We present a criteria affirming the existence of discrete ground states of the Dirac operators which describe the fermion scattering on topological solitons in the nonlinear $O(3)$ σ-model. Additionally, we investigate a sufficient condition that elucidates the phenomenon of supersymmetry breaking within the supersymmetric quantum mechanics associated with this Dirac operator.
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Funakawa et al. (2024) studied this question.
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