SupersymmetricQ-balls and boson stars in(d+1)dimensions

Abstract

We construct supersymmetric $Q$-balls and boson stars in $(d+1)$ dimensions. These nontopological solitons are solutions of a scalar field model with global $U(1)$ symmetry and a scalar field potential that appears in gauge-mediated supersymmetry breaking in the minimal supersymmetric extension of the standard model. We are interested in both the asymptotically flat as well as in the asymptotically anti-de Sitter (AdS) solutions. In particular, we show that for our choice of the potential gravitating, asymptotically flat boson stars exist in $(2+1)$ dimensions. We observe that the behavior of the mass and charge of the asymptotically flat solutions at the approach of the maximal frequency depends strongly on the number of spatial dimensions. In particular, we find that in the ``thick-wall limit'' $Q$-balls are always unstable in flat space-time, but that they can become stable in AdS. Moreover, for the asymptotically AdS solutions the model on the conformal boundary can be interpreted as describing $d$-dimensional condensates of scalar glueballs.