Abstract We develop a rigid N= (1, 1) N = (1, 1) superspace framework for spatially inhomogeneous impurity deformations in D=1+1 D = 1 + 1 dimensions by embedding the impurity profile into a real background superfield (spurion). This spurionic completion provides a manifestly supersymmetric description at the level of the action and offers a systematic route to identify which inhomogeneous backgrounds preserve a nontrivial subset of supercharges. Focusing on static interface-type configurations, we determine the half-BPS condition on the spurion background and the corresponding supersymmetry projector. In the resulting half-BPS sector we derive the associated first-order BPS equation for static bosonic matter configurations and establish an exact Bogomol’nyi completion of the static energy, yielding a sharp bound saturated by BPS solutions. We further comment on how explicit coordinate dependence and derivative-dependent impurity couplings can obstruct the Bogomol’nyi structure, thereby motivating spurionic extensions that retain supersymmetric control over inhomogeneous deformations.
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D. Bazeia
A. C. Lehum
The European Physical Journal C
Universidade Federal do Pará
Universidade Federal da Paraíba
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Bazeia et al. (Wed,) studied this question.
www.synapsesocial.com/papers/69fd7ef7bfa21ec5bbf07470 — DOI: https://doi.org/10.1140/epjc/s10052-026-15714-z