Do holographic CFT states have unique semiclassical bulk duals?

TL;DR

The paper examines an ambiguity in the AdS/CFT dictionary where a single holographic CFT state can admit two semiclassical bulk descriptions: one with a closed universe derived from the gravitational path integral and another without a closed universe via the extrapolate dictionary. It analyzes a concrete AdS3/CFT2 setup with a PETS state that yields Description 1 (closed universe) and Description 2 (no closed universe), and surveys three potential resolutions—ensemble averaging, absence of a semiclassical closed universe, and physics beyond AdS/CFT—discussing implications for black hole interiors and the role of the gravitational path integral. The authors articulate how wormhole corrections affect inner products, propose a flowchart of resolution options, and highlight the need for a deeper understanding of the AdS/CFT dictionary to resolve the tension and understand bulk observer experiences. The work emphasizes fundamental limits of the bulk/boundary correspondence, informs discussions on factorization and the black hole information puzzle, and points toward nonperturbative bulk ingredients or observer-aware formulations as possible paths forward.

Abstract

We discuss a situation where a holographic CFT state has multiple semiclassical bulk duals. In our example, a given holographic state has two simple, semiclassical descriptions, one with a closed universe, constructed using the gravitational path integral, and one without a closed universe, constructed using the extrapolate dictionary. This highlights an ambiguity in the AdS/CFT dictionary. We propose various options for resolving this tension although none are perfectly satisfactory. We also discuss what this implies for the black hole interior and the gravitational path integral.

Figures (4)

• Figure 1: The Euclidean saddle computing $\braket{\Psi_i|\Psi_i}$ is built up from two thermal AdS saddles by gluing the boundaries of the yellow regions (orange lines) to each other. The two green (red) lines---i.e. operator insertions in the bra (ket)---are identified. The jump in extrinsic curvature is supported by the matter shock produced by the operator insertions in the bra and ket. The time symmetric slice contains two AdS spaces (blue) and a closed universe (yellow) giving us Description 1 Antonini:2023hdh.
• Figure 2: a) Description 2 consists of two AdS spaces (blue) that are entangled with each other (represented by the lines connecting them). b) The coefficients of the wavefunction $c_{jk}^{(i)}$ can be computed using the CFT path integral on a Riemann surface with operator insertions $\Phi_{j,k}$ and $\mathcal{O}^{(i)}$.
• Figure 3: Pictorial representation of how the non-perturbative gravitational path integral could yield Description 2. When additional, non-perturbative ingredients are taken into account, "half-wormhole"-like saddles (center figure) can contribute to the path integral Saad:2021rcuMukhametzhanov:2021neaMukhametzhanov:2021hdiGesteau:2024gzf, with the closed universe replaced by some non-semiclassical correlation. The sum of such saddles and the semiclassical saddle associated with Description 1 (left figure) could be equivalent to a Euclidean geometry without a closed universe (right figure), which would lead to Description 2.
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