Abstract
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 \( \mathcal{N}=1 \) theories with 3d defects preserving 3d \( \mathcal{N}=1 \) 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. We also derive the defect multiplet by using a superspace Noether procedure.
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Drukker, N., Martelli, D. & Shamir, I. The energy-momentum multiplet of supersymmetric defect field theories. J. High Energ. Phys. 2017, 10 (2017). https://doi.org/10.1007/JHEP08(2017)010
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DOI: https://doi.org/10.1007/JHEP08(2017)010