Well-separated soliton-antisoliton pairs with an adjoint Higgs field in 4D space

We present single soliton states and soliton-antisoliton states with an adjoint Higgs field in 4D flat space. The action of a single soliton state diverges, while the action of soliton-antisoliton states converges. This means such solitons can exist in soliton-antisoliton states, although they cannot exist individually. The interaction in a soliton-antisoliton state takes a logarithmic dependence on separation. Such soliton-antisoliton states exhibit stability under a scaling transformation.