Supersymmetry in Boundary Integrable Models

TL;DR

This paper explores how $N=2$ supersymmetry influences boundary integrable models, identifying supersymmetric boundary conditions, constructing effective boundary actions, and analyzing symmetry properties of scattering matrices.

Contribution

It identifies $N=2$ supersymmetric boundary integrable models, constructs their boundary Landau-Ginzburg formulations, and analyzes the symmetry of boundary reflection matrices.

Findings

Boundary bosonic potential is $|W|^2$, with $W$ as the bulk superpotential.

Supersymmetry constrains boundary actions and reflection matrices.

Some $N=2$ supersymmetry-preserving reflection matrices are explicitly given.

Abstract

Quantum integrable models that possess $N=2$ supersymmetry are investigated on the half-space. Conformal perturbation theory is used to identify some $N=2$ supersymmetric boundary integrable models, and the effective boundary Landau-Ginzburg formulations are constructed. It is found that $N=2$ supersymmetry largely determines the boundary action in terms of the bulk, and in particular, the boundary bosonic potential is $|W|^2$, where $W$ is the bulk superpotential. Supersymmetry is also investigated using the affine quantum group symmetry of exact scattering matrices, and the affine quantum group symmetry of boundary reflection matrices is analyzed both for supersymmetric and more general models. Some $N=2$ supersymmetry preserving boundary reflection matrices are given, and their connection with the boundary Landau-Ginzburg actions is discussed.