What becomes of vortices in theories with flat directions

In many theories with flat directions of scalar potential, static vortex solutions do not exist for a generic choice of vacuum. In tow Euclidean dimensions, we find their substitutes — constrained instantons consisting of compact core formed by Abrikosov-Nielsen-Olesen vortex and long-ranged cloud of modulus field. In (3 + 1) dimensions, an initial compact configuration of string topology evolves in such a way that at every point in space the modulus relaxes, in a universal manner, to one and the same value characteristic to the theory.