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Do holographic CFT states have unique semiclassical bulk duals?

Antonini, Stefano, Rath, Pratik·2025·International Journal of Modern Physics D
DOI 10.1142/s0218271825440250
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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 is perfectly satisfactory. We also discuss what this implies for the black hole interior and the gravitational path integral.

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Figures

FIG. 1 The Euclidean saddle computing ⟨ Ψ i | Ψ 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 [35].
FIG. 1 The Euclidean saddle computing ⟨ Ψ i | Ψ 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 [35].CC-BY · From the PDF
FIG. 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 ( i ) jk can be computed using the CFT path integral on a Riemann surface with operator insertions Φ j,k and O ( i ) .
FIG. 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 ( i ) jk can be computed using the CFT path integral on a Riemann surface with operator insertions Φ j,k and O ( i ) .CC-BY · From the PDF
Image 3
CC-BY · From the PDF
FIG. 3 Pictorial representation of how the non-perturbative gravitational path integral could yield Description 2. When additional, non-perturbative ingredients are taken into account, 'halfwormhole'-like saddles (center figure) can contribute to the path integral [14-17], 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.
FIG. 3 Pictorial representation of how the non-perturbative gravitational path integral could yield Description 2. When additional, non-perturbative ingredients are taken into account, 'halfwormhole'-like saddles (center figure) can contribute to the path integral [14-17], 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.CC-BY · From the PDF

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Research works printed but not linked: 42

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Metadata

Authors
Antonini, S., & Rath, P.
Venue
International Journal of Modern Physics D
Publisher
World Scientific Pub Co Pte Ltd
Published
2025-09-29
Volume
34
Issue
16
ISSN
  • 0218-2718
  • 1793-6594
DOI
10.1142/s0218271825440250
Cited by
18
References
7
Language
en
Funders
  • the Department of Energy, Office of Science, Office of High Energy Physics (DE-SC0019380)
  • the U.S. Department of Energy (DE-FOA-0002563)

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