WHAT BECOMES OF VORTICES IN THEORIES WITH FLAT DIRECTIONS

In many theories with flat directions of scalar potential, static vort ex solutions do not exist for a generic choice of vacuum. In two Eucli dean dimensions, we find their substitutes - constrained instantons co nsisting 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 a t every point in space the modulus relaxes, in a universal manner, to one and the same value characteristic to the theory.