Supersymmetric, Integrable Boundary Field Theories

TL;DR

This paper explores supersymmetric integrable quantum field theories with boundaries, revealing how $N=2$ supersymmetry constrains boundary actions, and constructs exact boundary reflection matrices preserving supersymmetry.

Contribution

It identifies $N=2$ supersymmetric boundary integrable models, constructs their boundary Landau-Ginzburg actions, and describes exact supersymmetry-preserving boundary reflection matrices.

Findings

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

Supersymmetry constrains boundary actions in terms of bulk properties.

Exact $N=2$ supersymmetric boundary reflection matrices are constructed.

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 actions 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 discussed from the perspective of the affine quantum group symmetry of exact scattering matrices, and exact $N=2$ supersymmetry preserving boundary reflection matrices are described.