The energy-momentum multiplet of supersymmetric defect field theories

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.

42 pages, v2: Fixed TeX package problem, v3: Minor corrections

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• A Sum Rule for Boundary Contributions to the Trace Anomaly
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