Exact Gravity Dual of a Gapless Superconductor

A model of an exact gravity dual of a gapless superconductor is presented in which the condensate is provided by a charged scalar field coupled to a bulk black hole of hyperbolic horizon in asymptotically AdS spacetime. Below a critical temperature, the black hole acquires its hair through a phase transition while an electromagnetic perturbation of the background Maxwell field determines the conductivity of the boundary theory.