Twisted algebra R-matrices and S-matrices for $b_n^{(1)}$ affine Toda solitons and their bound states

TL;DR

This paper constructs new R-matrices for twisted quantum affine algebras and uses them to develop S-matrices for affine Toda solitons and their bound states, linking breathers to particles.

Contribution

It introduces novel R-matrices for specific twisted quantum affine algebras and applies them to derive S-matrices for affine Toda solitons and bound states.

Findings

New R-matrices for $U_q(a^{(2)}_{2n-1})$ and $U_q(e^{(2)}_6)$

Construction of S-matrices for $b^{(1)}_n$ affine Toda solitons

Identification of breathers with $b^{(1)}_n$ particles

Abstract

We construct new $U_q(a^{(2)}_{2n-1})$ and $U_q(e^{(2)}_6)$ invariant $R$-matrices and comment on the general construction of $R$-matrices for twisted algebras. We use the former to construct $S$-matrices for $b^{(1)}_n$ affine Toda solitons and their bound states, identifying the lowest breathers with the $b^{(1)}_n$ particles.