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Bulk Cluster Decomposition in AdS/CFT and A No-Go Theorem for Correlators in Microstates of Extremal Black Holes

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Byungwoo Kang

High Energy Physics - Theory · Submitted 13 May 2013

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

The authors' main claim Applying the thermo-field double formalism to extremal black holes in AdS with a macroscopic horizon, we show that (1) there exists a natural basis for the degenerate microstates of an extremal black hole, and (2) cluster decomposition in the bulk implies that all correlators are exactly the same for every microstate of the extremal black hole.

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arXiv ID1305.2797 (version 2)
Pith IDMGV4TRH5, Pith's permanent record of this paper and its review
CitationByungwoo Kang. "Bulk Cluster Decomposition in AdS/CFT and A No-Go Theorem for Correlators in Microstates of Extremal Black Holes." arXiv:1305.2797 (2013). https://pith.science/paper/MGV4TRH5
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,055 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.46 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.19 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Applying the thermo-field double formalism to extremal black holes in AdS with a macroscopic horizon, we show that (1) there exists a natural basis for the degenerate microstates of an extremal black hole, and (2) cluster decomposition in the bulk implies that all correlators are exactly the same for every microstate of the extremal black hole. The latter statement can be interpreted in two ways. First, at the fully non-perturbative level of AdS/CFT at finite N, it means that cluster decomposition does not hold in the bulk. This may be viewed as a sharp manifestation of the bulk non-locality at finite N. Second, at the level of the perturbation theory in 1/N, in which case we expect the bulk cluster decomposition, no measurement of either boundary operators or bulk field operators can distinguish the different microstates. The latter interpretation may exclude some versions of the fuzzball conjecture that assert that different microstates of a black hole are realized in the bulk as different metric and field configurations.

background contribution method result interpretation main claim

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 Applying the thermo-field double formalism to extremal black holes in AdS with a macroscopic horizon, we show that (1) there exists a natural basis for the degenerate microstates of an extremal black hole, and (2) cluster decomposition in the bulk implies that all correlators are exactly the same for every microstate of the extremal black hole. result 0.91 0.92 0.88 asserted 1.00
s1 The latter statement can be interpreted in two ways. interpretation 0.99 0.29 0.04 asserted 0.79
s2 First, at the fully non-perturbative level of AdS/CFT at finite N, it means that cluster decomposition does not hold in the bulk. interpretation 1.00 0.54 0.23 asserted 0.98
s3 This may be viewed as a sharp manifestation of the bulk non-locality at finite N. interpretation 1.00 0.37 0.08 hedged possibility 0.98
s4 Second, at the level of the perturbation theory in 1/N, in which case we expect the bulk cluster decomposition, no measurement of either boundary operators or bulk field operators can distinguish the different microstates. interpretation 1.00 0.44 0.22 asserted 0.65
s5 The latter interpretation may exclude some versions of the fuzzball conjecture that assert that different microstates of a black hole are realized in the bulk as different metric and field configurations. interpretation 1.00 0.17 0.10 hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.79.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Applying the thermo-field double formalism to extremal black holes in AdS with a macroscopic horizon, we show that (1) there exists a natural basis for the degenerate microstates of an extremal black hole, and (2) cluster decomposition in the bulk implies that all correlators are exactly the same for every microstate of the extremal black hole. The latter statement can be interpreted in two ways. First, at the fully non-perturbative level of AdS/CFT at finite N, it means that cluster decomposition does not hold in the bulk. This may be viewed as a sharp manifestation of the bulk non-locality at finite N. Second, at the level of the perturbation theory in 1/N, in which case we expect the bulk cluster decomposition, no measurement of either boundary operators or bulk field operators can distinguish the different microstates. The latter interpretation may exclude some versions of the fuzzball conjecture that assert that different microstates of a black hole are realized in the bulk as different metric and field configurations.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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What it cites · 31 sentences without a confident label

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  • In [ref] , the authors argued that the probability of a large deviation from a universal value of probe correlators in microstates of the AdS Schwarzschild black hole in five dimensions is of order $e^-S∼e^-N^2$, where $S$ is the black hole entropy.

    The Library of Babel: On the origin of gravitational thermodynamics · The main argument and discussion · 1.00

Cites as support 7 papers
  • In fact, it has been shown that, for cetain ranges of charges or chemical potentials, (near-)extremal charged and/or rotating black holes with a macroscopic horizon are the dominant saddles in the zero temperature limit [ref] .[In certain cases, it has been only shown that they are locally stable due to difficulties in finding competing saddles in a given ensemble.

    Hamiltonian thermodynamics of the Reissner-Nordstr\"om-anti-de Sitter black hole · Introduction and summary · 0.97

  • In fact, it has been shown that, for cetain ranges of charges or chemical potentials, (near-)extremal charged and/or rotating black holes with a macroscopic horizon are the dominant saddles in the zero temperature limit [ref] .[In certain cases, it has been only shown that they are locally stable due to difficulties in finding competing saddles in a given ensemble.

    Thermodynamics of Reissner-Nordstrom-anti-de Sitter black holes in the grand canonical ensemble · Introduction and summary · 0.97

  • In fact, it has been shown that, for cetain ranges of charges or chemical potentials, (near-)extremal charged and/or rotating black holes with a macroscopic horizon are the dominant saddles in the zero temperature limit [ref] .[In certain cases, it has been only shown that they are locally stable due to difficulties in finding competing saddles in a given ensemble.

    Rotation and the AdS/CFT correspondence · Introduction and summary · 0.97

Cites as background 10 papers
  • Nice discussions of superradiance and its relation to the instability of rotating black holes can be found in [ref] .] The maximally extended solutions of these black holes correspond to thermo-field double states in the boundary theory at fixed charges or chemical potentials [ref] .

    Superradiance and Instability of Black Holes · Introduction and summary · 0.90

  • Nice discussions of superradiance and its relation to the instability of rotating black holes can be found in [ref] .] The maximally extended solutions of these black holes correspond to thermo-field double states in the boundary theory at fixed charges or chemical potentials [ref] .

    Instabilities of Kerr-AdS_5 x S^5 Spacetime · Introduction and summary · 0.90

  • Nice discussions of superradiance and its relation to the instability of rotating black holes can be found in [ref] .] The maximally extended solutions of these black holes correspond to thermo-field double states in the boundary theory at fixed charges or chemical potentials [ref] .

    Eternal Black Holes in AdS · Introduction and summary · 0.90

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