  We present a detailed study of a single vortex in a holographic symmetry
breaking phase. At low energies the system flows to an nontrivial conformal
fixed point. Novel vortex physics arises from the interaction of these gapless
degrees of freedom with the vortex: at low energies the vortex may be
understood as a conformal defect in this low energy theory. Defect conformal
symmetry allows the construction of a simple infrared geometry describing a new
kind of extremal horizon: a Poincare horizon with a small bubble of magnetic
Reissner-Nordstrom horizon inside it that carries a single unit of magnetic
flux and a finite amount of entropy even at zero temperature. We also construct
the full geometry describing the vortex at finite temperature in a UV complete
theory. We study both superfluid and superconducting boundary conditions and
calculate thermodynamic properties of the vortex. A study of vortex stability
reveals that the dual superconductor can be Type I or Type II, depending on the
charge of the condensed scalar. Finally, we study forces on a moving vortex at
finite temperature from the point of view of defect conformal symmetry and show
that these forces can be expressed in terms of Kubo formulas of defect CFT
operators.
