The energy-momentum multiplet of supersymmetric defect field theories

Understand

Defects in field theories break translation invariance, resulting in the non-conservation of the energy-momentum tensor in the directions normal to the defect.

• This violation is known as the displacement operator.
• We study 4d ${\cal N}=1$ theories with 3d defects preserving 3d ${\cal N}=1$ supersymmetry by analyzing the embedding of the 3d superspace in the 4d superspace.
• We use this to construct the energy-momentum multiplet of such defect field theories, which we call the defect multiplet and show how it incorporates the displacement operator.