No abstract

In this paper we examine the properties of U (1) gauged Q-balls in two models with different scalar field potentials. The obtained results demonstrate that in the general case U (1) gauged Q-balls possess properties, which differ considerably from those of Q-balls in the nongauged case with the same forms of the scalar field potential. In particular, it is shown that in some cases the charge of U (1) gauged Q-ball can be bounded from above, whereas it is not so for the corresponding nongauged Q-ball. Our conclusions are supported both by analytical considerations and numerical calculations.

In 5+1 dimensions, we construct a vortex-like solution on a two-dimensional sphere. We study fermionic zero modes in the background of this solution and relate them to the replication of fermion families in the Standard Model. In particular, using a compactified space removes the need for the difficult localisation of gauge fields, while the present procedure (rather than naive compactification on a disk) also removes spurious fermionic modes.

Explicit solutions for extended objects of a Q-ball type were found analytically in a model describing complex scalar field with piecewise parabolic potential in (3+1)and (1+1)-dimensional space-times. Such a potential provides a variety of solutions which were thoroughly examined. It was shown that, depending on the values of the parameters of the model and according to the known stability criteria, there exist stable and unstable solutions. The classical stability of solutions in (1+1)-dimensional spacetime was examined in the linear approximation and it was shown explicitly that the spectrum of linear perturbations around some solutions contains exponentially growing modes while it is not so for other solutions. *

We provide a review of non-topological solitonic solutions arising in theories with a complex scalar field and global or gauge U (1)-symmetry. It covers Q-balls, homogeneous charged scalar condensates, and nonlinear localized holes and bulges in a classically stable condensate. A historical overview is followed by the discussion of properties of solutions, including their stability, from different perspectives. Solitons in models with additional massive degrees of freedom are also revisited, and their relation to one-field Q-balls is showed. We also discuss theories with a gauge field giving rise to gauged Q-balls and theories with dynamical gravity giving rise to boson stars.