Trigonometric S-Matrices, Affine Toda Solitons and Supersymmetry

TL;DR

This paper constructs exact S-matrices for affine Toda solitons using quantum group invariants, analyzes their bound states, and explores their relation to supersymmetric theories, providing insights into integrable quantum field theories.

Contribution

It introduces new exact S-matrices for affine Toda solitons based on quantum group invariants and connects them with supersymmetric models, including N=1 and N=2 theories.

Findings

Constructed S-matrices using U_q(a_n^(1)) and U_q(a_2n^(2)) invariants.

Analyzed pole structures to identify soliton bound states.

Discussed the relation between these S-matrices and supersymmetric models.

Abstract

Using U_q(a_n^(1))- and U_q(a_2n^(2))-invariant R-matrices we construct exact S-matrices in two-dimensional space-time. These are conjectured to describe the scattering of solitons in affine Toda field theories. In order to find the spectrum of soliton bound states we examine the pole structure of these S-matrices in detail. We also construct the S-matrices for all scattering processes involving scalar bound states. In the last part of this paper we discuss the connection of these S-matrices with minimal N=1 and N=2 supersymmetric S-matrices. In particular we comment on the folding from N=2 to N=1 theories.