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 fulfills these requirements. We further identify a generic U(1) breaking term in the scalar potential and discuss its effect of rendering Q-balls unstable.