Abstract
We find supersymmetric extensions of the half-BPS soliton-impurity models in (1+1) dimensions which preserve half of the \( \mathcal{N} \) = 1 supersymmetry. This is related to the fact that in the bosonic sector (i.e., the half-BPS soliton-impurity model), only one soliton (for example, the kink) is a BPS configuration which solves the pertinent Bogomolnyi equation and saturates the topological energy bound. On the other hand, the topological charge conjugate state (the antikink) is not a BPS solution. This means that it obeys the full Euler-Lagrange equation and does not saturate the topological energy bound. The supersymmetric approach also allows us to construct half-BPS soliton-impurity models in (2+1) dimensions. Concretely, in the case of the CP1 model, its BPS impurity generalisation preserves one-quarter of the \( \mathcal{N} \) = 2 SUSY, while for the Abelian Higgs model at critical coupling both impurity generalisations preserving one-quarter (the case of a new, so-called Higgs impurity) as well as one-half of the \( \mathcal{N} \) = 2 SUSY (the case of the previously known magnetic impurity) are possible. We also discuss a possible relation between the BPS CP1-impurity model and the Dzyaloshinskii-Moriya interaction energy.
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Adam, C., Queiruga, J.M. & Wereszczynski, A. BPS soliton-impurity models and supersymmetry. J. High Energ. Phys. 2019, 164 (2019). https://doi.org/10.1007/JHEP07(2019)164
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DOI: https://doi.org/10.1007/JHEP07(2019)164