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A<sc>bstract</sc> Conformal Freeze-in (COFI) scenario postulates a dark sector described by a conformal field theory (CFT) at energies above the “gap scale” in the keV – MeV range. At the gap scale, the dark CFT undergoes confinement, and one of the resulting bound states is identified as the dark matter candidate. In this paper, we study this model in the context of the AdS/CFT correspondence with a focus on the mechanism of the infrared (IR) breaking of conformal invariance in the dark sector. We construct the holographic dual to the conformal dark sector, given by a Randall-Sundrum-like model in 5D, where the Standard Model (SM) fields and the dark matter candidate are placed on the ultraviolet (UV) and IR branes respectively. The separation between the UV and IR branes is stabilized by a bulk scalar field, naturally generating a hierarchy between the electroweak scale and the gap scale. We find that the parameter space of COFI comprises two distinct branches of CFT’s living on the Anti-de-Sitter (AdS) boundary, each corresponding to a different UV boundary condition. The two branches of CFT’s result in different radion potentials. The confinement of the CFT is dual to the spontaneous symmetry breaking by the 5D radion potential. We then use this dual 5D setup to study the cosmological confining phase transition in the dark sector. We find the viable parameter space of the theory which allows the phase transition to complete promptly without significant supercooling.