Spectral energy of Dirac operators for fermion scattering on topological solitons in the nonlinear $O(3)$ $σ$-model

Daiju Funakawa, Satoshi Okumura, Yuki Ueda

Published 2024-05-17Version 1

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 $O(3)$ $\sigma$-model. Additionally, we investigate a sufficient condition that elucidates the phenomenon of supersymmetry breaking within the supersymmetric quantum mechanics associated with this Dirac operator.