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Scalar fields, impurities and supersymmetry

  • D. Bazeia
  • A. C. Lehum
  • G. S. Santiago
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Abstract

We develop a rigid 𝒩=(1,1) superspace formulation for multifield scalar models coupled to localized impurities through spurion superfields in two-dimensional spacetime. The spurionic completion gives a manifestly supersymmetric action and provides a systematic framework for describing interacting scalar fields in the presence of impurity backgrounds. In this setting, supersymmetry acts as an organizing principle for a controlled bosonic half-BPS sector, with the preserved projector selecting the impurity-compatible first-order equations. We derive the corresponding coupled BPS equations, energy density, boundary conditions, and Bogomol'nyi bound, showing that localized impurities deform the BPS profiles and redistribute the local energy density while leaving the total BPS energy fixed by the topological boundary term. We illustrate the formalism through representative one-, two-, and three-field models, analyzing the resulting BPS configurations and their local energy density profiles.

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Cite

BibTeXRIS
BibTeX
@misc{bazeia2026scalar,
  title = {{Scalar fields, impurities and supersymmetry}},
  author = {D. Bazeia and A. C. Lehum and G. S. Santiago},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.09406},
  eprint = {2607.09406},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.09406},
}
RIS
TY  - UNPB
TI  - Scalar fields, impurities and supersymmetry
AU  - D. Bazeia
AU  - A. C. Lehum
AU  - G. S. Santiago
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2607.09406
UR  - https://arxiv.org/abs/2607.09406
AB  - We develop a rigid 𝒩=(1,1) superspace formulation for multifield scalar models coupled to localized impurities through spurion superfields in two-dimensional spacetime. The spurionic completion gives a manifestly supersymmetric action and provides a systematic framework for describing interacting scalar fields in the presence of impurity backgrounds. In this setting, supersymmetry acts as an organizing principle for a controlled bosonic half-BPS sector, with the preserved projector selecting the impurity-compatible first-order equations. We derive the corresponding coupled BPS equations, energy density, boundary conditions, and Bogomol'nyi bound, showing that localized impurities deform the BPS profiles and redistribute the local energy density while leaving the total BPS energy fixed by the topological boundary term. We illustrate the formalism through representative one-, two-, and three-field models, analyzing the resulting BPS configurations and their local energy density profiles.
ER  -