Scanning Tunneling Macroscopy, Black Holes, and AdS/CFT Bulk Locality

Soo-Jong Rey; Vladimir Rosenhaus

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Scanning Tunneling Macroscopy, Black Holes, and AdS/CFT Bulk Locality

Soo-Jong Rey, Vladimir Rosenhaus

High Energy Physics - Theory · Submitted 16 Mar 2014

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Our results demonstrate that, if there is a black hole of any size in the bulk, then sub-AdS bulk locality is no longer well-encoded in boundary data in terms of local CFT operators.

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What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.73 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.72 · compares with prior results 0.19 · mentions code or data availability 0.01.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We establish resolution bounds on reconstructing a bulk field from boundary data on a timelike hypersurface. If the bulk only supports propagating modes, reconstruction is complete. If the bulk also supports evanescent modes, local reconstruction is not achievable unless one has exponential precision in knowledge of the boundary data. Without exponential precision, for a Minkowski bulk, one can reconstruct a spatially coarse-grained bulk field, but only out to a depth set by the coarse-graining scale. For an asymptotically AdS bulk, reconstruction is limited to a spatial coarse-graining proper distance set by the AdS scale. AdS black holes admit evanescent modes. We study the resolution bound in the large AdS black hole background and provide a dual CFT interpretation. Our results demonstrate that, if there is a black hole of any size in the bulk, then sub-AdS bulk locality is no longer well-encoded in boundary data in terms of local CFT operators. Specifically, in order to probe the bulk on sub-AdS scales using only boundary data in terms of local operators, one must either have such data to exponential precision or make further assumptions about the bulk state.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We establish resolution bounds on reconstructing a bulk field from boundary data on a timelike hypersurface.	contribution 0.92	0.93	0.11	asserted 1.00
s1	If the bulk only supports propagating modes, reconstruction is complete.	result 1.00	0.71	0.05	asserted 1.00
s2	If the bulk also supports evanescent modes, local reconstruction is not achievable unless one has exponential precision in knowledge of the boundary data.	result 0.99	0.68	0.17	asserted 0.99
s3	Without exponential precision, for a Minkowski bulk, one can reconstruct a spatially coarse-grained bulk field, but only out to a depth set by the coarse-graining scale.	result 0.99	0.77	0.06	asserted 0.72
s4	For an asymptotically AdS bulk, reconstruction is limited to a spatial coarse-graining proper distance set by the AdS scale.	result 0.99	0.76	0.09	asserted 1.00
s5	AdS black holes admit evanescent modes.	background 0.66	0.26	0.03	asserted 1.00
s6	We study the resolution bound in the large AdS black hole background and provide a dual CFT interpretation.	contribution 1.00	0.93	0.06	asserted 0.84
s7	Our results demonstrate that, if there is a black hole of any size in the bulk, then sub-AdS bulk locality is no longer well-encoded in boundary data in terms of local CFT operators.	result 0.57	0.85	0.86	asserted 1.00
s8	Specifically, in order to probe the bulk on sub-AdS scales using only boundary data in terms of local operators, one must either have such data to exponential precision or make further assumptions about the bulk state.	result 0.53	0.77	0.39	asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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The paper

Original abstract

We establish resolution bounds on reconstructing a bulk field from boundary data on a timelike hypersurface. If the bulk only supports propagating modes, reconstruction is complete. If the bulk also supports evanescent modes, local reconstruction is not achievable unless one has exponential precision in knowledge of the boundary data. Without exponential precision, for a Minkowski bulk, one can reconstruct a spatially coarse-grained bulk field, but only out to a depth set by the coarse-graining scale. For an asymptotically AdS bulk, reconstruction is limited to a spatial coarse-graining proper distance set by the AdS scale. AdS black holes admit evanescent modes. We study the resolution bound in the large AdS black hole background and provide a dual CFT interpretation. Our results demonstrate that, if there is a black hole of any size in the bulk, then sub-AdS bulk locality is no longer well-encoded in boundary data in terms of local CFT operators. Specifically, in order to probe the bulk on sub-AdS scales using only boundary data in terms of local operators, one must either have such data to exponential precision or make further assumptions about the bulk state.

