Holography for a small world

The holographic principle asserts that the complete description of the interior of a sphere is a theory which not only lives on the surface of the sphere, but also has A/4 binary degrees of freedom. In this context we revisit the question of whether AdS/CFT is fully holographic. We construct states which are localized deep in the interior yet are encoded on short scales in the CFT, seemingly in conflict with the UV/IR prescription. We make a proposal to address the more basic question of which CFT states are sufficient to describe physics within a certain region of the bulk.