Holography from the Wheeler-DeWitt equation

In a theory of quantum gravity, states can be represented as wavefunctionals that assign an amplitude to given configuration matter fields and the metric on spatial slice. These must obey set constraints consequence diffeomorphism invariance theory, most important which is known Wheeler-DeWitt equation. We study these perturbatively by expanding them leading nontrivial order in Newton's constant about background AdS spacetime. show that, even within perturbation any wavefunctional solves have specific correlations between component at infinity energetic excitations or transverse-traceless gravitons. disallow strictly localized excitations. prove two density matrices coincide boundary for infinitesimal interval time everywhere bulk. This analysis establishes perturbative version holography theories gravity coupled AdS.