# The energy-momentum multiplet of supersymmetric defect field theories

## TL;DR

This paper constructs the energy-momentum multiplet for 4d ${
m N}=1$ supersymmetric theories with 3d defects, incorporating the displacement operator, using superspace embedding and Noether procedures.

## Contribution

It introduces the defect multiplet for supersymmetric defect theories and demonstrates its construction via superspace embedding and Noether methods.

## Key findings

- Constructed the defect multiplet including the displacement operator.
- Embedded 3d superspace into 4d superspace for analysis.
- Derived the defect multiplet using a superspace Noether procedure.

## 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 ${\cal N}=1$ 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. We also derive the defect multiplet by using a superspace Noether procedure.