Abstract
We study effects of backreaction of the fermionic modes localized by the baby Skyrmion in the (2+1)-dimensional Skyrme model. It is shown that there is a tower of fermionic modes of two different types, localized by the soliton, however there is only one fermionic level, which flows from positive to negative value as coupling increases. Considering the strong coupling regime we observe that the coupling of the bosonic field to the fermions may strongly deform the Skyrmion, in particular the regions of negative topological charge density appear.
Highlights
JHEP10(2018)081 invariance is broken, so there are only 3 bosonic modes
We study effects of backreaction of the fermionic modes localized by the baby Skyrmion in the (2+1)-dimensional Skyrme model
It is shown that there is a tower of fermionic modes of two different types, localized by the soliton, there is only one fermionic level, which flows from positive to negative value as coupling increases
Summary
The Lagrangian density of the coupled fermion-Skyrmion system in (2+1) dimensions can be written as. The topological restriction on the field φ is that on the spatial boundary φ∞ = (0, 0, 1) This allows a one-point compactification of the domain space R2 to S2 and the field of the finite energy soliton solutions of the model, so called baby Skyrmions, is a map φ : S2 → S2 which belongs to an equivalence class characterized by the homotopy group π2(S2) = Z. The coupling constant g and the fermions mass m are parameters of the model. There are five parameters of the coupled fermion-Skyrmion system (2.1), κ0, κ2, κ4, g and m. Considering the model (2.1) we do not impose the usual assumption that the Skyrmion is a fixed static background field [12, 33,34,35]. The field equation for the Skyrme field can be conveniently written in the form
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