Covariant Constraints on Hole-ography

TL;DR

This paper demonstrates that certain bulk surfaces in AdS, specifically inside holographic screens, cannot be fully reconstructed using existing hole-ography methods, highlighting limitations in the current holographic reconstruction framework.

Contribution

It proves the existence of unreconstructable surfaces within holographic screens in AdS, revealing fundamental limitations of hole-ography in certain symmetric bulk regions.

Findings

Surfaces inside holographic screens cannot be fully reconstructed.

Reconstruction limitations are linked to the Bousso bound and coarse-graining.

Classical results suggest potential quantum extensions.

Abstract

Hole-ography is a prescription relating the areas of surfaces in an AdS bulk to the differential entropy of a family of intervals in the dual CFT. In (2+1) bulk dimensions, or in higher dimensions when the bulk features a sufficient degree of symmetry, we prove that there are surfaces in the bulk that cannot be completely reconstructed using known hole-ographic approaches, even if extremal surfaces reach them. Such surfaces lie in easily identifiable regions: the interiors of holographic screens. These screens admit a holographic interpretation in terms of the Bousso bound. We speculate that this incompleteness of the reconstruction is a form of coarse-graining, with the missing information associated to the holographic screen. We comment on perturbative quantum extensions of our classical results.