Jeff, holographic superconductivity/superfluidity is fairly simple conceptually and mechanically. The basic physics is breaking spontaneously an Abelian global symmetry. After you translate that to AdS language, this has to do with the existence of solutions to certain differential equations, with certain boundary conditions. The solutions can be constructed numerically (or in some cases analytically), but even without an explicit solution there are some arguments to demonstrate that such solutions exist. The first paper in the series by Horowitz, Hartnoll and Herzog may be a good one to follow.

This post imported from StackExchange Physics at 2014-04-01 16:20 (UCT), posted by SE-user user566