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Wormholes from heavy operator statistics in AdS/CFT

Sasieta, Martin·2023·Journal of High Energy Physics
DOI 10.1007/jhep03(2023)158
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Abstract

We construct higher dimensional Euclidean AdS wormhole solutions that reproduce the statistical description of the correlation functions of an ensemble of heavy CFT operators. We consider an operator which effectively backreacts on the geometry in the form of a thin shell of dust particles. Assuming dynamical chaos in the form of the ETH ansatz, we demonstrate that the semiclassical path integral provides an effective statistical description of the microscopic features of the thin shell operator in the CFT. The Euclidean wormhole solutions provide microcanonical saddlepoint contributions to the cumulants of the correlation functions over the ensemble of operators. We finally elaborate on the role of these wormholes in the context of non-perturbative violations of bulk global symmetries in AdS/CFT.

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Figures

Figure 1 Geometry of the saddlepoint manifold X for τ ∈ [0 , β/ 2] . The case a ) for τ < τ c , in which the right patch X + does not include the tip of the right disk. The case b ) for τ > τ c , in which the solution includes both tips.
Figure 1 Geometry of the saddlepoint manifold X for τ ∈ [0 , β/ 2] . The case a ) for τ < τ c , in which the right patch X + does not include the tip of the right disk. The case b ) for τ > τ c , in which the solution includes both tips.CC-BY · From the PDF
Figure 2 The different regions in the decomposition of the gravitational action I [ X ] . The green region X s accounts for the intrinsic contribution from the shell.
Figure 2 The different regions in the decomposition of the gravitational action I [ X ] . The green region X s accounts for the intrinsic contribution from the shell.CC-BY · From the PDF
Figure 3 The numerical value of the envelope function as a function of the energy difference | ω | for the thin shell operator in d = 2 . In this case the critical value is ω c = Gm 2 ∼ m , independent of ¯ E .
Figure 3 The numerical value of the envelope function as a function of the energy difference | ω | for the thin shell operator in d = 2 . In this case the critical value is ω c = Gm 2 ∼ m , independent of ¯ E .CC-BY · From the PDF
Figure 4 The wormhole X is deconstructed on the left figure. It corresponds to a portion of an Euclidean black hole, cut by the trajectories of two thin shells, which are then identified. On the right, the resulting R × S 1 × S d -1 topology connecting both boundaries. The mass M of the wormhole only depends on the combination β + β ′ .
Figure 4 The wormhole X is deconstructed on the left figure. It corresponds to a portion of an Euclidean black hole, cut by the trajectories of two thin shells, which are then identified. On the right, the resulting R × S 1 × S d -1 topology connecting both boundaries. The mass M of the wormhole only depends on the combination β + β ′ .CC-BY · From the PDF
Figure 5 Renormalized action of the wormhole ∆ I [ X ] as a function of the temperature, for d = 2 . The Hawking-Page transition at β HP = 2 π affects the normalization of the amplitude.
Figure 5 Renormalized action of the wormhole ∆ I [ X ] as a function of the temperature, for d = 2 . The Hawking-Page transition at β HP = 2 π affects the normalization of the amplitude.CC-BY · From the PDF
Figure 6 Deconstruction of the AdS wormhole. The geometry corresponds to a portion of Euclidean AdS, cut by the trajectories of two thin shells, which are then identified. The periodicity β AdS of the AdS solution only depends on the combination β + β ′ .
Figure 6 Deconstruction of the AdS wormhole. The geometry corresponds to a portion of Euclidean AdS, cut by the trajectories of two thin shells, which are then identified. The periodicity β AdS of the AdS solution only depends on the combination β + β ′ .CC-BY · From the PDF
Figure 7 There is an exchange in dominance between the black wormhole X bh and the AdS wormhole X AdS , at β = β ′ HP . In d = 2 , we have numerically checked that β ′ HP ≥ 2 π , and d β ′ HP / d m> 0 .
Figure 7 There is an exchange in dominance between the black wormhole X bh and the AdS wormhole X AdS , at β = β ′ HP . In d = 2 , we have numerically checked that β ′ HP ≥ 2 π , and d β ′ HP / d m> 0 .CC-BY · From the PDF
Figure 8 The two-point wormhole is deconstructed on the left figure. It corresponds to a pair of Euclidean black holes, glued together by the trajectories of two thin shells. On the right, the resulting R × S 1 × S d -1 topology connecting both boundaries.
Figure 8 The two-point wormhole is deconstructed on the left figure. It corresponds to a pair of Euclidean black holes, glued together by the trajectories of two thin shells. On the right, the resulting R × S 1 × S d -1 topology connecting both boundaries.CC-BY · From the PDF
Figure 9 Three-boundary wormhole X (3) bh constructed by gluing two Euclidean black holes of masses M ± along the trajectories of three thin shells.
Figure 9 Three-boundary wormhole X (3) bh constructed by gluing two Euclidean black holes of masses M ± along the trajectories of three thin shells.CC-BY · From the PDF
Figure 10 Saddlepoint manifold X for τ < τ c .
Figure 10 Saddlepoint manifold X for τ < τ c .CC-BY · From the PDF

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Metadata

Authors
Sasieta, M.
Venue
Journal of High Energy Physics
Publisher
Springer Science and Business Media LLC
Published
2023-03-21
Volume
2023
Issue
3
ISSN
1029-8479
DOI
10.1007/jhep03(2023)158
Cited by
43
References
6
Language
en
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Sasieta, M. (2023). Wormholes from heavy operator statistics in AdS/CFT. Journal of High Energy Physics. https://doi.org/10.1007/jhep03(2023)158