We study the breaking of an Abelian symmetry close to the horizon of a black string as well as close to the tip of a solitonic, cigar-shaped solution in ($3+1$)-dimensional anti-de Sitter space-time. We use these solutions to describe holographic superfluids away from the probe limit, i.e. taking backreaction into account. We observe that up to four phases exist in this model representing the duals of black string solutions with and without scalar hair and solitonic, cigar-shaped solutions with and without scalar hair, respectively. We construct the full phase diagram that describes the phase transitions between fluids and superfluids, between insulators and superfluids, as well as between insulators and fluids. In the probe limit the phase transition from fluids to black string superfluids changes from being second order to first order for sufficiently large values of the superfluid velocity and/or the angular momentum of the dual black string. We find that if we take backreaction into account phase transitions that are first order for weak backreaction become again second order for sufficiently strong backreaction. Moreover, we find a new type of insulator/superfluid phase transition for strong backreaction and vanishing superfluid velocity as well as a new type of fluid/superfluid phase transition that exists only for nonvanishing superfluid velocity.

• Received 9 February 2011

DOI:https://doi.org/10.1103/PhysRevD.83.126008