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We study the breaking of an Abelian symmetry close to the horizon of anuncharged rotating Anti-de Sitter black string in 3+1 dimensions. The boundarytheory living on R^2 x S^1 has no rotation, but a magnetic field that isaligned with the axis of the black string. This boundary theory decribesnon-rotating (2+1)-dimensional holographic superfluids with non-vanishingsuperfluid velocity. We study these superfluids in the grand canonical ensembleand show that for sufficiently small angular momentum of the dual black stringand sufficiently small superfluid velocity the phase transition is 2nd order,while it becomes 1st order for larger superfluid velocity. Moreover, we observethat the phase transition is always 1st order above a critical value of theangular momentum independent of the choice of the superfluid velocity.

Holographic superfluids as duals of rotating black strings