Reflection Matrices for Integrable $N=1$ Supersymmetric Theories

TL;DR

This paper derives exact reflection matrices for two-dimensional integrable N=1 supersymmetric theories with boundaries, revealing a universal ratio and connecting quantum results to classical boundary actions.

Contribution

It introduces universal reflection amplitude ratios and proposes exact reflection matrices for supersymmetric models, extending integrability and boundary analysis to supersymmetric theories.

Findings

Universal ratio between supersymmetric reflection amplitudes

Exact reflection matrices for supersymmetric Yang-Lee and sine-Gordon models

Connection between quantum reflection matrices and classical boundary actions

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 \cite{IOZ}.