BPS soliton-impurity models and supersymmetry

Abstract

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.

Instantons in chiral magnets

“…They appear for unwinding a skyrmion line in a skyrmion lattice [20] and form a stable crystal in certain parameter region [21]. One of recent interesting theoretical developments might be the finding of a critical coupling at which the strength of DM interaction and Zeeman magnetic field or magnetic anisotropy are balanced [22][23][24][25], analogous to superconductors at the critical coupling between types I and II. In this case, it allows so-called Bogomol'yi-Prasad-Sommerfield (BPS) topological solitons [26,27], i. e. the most stable configurations with a fixed boundary condition (or a topological sector), which were originally found for magnetic monopoles and other topological solitons in high energy physics and now are realized in superconductors at the critical coupling.…”

“…There are several interesting avenues related to this work. While we have considered one-dimensional chiral magnets in this letter, we can generalize our approach to higher-dimensional systems [22][23][24][25]. In particular, the 2D model allows a topologically conserved skyrmion current and Hopf terms, thus involves rich theoretical structures.…”

Background fields and self-dual Skyrmions

“…Moreover, the background field deformed Bogomol'nyi equation still supports infinitely many Skyrmions with arbitrary value of the baryon index. Similar computations were presented for the BPS baby Skyrme model in [34]. The pertinent energy functional reads…”

Report on scipost_201905_00004v1

“…The energy functional defining the gauged sigma model we want to consider is 11) or, in local coordinates and in terms of…”