Deconstruction and holography

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.