BPS soliton-impurity models and supersymmetry

• Published in: The journal of high energy physics 2019-07, Vol.2019 (7), p.1-27, Article 164
• Main Authors: Adam, C., Queiruga, Jose M., Wereszczynski, A.
• Format: Article
• Language: English
• Subjects: Classical and Quantum Gravitation; Elementary Particles; Euler-Lagrange equation; Extended Supersymmetry; Field Theories in Lower Dimensions; High energy physics; Impurities; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Solitary waves; Solitons Monopoles and Instantons; String Theory; Supersymmetric Gauge Theory; Supersymmetry; Topology
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP07(2019)164

A bstract We find supersymmetric extensions of the half-BPS soliton-impurity models in (1+1) dimensions which preserve half of the 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 CP 1 model, its BPS impurity generalisation preserves one-quarter of the 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 N = 2 SUSY (the case of the previously known magnetic impurity) are possible. We also discuss a possible relation between the BPS CP 1 -impurity model and the Dzyaloshinskii-Moriya interaction energy.