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The Noether charge entropy in anti-deSitter space and its field theory dual

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Ram Brustein, Dan Gorbonos

High Energy Physics - Theory · Submitted 10 Feb 2009

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

The authors' main claim We interpret the variation of the entropy density operator from the horizon to the boundary as due to the renormalization of the effective gravitational couplings as they flow from the ultra-violet to the infra-red.

how it is stated · asserted 0.90 read the record →

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arXiv ID0902.1553 (version 3)
Pith ID7V6XGZF4, Pith's permanent record of this paper and its review
CitationDan Gorbonos, Ram Brustein. "The Noether charge entropy in anti-deSitter space and its field theory dual." arXiv:0902.1553 (2009). https://pith.science/paper/7V6XGZF4
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,951 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.36 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.46 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

We express the Noether charge entropy density of a black brane in anti-deSitter space in terms of local operators in the anti-deSitter space bulk. We find that Wald's expression for the Noether charge entropy needs to be modified away from the horizon by an additional term that vanishes on the horizon. We then determine the field theory dual of the Noether charge entropy for theories that asymptote to Einstein theory. We do so by calculating the value of the entropy density at the anti-deSitter space boundary and applying the standard rules of the AdS/CFT correspondence. We interpret the variation of the entropy density operator from the horizon to the boundary as due to the renormalization of the effective gravitational couplings as they flow from the ultra-violet to the infra-red. We discuss the cases of Einstein-Hilbert theory and f(R) theories in detail and make general comments about more complicated cases.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We express the Noether charge entropy density of a black brane in anti-deSitter space in terms of local operators in the anti-deSitter space bulk. contribution 0.92 0.94 0.20 asserted 1.00
s1 We find that Wald's expression for the Noether charge entropy needs to be modified away from the horizon by an additional term that vanishes on the horizon. result 1.00 0.94 0.31 asserted 1.00
s2 We then determine the field theory dual of the Noether charge entropy for theories that asymptote to Einstein theory. contribution 0.98 0.95 0.16 asserted 0.99
s3 We do so by calculating the value of the entropy density at the anti-deSitter space boundary and applying the standard rules of the AdS/CFT correspondence. method 1.00 0.93 0.10 asserted 0.99
s4 We interpret the variation of the entropy density operator from the horizon to the boundary as due to the renormalization of the effective gravitational couplings as they flow from the ultra-violet to the infra-red. interpretation 1.00 0.81 0.35 asserted 0.90
s5 We discuss the cases of Einstein-Hilbert theory and f(R) theories in detail and make general comments about more complicated cases. contribution 0.95 0.87 0.06 asserted 0.71

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

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  • references and citing sentences
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  • C citations
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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

We express the Noether charge entropy density of a black brane in anti-deSitter space in terms of local operators in the anti-deSitter space bulk. We find that Wald's expression for the Noether charge entropy needs to be modified away from the horizon by an additional term that vanishes on the horizon. We then determine the field theory dual of the Noether charge entropy for theories that asymptote to Einstein theory. We do so by calculating the value of the entropy density at the anti-deSitter space boundary and applying the standard rules of the AdS/CFT correspondence. We interpret the variation of the entropy density operator from the horizon to the boundary as due to the renormalization of the effective gravitational couplings as they flow from the ultra-violet to the infra-red. We discuss the cases of Einstein-Hilbert theory and f(R) theories in detail and make general comments about more complicated cases.

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How the literature uses it

5 arXiv papers cite this in 11 sentences

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

Papers citing it · 7 sentences without a confident label

Uses its method or tool 1 paper
  • Next we use Brown`s methods [ref] as applied in [ref] to show that the Lie derivative of the area of the $D-2$ hypersurface is canonically conjugate to the Wald entropy.

    Wave function of the quantum black hole · Introduction · 0.95

Cites it as support 1 paper

What it cites · 15 sentences without a confident label

Uses the method or tool of 3 papers
  • Then we can use Eq. ([ref]) to obtain the expectation value of the dual operator from the value of the conjugate momentum on the boundary after an appropriate renormalization (for details see [ref] ), [equation]

    AdS/CFT correspondence and Geometry · Conjugate variables and Hamiltonian holography · 0.96

  • Following [ref] we introduce an additional auxiliary field $P^αβ$ and treat $K_αβ$ as an independent variable, [equation] Integrating by parts the term $1/4 π G_d+1 √(-h) U^rβγrK̇_βγ$ in Eq. ([ref]) we find that the conjugate variables to [equation] are [equation]

    Black Hole Entropy and the Hamiltonian Formulation of Diffeomorphism Invariant Theories · The dual of $∂L/∂R_rbcr$ · 0.98

  • If matter fields (collectively denoted by $Φ_A$) and their covariant derivatives appear in $L$, the covariant derivatives have to be expressed in terms of the Riemann tensor prior to evaluation of the functional derivative [ref] .

    Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy · The decomposition of the action with respect to a radial hypersurface · 0.89

Cites as background 3 papers

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