Trigonometric S Matrices, Affine Toda Solitons and Supersymmetry

Abstract

Using U q (a (1) n )-and U q (a (2) 2n )-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. a

Soliton S matrices for the critical A chain

“…We compute by Bethe Ansatz both bulk and boundary hole scattering matrices. Our result for the bulk S matrix coincides with the soliton S matrix for the A (1) N −1 Toda field theory with imaginary coupling [4]- [6]. We also generalize the Ghoshal-Zamolodchikov [7] boundary crossing relation to the A (1) N −1 case (for which the bulk S matrix does not have crossing symmetry), and use it to help verify our result for the boundary S matrix.…”

“…The factors e ±yλ(1) in the boundary S matrices were unfortunately omitted in[3] 6. In[9] we use a slightly different definition of the boundary parameters ξ ∓ .…”

Integrable quantum field theories with OSP(m/2n) symmetries

“…= −e (−n+1/2)|ω| sinh |ω| cosh(n+1/2)|ω| . It is easy to check that the corresponding kernel coincides with σ + 3 − σ + 2 for N = 1 − 2n, and with the corresponding S matrix element in the a (2) 2n scattering theory [67]. The couplings between pseudoparticles can also be checked to arise from the structure of solutions of the a (2) 2n Bethe equations, generalizing the a …”

Restoring unitarity in the q-deformed world-sheet S-matrix

“…We can summarize the complete S-matrix in the following way: 29) where the kinks K ab (θ) are required to satisfy the adjacency condition |a − b| = 1 2…”