Holography from the Wheeler-DeWitt equation

Understand

In a theory of quantum gravity, states can be represented as wavefunctionals that assign an amplitude to a given configuration of matter fields and the metric on a spatial slice.

• These wavefunctionals must obey a set of constraints as a consequence of the diffeomorphism invariance of the theory, the most important of which is known as the Wheeler-DeWitt equation.
• We study these constraints perturbatively by expanding them to leading nontrivial order in Newton's constant about a background AdS spacetime.
• We show that, even within perturbation theory, any wavefunctional that solves these constraints must have specific correlations between a component of the metric at infinity and energetic excitations of matter fields or transverse-traceless gravitons.