  Vortex solutions are topologically stable field configurations that can play
an important role in condensed matter, field theory, and cosmology. We
investigate vortex configuration in a 2+1 dimensional Abelian Higgs theory
supplemented by higher order derivative self-interactions, related with
Galileons. Our vortex solutions have features that make them qualitatively
different from well-known Abrikosov-Nielsen-Olesen configurations, since the
derivative interactions turn on gauge invariant field profiles that break axial
symmetry. By promoting the system to a 3+1 dimensional string configuration, we
study its gravitational backreaction. Our results are all derived within a
specific, analytically manageable system, and might offer indications for
understanding Galileonic interactions and screening mechanisms around
configurations that are not spherically symmetric, but only at most
cylindrically symmetric.
