From topological to non-topological solitons: kinks, domain walls and Q-balls in a scalar field model with non-trivial vacuum manifold

Abstract

We consider a scalar field model with a self-interaction potential that possesses a discrete vacuum manifold. We point out that this model allows for both topological as well as non-topological solitons. In (1+1) dimensions both type of solutions have finite energy, while in (3+1) dimensions, the topological solitons have finite energy per unit area only and correspond to domain walls. Non-topological solitons with finite energy do exist in (3+1) dimensions due to a non-trivial phase of the scalar field and an associated U(1) symmetry of the model, though. We construct these so-called Q-ball solutions numerically, point out the differences to previous studies with different scalar field potentials and also discuss the influence of a minimal coupling to both gravity as well as a U(1) gauge field. In this latter case, the conserved Noether charge Q can be interpreted as the electric charge of the solution.

17 pages including 9 figures; v2: conclusions extended, references added, matches version accepted for publication in Phys. Rev. D

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• Classical transitions with the topological number changing in the early Universe
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• Origin of nontopological soliton dark matter: solitosynthesis or phase transition
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• Solitonic Boson Stars: Numerical solutions beyond the thin-wall approximation
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