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

TL;DR

This paper derives exact S-matrices for bound states in the $a_2^{(1)}$ affine Toda soliton theory, revealing detailed pole structures and interactions of breathers and excited solitons.

Contribution

It provides explicit S-matrix expressions for bound states in $a_2^{(1)}$ affine Toda theory, expanding understanding of soliton interactions and pole structures.

Findings

Explicit S-matrix elements for breathers and excited solitons

Detailed analysis of pole structures and their physical interpretation

Identification of generalized Coleman-Thun mechanisms in pole explanations

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.