Q-Balls and the Proton Stability in Supersymmetric Theories

Abelian non-topological solitons with Baryon and/or Lepton quantum numbers naturally appear in the spectrum of the minimal supersymmetric standard model. They arise as a consequence of the existence of flat directions in the potential lifted by non renormalizable operators and SUSY breaking. We examine the conditions that these operators should satisfy in order to ensure proton stability and present a realistic string model which fulfils these requirements. We further identify a generic U(1) breaking term in the scalar potential and discuss its effect of rendering Q-balls unstable.