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

Understand

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.