  We construct supersymmetric Q-balls and boson stars in (d+1) dimensions.
These non-topological solitons are solutions of a scalar field model with
global U(1) symmetry and a scalar field potential that appears in
gauge-mediated supersymmetry (SUSY) breaking in the minimal supersymmetric
extension of the Standard Model (MSSM). 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 behaviour 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. For the asymptotically AdS solutions, the model
on the conformal boundary can be interpreted as describing d-dimensional
condensates of scalar glueballs.
