Reflection matrices for integrable N = 1 supersymmetric theories

Abstract

We study two-dimensional integrable N = 1 supersymmetric theories (without topological charges) in the presence of a boundary. We find a universal ratio between the reflection amplitudes for particles that are related by supersymmetry and we propose exact reflection matrices for the supersymmetric extensions of the multi-component Yang-Lee models and for the breather multiplets of the supersymmetric sine-Gordon theory. We point out the connection between our reflection matrices and the classical boundary actions for the supersymmetric sine-Gordon theory as constructed by Inami, Odake and Zhang [1].

The scaling supersymmetric Yang–Lee model with boundary

“…Several important problems remain to be solved, including the relation of the parameter λ B in the action to the parameter b of the boundary S matrix; and the identification of the operator Θ in (4.5) with the operator γ(−1) F in (4.34). It would also be interesting to consider other conformal boundary conditions, as well as extend the present study to the full family of integrable models with N = 1 supersymmetry [19], [26].…”

“…For this value of b, the boundary S matrix S(θ) is diagonal. We recall that Moriconi and Schoutens proposed [26] two diagonal boundary S matrices for the boundary SYL model (although without reference to any specific boundary conditions), which they designated R [1] (1) and R [1] (2) . Our boundary S matrix for b = 0 differs from R [1] (2) by the CDD factor, i.e.,…”

“…We support this picture by identifying a supersymmetry-like integral of motion, and by studying massless boundary flow using the boundary TBA. Some related work was done by Moriconi and Schoutens in [26]. These authors proposed two diagonal boundary S matrices for the boundary SYL model, without reference to any specific boundary conditions.…”

On the Perturbative Expansion of Boundary Reflection Factors of the Supersymmetric Sinh–gordon Model

“…Moriconi and Schoutens [16] assumed that the reflection matrix can be factorised similarly and will therefore take the form,…”

“…and by boundary crossing unitarity [14,21] 16) which must be satisfied by the full reflection factor. Because of the factorised forms of both the S-matrix and the reflection factor, and the fact that we shall choose the bosonic part of the reflection factor to satisfy (4.16) in conjunction with the sinh-Gordon S-matrix (4.5), these conditions lead to…”