Defect multiplets of N=1 supersymmetry in 4d

TL;DR

This paper classifies defect multiplets in 4d $ =1$ supersymmetric theories, detailing how defects break symmetries and introduce localized contributions that form multiplets and generate displacement operators.

Contribution

It provides a classification of defect multiplets for half-BPS defects in 4d $ =1$ theories, extending the understanding of symmetry breaking and localized contributions.

Findings

Classification of defect multiplets for 3d and 2d defects.

Identification of localized terms and their relation to symmetry breaking.

Derivation of the displacement operator from defect multiplets.

Abstract

Any 4d theory possessing $\mathcal{N}=1$ supersymmetry admits a so called $\mathcal{S}$-multiplet, containing the conserved energy-momentum tensor and supercurrent. When a defect is introduced into such a theory, the $\mathcal{S}$-multiplet receives contributions localised on the defect, which indicate the breaking of some translation symmetry and consequently also some supersymmetries. We call this the defect multiplet. We classify such terms corresponding to half-BPS defects which can be either three-dimensional, preserving 3d $\mathcal{N}=1$, or two-dimensional, preserving $\mathcal{N}=(0,2)$. The new terms localised on the defect furnish multiplets of the reduced symmetry and give rise to the displacement operator.