Affine Toda Solitons

Abstract

Using Hollowood's conjecture for the S-matrix for elementary solitons in complex $a_n^{(1)}$ affine Toda field theories we examine the interactions of bound states of solitons in $a_2^{(1)}$ theory. The elementary solitons can form two different kinds of bound states: scalar bound states (the so-called breathers), and excited solitons, which are bound states with non-zero topological charge. We give explicit expressions of all S-matrix elements involving the scattering of breathers and excited solitons and examine their pole structure in detail. It is shown how the poles can be explained in terms of on-shell diagrams, several of which involve a generalized Coleman-Thun mechanism.

Comments to figure 1 changed, some misprints corrected, 31 pages, LATEX. (Version accepted for publication in NUCLEAR PHYSICS B)

References in corpus (12)

• Quantum Solitons in Affine Toda Field Theories
• Exact S-Matrices for Nonsimply-Laced Affine Toda Theories
• Affine Toda Solitons and Vertex Operators
• Quantizing SL(N) Solitons and the Hecke Alegbra
• On a generalised bootstrap principle
• Affine Toda Solitons and Automorphisms of Dynkin Diagrams
• Infinite Families of Gauge-Equivalent $R$-Matrices and Gradations of Quantized Affine Algebras
• Connection between the Affine and Conformal Affine Toda Models and their Hirota's Solution
• Quantum Soliton Mass Corrections in SL(N) Affine Toda Theory
• The Topological Charges of the $a_n^{(1)}$ Affine Toda Solitons
• A representation of the exchange relation for affine Toda field theory
• Integrable vector perturbations of W-invariant theories and their quantum group symmetry

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