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Entanglement Entropy on Fuzzy Spaces

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Djamel Dou, Badis Ydri

General Relativity and Quantum Cosmology · Submitted 29 Apr 2006

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

The authors' main claim In both models we evaluate numerically the resulting entropies and find that they are proportional to the number of boundary degrees of freedom.

how it is stated · asserted 1.00 read the record →

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arXiv IDgr-qc/0605003 (version 3)
Pith IDMKJ546C5, Pith's permanent record of this paper and its review
CitationBadis Ydri, Djamel Dou. "Entanglement Entropy on Fuzzy Spaces." arXiv:gr-qc/0605003 (2006). https://pith.science/paper/MKJ546C5
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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, 4,218 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.70 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.29 · compares with prior results 0.11 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We study the entanglement entropy of a scalar filed in 2+1 spacetime where space is modeled by a fuzzy sphere and a fuzzy disc. In both models we evaluate numerically the resulting entropies and find that they are proportional to the number of boundary degrees of freedom. In the Moyal plan limit of the fuzzy disc the entanglement entropy per unit area (length) diverges if the ignored region is of infinite size. The divergence is (interpreted) of IR-UV mixing origin. In general we expect the entanglement entropy per unit area to be finite on a non-commutative space if the ignored region is of finite size.

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 study the entanglement entropy of a scalar filed in 2+1 spacetime where space is modeled by a fuzzy sphere and a fuzzy disc. contribution 0.96 0.92 0.05 asserted 0.95
s1 In both models we evaluate numerically the resulting entropies and find that they are proportional to the number of boundary degrees of freedom. result 0.99 0.96 0.58 asserted 1.00
s2 In the Moyal plan limit of the fuzzy disc the entanglement entropy per unit area (length) diverges if the ignored region is of infinite size. result 1.00 0.82 0.14 asserted 1.00
s3 The divergence is (interpreted) of IR-UV mixing origin. interpretation 1.00 0.51 0.12 asserted 0.67
s4 In general we expect the entanglement entropy per unit area to be finite on a non-commutative space if the ignored region is of finite size. interpretation 0.91 0.19 0.32 hedged possibility 0.51

What kind of paper the classifier reports this is: simulation study 0.86 · evidence from simulation or computation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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 study the entanglement entropy of a scalar filed in 2+1 spacetime where space is modeled by a fuzzy sphere and a fuzzy disc. In both models we evaluate numerically the resulting entropies and find that they are proportional to the number of boundary degrees of freedom. In the Moyal plan limit of the fuzzy disc the entanglement entropy per unit area (length) diverges if the ignored region is of infinite size. The divergence is (interpreted) of IR-UV mixing origin. In general we expect the entanglement entropy per unit area to be finite on a non-commutative space if the ignored region is of finite size.

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References
How the literature uses it

9 arXiv papers cite this in 14 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 · 10 sentences without a confident label

Compares with it 1 paper
  • Previous works on the entanglement of a free field on a fuzzy sphere involved similar wavefunctions but a different factorization of the Hilbert space, which was inspired instead by coherent states [ref] .

    Deep Quantum Geometry of Matrices · Fuzzy sphere in the mini-BMN model · 0.96

Cites it as background 3 papers

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