Extension of the HKLL bulk reconstruction for small ∆

Aoki, Sinya; Balog, J.

doi:10.1007/jhep05(2023)034

J. High Energ. Phys.

2023

DOI: 10.1007/jhep05(2023)034

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Extension of the HKLL bulk reconstruction for small ∆

Sinya Aoki

J. Balog

Abstract: We re-analyse the bulk reconstruction for a scalar field in Lorentzian AdS spacetime, both for the case of even and odd dimensions, for an extended range of conformal dimensions where the original HKLL reconstruction has to be modified. We also discuss the use of space-like Green’s functions in the bulk reconstruction. We demonstrate that in the extended range also the singular part of the Green’s function, omitted in the original papers, has be included. The results are particularly simple and physically inte… Show more

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2024

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Cited by 2 publications

References 25 publications

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Bulk modified gravity from a thermal CFT by the conformal flow

Aoki,

Shimada,

Balog

et al. 2024

Phys. Rev. D

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We construct a bulk spacetime from a boundary conformal field theory, O(N) free scalar model, at finite temperature using a smearing technique, called a conformal flow. The bulk metric is constructed from the thermal two-point function of the smeared boundary elementary field in such a way that it can be interpreted as an information metric associated with the boundary thermofield double state. Near the boundary (UV region), an asymptotically anti–de Sitter (AdS) spacetime is obtained with a leading order perturbation of scalar mode. Based on the falloff behavior of the perturbations and the O(N) symmetry in the conformal field theory, we argue that the corresponding bulk theory is a modified gravity with scalar mode such as f(R) gravity rather than Einstein’s general relativity coupled minimally to matter fields. Moving to the Einstein frame, we show that the metric is asymptotically the same as the AdS black brane solution. On the other hand, deep in the bulk (IR region), the spacetime turns out to be conformally equivalent to the near horizon limit of AdS extremal black brane, though it is no longer a solution of f(R) gravity, and hence more general classes of modified gravity need to be considered. Published by the American Physical Society 2024

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Bulk modified gravity from a thermal CFT by the conformal flow

Aoki,

Shimada,

Balog

et al. 2024

Phys. Rev. D

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CFT reconstruction of local bulk operators in half-Minkowski space

Bhattacharyya,

Dogra,

Roy

2024

Phys. Rev. D

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We construct a holographic map that reconstructs massless fields (scalars, Maxwell field, and Fierz-Pauli field) in half-Minkowski spacetime in d+1 dimensions terms of smeared primary operators in a large-N factorizable CFT in Rd−1,1. This map is based on a Weyl (rescaling) transformation from the Poincaré wedge of AdS to the Minkowski half-space and on the Hamilton-Kabat-Lifschytz-Lowe smearing function, which reconstructs local bulk operators in the Poincaré AdS in terms of smeared operators on the conformal boundary of the Poincaré wedge. The massless scalar field is reconstructed up to the level of two-point functions, while the Maxwell field and massless spin-2 fields are reconstructed at the level of the one-point function. We also discuss potential ways the map can be generalized to higher dimensions, and to the full Minkowski space. Published by the American Physical Society 2024

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Extension of the HKLL bulk reconstruction for small ∆

Cited by 2 publications

References 25 publications

Bulk modified gravity from a thermal CFT by the conformal flow

Bulk modified gravity from a thermal CFT by the conformal flow

CFT reconstruction of local bulk operators in half-Minkowski space

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