Building a nest at tree level: Classical metastability and nontrivial vacuum structure in supersymmetric field theories

Abstract

It is becoming increasingly clear that metastable vacua may play a prominent role in supersymmetry breaking. To date, however, this idea has been realized only in models where nonperturbative dynamics complicates the analysis of metastability. In this paper, we present a simple construction in which metastable vacua occur classically, i.e., at tree level, and in which supersymmetry breaking is sourced by both $D$ terms and $F$ terms. All relevant dynamics is perturbative, and hence calculations of vacuum energies and lifetimes can be performed explicitly. Moreover, we find that our construction can even give rise to multiple nonsupersymmetric vacua which are degenerate. The nontrivial vacuum structure of such models therefore suggests that they can provide a rich arena for future studies of vacuum metastability in supersymmetric field theories. Our results may also have important consequences for ${Z}^{\ensuremath{'}}$ phenomenology and the string landscape.