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

TL;DR

This paper explores various soliton solutions in a scalar field model with a non-trivial vacuum manifold, including topological domain walls and non-topological Q-balls, analyzing their properties and effects of coupling to gravity and gauge fields.

Contribution

It introduces a comprehensive analysis of both topological and non-topological solitons in a scalar field model with a discrete vacuum manifold, including numerical construction and effects of gauge and gravitational coupling.

Findings

Finite energy topological solitons in (1+1) dimensions

Existence of finite energy non-topological Q-balls in (3+1) dimensions

Influence of gauge and gravitational coupling on soliton properties

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.