  Topological excitations are believed to play an important role in different
areas of physics. For example, one case of topical interest is the use of dual
models of quantum cromodynamics to understand properties of its vacuum and
confinement through the condensation of magnetic monopoles and vortices. Other
applications are related to the role of these topological excitations,
nonhomogeneous solutions of the field equations, in phase transitions
associated to spontaneous symmetry breaking in gauge theories, whose study is
of importance in phase transitions in the early universe, for instance. Here we
show a derivation of a model dual to the scalar Abelian Higgs model where its
topological excitations, namely vortex-strings, become manifest and can be
treated in a quantum field theory way. The derivation of the nontrivial
contribution of these vacuum excitations to phase transitions and its analogy
with superconductivity is then made possible and they are studied here.
