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Derived Categories and Zero-Brane Stability

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Paul S. Aspinwall, Albion Lawrence

High Energy Physics - Theory · Submitted 17 Apr 2001

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

The authors' main claim We then argue that any 0-brane on any Calabi-Yau threefold must become unstable along some path in the Kahler moduli space.

how it is stated · asserted 0.91 read the record →

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arXiv IDhep-th/0104147 (version 3)
Pith IDT2JMWTY3, Pith's permanent record of this paper and its review
CitationAlbion Lawrence, Paul S. Aspinwall. "Derived Categories and Zero-Brane Stability." arXiv:hep-th/0104147 (2001). https://pith.science/paper/T2JMWTY3
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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, 3,556 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.75 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We define a particular class of topological field theories associated to open strings and prove the resulting D-branes and open strings form the bounded derived category of coherent sheaves. This derivation is a variant of some ideas proposed recently by Douglas. We then argue that any 0-brane on any Calabi-Yau threefold must become unstable along some path in the Kahler moduli space. As a byproduct of this analysis we see how the derived category can be invariant under a birational transformation between Calabi-Yaus.

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 define a particular class of topological field theories associated to open strings and prove the resulting D-branes and open strings form the bounded derived category of coherent sheaves. contribution 0.89 0.95 0.50 asserted 1.00
s1 This derivation is a variant of some ideas proposed recently by Douglas. background 0.94 0.18 0.03 asserted 0.94
s2 We then argue that any 0-brane on any Calabi-Yau threefold must become unstable along some path in the Kahler moduli space. result 0.95 0.85 0.63 asserted 0.91
s3 As a byproduct of this analysis we see how the derived category can be invariant under a birational transformation between Calabi-Yaus. result 0.88 0.88 0.09 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.96.

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
levels run
  • 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 define a particular class of topological field theories associated to open strings and prove the resulting D-branes and open strings form the bounded derived category of coherent sheaves. This derivation is a variant of some ideas proposed recently by Douglas. We then argue that any 0-brane on any Calabi-Yau threefold must become unstable along some path in the Kahler moduli space. As a byproduct of this analysis we see how the derived category can be invariant under a birational transformation between Calabi-Yaus.

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References
How the literature uses it

19 arXiv papers cite this in 22 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 · 11 sentences without a confident label

Compares with it 1 paper
  • To conclude, we will briefly discuss the relation to two previous constructions, those of Aspinwall and Lawrence [ref] and of Diaconescu [ref] .

    Topological D-branes from Descent · Previous constructions · 0.93

Cites it as background 9 papers
  • At large volume for instance B-type D-branes have a geometric realisation in terms of bounded complexes of coherent sheaves on the target space [ref] , and as mentioned above, using target space geometric arguments one can determine their monodromies around the singular points in Kähler moduli space.

    Defects and D-Brane Monodromies · D-brane Monodromies in Kähler moduli space · 0.81

  • In the large volume limit, D-branes on a Calabi-Yau threefold $X$ can be viewed as objects in the derived category of coherent sheaves $(X)$ [ref] .

    Vafa-Witten invariants from exceptional collections · D-branes and coherent sheaves · 0.99

  • Their topological properties are encoded in D-brane categories [ref] whose objects and morphisms describe branes and open strings, respectively.

    Matrix factorisations and open topological string theory · Introduction · 0.91

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