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References

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Bulk Locality and Quantum Error Correction in AdS/CFT
hep-th 2014-11 accept novelty 8.0 of 10

The AdS-Rindler reconstruction of bulk fields is dual, on the boundary, to operator algebra quantum error correction, so bulk locality is a property of a protected code subspace rather than an operator identity.
Islands with Gravitating Baths: Towards ER = EPR
hep-th 2021-03 conditional novelty 7.0 of 10

In a two-dimensional JT gravity toy model, strong entanglement between two black holes flips the dominant saddle from two disconnected geometries to a single wormhole-connected one, realising ER=EPR in the static case...
Gravitational Reconstruction in $AdS_{4}$
hep-th 2026-10 accept novelty 6.0 of 10

The authors give explicit real-space boundary-to-bulk kernels for linearized gravitons in AdS4, covering spacelike boundary momentum, zero frequency, and curved conformally flat boundary frames, with the normalizable ...

How the literature uses it

21 arXiv papers cite this in 39 sentences

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Papers citing it · 28 sentences without a confident label

Contests it 1 paper

It was immediately realized, however, that in fact this expression for $K$ is not well-defined [ref] (see also [ref] ); the reason is that from Stirling's formula it is straightforward to see that at large $λ$ we have |N_ωλ|^2∼e^-π√(λ).

Bulk Locality and Quantum Error Correction in AdS/CFT · More details on AdS-Rindler reconstruction · contest 0.83

Uses its method or tool 1 paper

Following [ref] we consider a minimally coupled scalar field $Φ$ on a static spherically symmetric geometry described by the line element [equation] The Klein-Gordon equation in this background can be solved by separation of variables, $Φ(t,Ω,r)=e^-iωtY(Ω)ϕ(r)$, and with $d$ denoting the spatial dimension, the radial equation takes the form [equation] which is conveniently rewritten by replacing $ϕ(r)=u(r)/r^d-1/2$ and using “tortoise” coordinates, $r_*=r/f$: [equation] where the effective potential $V$ is given by [equation] The advantage of these coordinates is that we recognise the form of the radial time-independent Schrödinger equation, and can invoke our intuition about its solutions.

Quenched coupling, entangled equilibria, and correlated composite operators: a tale of two O(N) models · Effective potential for scalar waves around black holes · 0.91

Compares with it 3 papers

The results described in Section [ref] have an interesting counterpart in so-called evanescent modes in gravitational theories dual to strongly coupled gauge theories [ref] .

Quenched coupling, entangled equilibria, and correlated composite operators: a tale of two O(N) models · Horizon detection · 0.82
This potential shape is very similar to the case of a large black hole discussed in [ref] .

Thermofield Duality for Higher Spin Rindler Gravity · Evanescent Modes in Rindler-AdS · 1.00
Apart from some leading constants, the important part of this result for us is that in the large-k limit, the two-point function scales like $e^-αβk 2$ where[A similar factor appears in [ref] , although our expression is different.

A Bound on Thermal Relativistic Correlators at Large Spacelike Momenta · Two-point functions · 1.00

Cites it as support 1 paper

To reconstruct the bulk on sub-AdS scales, one would need to measure the boundary data to exponential precision [ref] .

Bulk-Boundary Duality, Gauge Invariance, and Quantum Error Correction · Free-field precursors · 0.97

Cites it as background 4 papers

Wave propagation in an AdS black hole background in standard gravity theory includes so called evanescent modes with an exponential fall-off towards the boundary whose existence is tied to the event horizon in the bulk spacetime geometry [ref] .

Black holes from large N singlet models · Evanescent modes · 0.93
We also give some relevant properties of this spacetime such as the presence of “evanescent” modes [ref] whose CFT reconstruction will be of particular interest.

Thermofield Duality for Higher Spin Rindler Gravity · Introduction · 0.88
For example, there has been some debate in the literature on highly spacelike modes [ref] where the ratio of value of the mode function near the horizon to its value at the boundary can vary exponentially with temperature.

Comments on the Necessity and Implications of State-Dependence in the Black Hole Interior · A state-independent mini-superspace bulk-boundary map outside the horizon · 0.83

What it cites · 12 sentences without a confident label

Cites as background 13 papers

Finding which CFT quantities encode the bulk and, if so, in what ways have been actively pursued recently, e.g. [ref] .

Bulk and Transhorizon Measurements in AdS/CFT · Introduction · 1.00
Finding which CFT quantities encode the bulk and, if so, in what ways have been actively pursued recently, e.g. [ref] .

Null Geodesics, Local CFT Operators and AdS/CFT for Subregions · Introduction · 1.00
Finding which CFT quantities encode the bulk and, if so, in what ways have been actively pursued recently, e.g. [ref] .

AdS black holes, the bulk-boundary dictionary, and smearing functions · Introduction · 1.00

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