Abstract

A defining feature of holographic dualities is that, along with the bulk equations of motion, boundary correlators at any given time $t$ determine those of observables deep in the bulk. We argue that this property emerges from the bulk gravitational Gauss law together with bulk quantum entanglement as embodied in the Reeh-Schlieder theorem. Stringy bulk degrees of freedom are not required and play little role even when they exist. As an example we study a toy model whose matter sector is a free scalar field. The energy density $\rho$ sources what we call a pseudo-Newtonian potential $\Phi$ through Poisson’s equation on each constant time surface, but there is no back-reaction of $\Phi$ on the matter. We show the Hamiltonian to be essentially self-adjoint on the domain generated from the vacuum by acting with boundary observables localized in an arbitrarily small neighborhood of the chosen time $t$. Since the Gauss law represents the Hamiltonian as a boundary term, the model is holographic in the sense stated above.