Marginal stability and the metamorphosis of Bogomol’nyi-Prasad-Sommerfield states

We discuss the restructuring of the BPS spectrum which occurs on certain submanifolds of the moduli or parameter space—the curves of the marginal stability (CMS)—using quasiclassical methods. We argue that in general a “composite” BPS soliton swells in coordinate space as one approaches the CMS and that, as a bound state of two “primary” solitons, its dynamics in this region is determined by nonrelativistic supersymmetric quantum mechanics. Near the CMS the bound state has a wave function which is highly spread out. Precisely on the CMS the bound state level reaches the continuum, the composite state delocalizes in coordinate space, and restructuring of the spectrum can occur. We present a detailed analysis of this behavior in a two-dimensional $\mathcal{N}=2\mathrm{}$ Wess-Zumino model with two chiral fields, and then discuss how it arises in the context of “composite” dyons near weak coupling CMS curves in $\mathcal{N}=2\mathrm{}$ supersymmetric gauge theories. We also consider cases where some states become massless on the CMS.