Classical solitons with no quantum counterparts and their supersymmetric revival

Abstract

We demonstrate the phenomenon stated in the title, using for illustration a two-dimensional scalar-field model with a triple-well potential V(Φ)=λ²Φ²/2m² ×(Φ² - m²/λ)². At the classical level, this system supports static topological solitons with finite energy. Upon quantisation, however, these solitons develop infinite energy, which cannot be renormalised away. Thus this quantised model has no soliton sector, even though classical solitons exist. Finally when the model is extended supersymmetrically by adding a Majorana field, finiteness of the soliton energy is recovered.