Non-abelian Q-balls in supersymmetric theories

We demonstrate the existence of non-abelian non-topological solitons such as Q-balls in the spectrum of Wess-Zumino models with non-abelian global symmetries. We conveniently name them Q-superballs and identify them for short as Q-sballs. More specifically, we show that in contrast to the non-supersymmetric case, they arise in renormalizable potentials with cubic self-interactions of only one dimensionful parameter and for the entire parameter space of the model available. We solve the field equations and present the explicit form of the Q-sball solution. We compute its main physical properties and observe that in the supersymmetrically invariant vacuum Q-sballs form domains of manifestly broken sypersymmetry.