Examples for BPS Solitons Destabilized by Quantum Effects

We investigate serval models for two scalar fields in one space dimension with topologically stable solitons that are constructed from BPS equations. The asymptotic behavior of these solitons fully determines their classical energies. A particular feature of the considered models is that there are several translationally invariant ground states that we call primary and secondary vacua. The former are those that are asymptotically assumed by the solitons. Solitons that occupy a secondary vacuum in finite but eventually large portions of space are classically degenerate. Thus the quantum contributions to the energies are decisive for the energetically favored soliton. While some of these solitons were constructed previously, we, for the first time, compute the leading (one-loop) quantum contribution their energies. In all cases considered we find that this contribution is not bounded from below and that it is the more negative the larger the region is in which the soliton approaches a secondary vacuum. This corroborates the conjecture, earlier inferred from the Shifman-Voloshin soliton, that the availability of secondary vacua destabilizes these solitons on the quantum level.