  It was recently pointed out that the physics of a single discrete
gravitational extra dimension exhibits a peculiar UV/IR connection relating the
UV scale to the radius of the effective extra dimension. Here we note that this
non-locality is a manifestation of holography, encoding the correct scaling of
the number of fundamental degrees of freedom of the UV theory. This in turn
relates the Wilsonian RG flow in the UV theory to the effective gravitational
dynamics in the extra dimension. The relevant holographic c-function is
determined by the expression for the holographic bound. Holography in this
context is a result of the requirements of unitarity and diffeomorphism
invariance. We comment on the relevance of this observation for the
cosmological constant problem.
