Holography from the Wheeler-DeWitt equation

Abstract

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. These correlations disallow strictly localized excitations. We prove perturbatively that two states or two density matrices that coincide at the boundary for an infinitesimal interval of time must coincide everywhere in the bulk. This analysis establishes a perturbative version of holography for theories of gravity coupled to matter in AdS.

Berry phases, wormholes and factorization in AdS/CFT

“…To conclude, we note that based on the results of this paper, there are many more interesting questions to be pursued in the future. For instance, it will be very interesting to connect our present construction to the split property in quantum mechanical systems and the lack thereof in gravitational systems as formulated extensively in [59,60]. It will also be extremely illuminating to understand the lack of factorization due to the non-exact symplectic form in terms of the emergent operator algebra of the dual CFT as discussed in a series of recent work [61][62][63].…”

The universality of islands outside the horizon

“…Recent research indicates that the bulk locality is absent in the gravitational system and the boundary system encodes all the bulk information [5][6][7][8][9]. Without the bulk locality, the whole system can not be divided into the black hole and Hawking radiation intrinsically.…”

“…Without the bulk locality, the whole system can not be divided into the black hole and Hawking radiation intrinsically. In this scenario, one can only collect the bulk information at the asymptotic boundary and then get a constant fine-grained entropy [6,8,9]. However, the bulk locality can be restored by gluing a non-gravitational system, which is called "bath" conventionally, to the black hole [6] with transparent boundary conditions, and one can thus calculate the fine-grained entropy of the Hawking radiation absorbed by the bath.…”

A comment on a fine-grained description of evaporating black holes with baby universes

“…4 H c Y h p Z s A s j C n q J 9 M 4 p h M D U R y x a j + y B q j I U 4 K W q f K 9 F v t z A 0 r 7 h p L l W 3 v d z m 0 D f t u t d i n / q 8 N X U 0 t S t a S q 1 m m b X K 1 Z 1 e u k e l X N g 8 3 M j + I h 7 r t e / B w P 0 N I p m z / Y 0 J i q F E j I l x F 1 o 3 G I p z i i 6 C k e j j G K R 4 h O M C p S R X S p i m e u H 9 A F Y I p l j I I w T F 2 h b d W N G 8 y 7 V l o F S g 5 M k 5 F 7 a 8 i z y q q X W k 6 j 1 Here the boundary energy H ∂ [h] is explicitly given by the integration of the ADM current J i over the conformal boundary ∂Σ [101],…”

“…Expanding (3.5) from the background metric, g ij = g 0 ij + κh ij , then look at the second order of the expansion gives (3.1). Details of the derivation can be found, for example in [101]. H ∂ [h] should be understood as the change of the mass of the black hole,…”