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Open String Invariants and Mirror Curve of the Resolved Conifold

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Jian Zhou

Algebraic Geometry · Submitted 4 Jan 2010

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

The authors' main claim This establishes local mirror symmetry for the resolved confolds for holomorphic disc invariants.

how it is stated · asserted 1.00 read the record →

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arXiv ID1001.0447 (version 1)
Pith IDWB3POENR, Pith's permanent record of this paper and its review
CitationJian Zhou. "Open String Invariants and Mirror Curve of the Resolved Conifold." arXiv:1001.0447 (2010). https://pith.science/paper/WB3POENR
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,646 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.41 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; .

For the resolved conifold with one outer D-brane in arbitrary framing, we present some results for the open string partition functions obtained by some operator manipulations. We prove some conjectures by Aganagic-Vafa and Aganagic-Klemm-Vafa that relates such invariants to the mirror curve of the resolved conifold. This establishes local mirror symmetry for the resolved confolds for holomorphic disc invariants. We also verify an integrality conjecture of such invariants by Ooguri-Vafa in this case and present closed formulas for some Ooguri-Vafa type invariants in genus 0 and arbitrary genera.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 For the resolved conifold with one outer D-brane in arbitrary framing, we present some results for the open string partition functions obtained by some operator manipulations. contribution 0.95 0.92 0.08 asserted 0.96
s1 We prove some conjectures by Aganagic-Vafa and Aganagic-Klemm-Vafa that relates such invariants to the mirror curve of the resolved conifold. result 0.61 0.90 0.34 asserted 1.00
s2 This establishes local mirror symmetry for the resolved confolds for holomorphic disc invariants. interpretation 0.92 0.80 0.58 asserted 1.00
s3 We also verify an integrality conjecture of such invariants by Ooguri-Vafa in this case and present closed formulas for some Ooguri-Vafa type invariants in genus 0 and arbitrary genera. result 0.82 0.93 0.13 asserted 1.00

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

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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

For the resolved conifold with one outer D-brane in arbitrary framing, we present some results for the open string partition functions obtained by some operator manipulations. We prove some conjectures by Aganagic-Vafa and Aganagic-Klemm-Vafa that relates such invariants to the mirror curve of the resolved conifold. This establishes local mirror symmetry for the resolved confolds for holomorphic disc invariants. We also verify an integrality conjecture of such invariants by Ooguri-Vafa in this case and present closed formulas for some Ooguri-Vafa type invariants in genus 0 and arbitrary genera.

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References
How the literature uses it

5 arXiv papers cite this in 7 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 · 3 sentences without a confident label

Uses its method or tool 1 paper
Cites it as background 3 papers

What it cites · 18 sentences without a confident label

Builds on 3 papers
  • This was extended by Aganagic, Klemm and Vafa [ref] to include the effect of framing, and the case of the resolved conifold was treated in [ref] .

    Disk Instantons, Mirror Symmetry and the Duality Web · Introduction · 0.85

  • Bouchard, Klemm, Mariño, Pasquetti [ref] extended this proposal to more general setting based on [ref] , including some conjectures on the framing transformation and the effects of phase changes of the D-branes.

    Remodeling the B-model · Introduction · 0.91

  • This recovers and generalizes some results by Aganagic-Vafa [ref] , Aganagic-Klemm-Vaf [ref] and Mariño-Vafa [ref] .

    Mirror Symmetry, D-Branes and Counting Holomorphic Discs · Ooguri-Vafa Integrality for One-Point Functions · 0.99

Uses the method or tool of 6 papers
  • By the theory of the topological vertex [ref] , the open string amplitude for the resolved conifold with one outer brane and framing $a$ can be computed as follows: Z^(a)(λ; t; ) = ∑_μ, ν, η q^a κ_μ/2 C_(0), μ, ν^t(q) ·Q^|ν| ·C_ν,(0), (0)(q) ·χ_μ(η)/z_η√(-1)^l(η) p_η(x), where $q = e^√(-1)λ$ and $Q = - e^-t$.

    The Topological Vertex · Open string amplitudes by the topological vertex · 0.98

  • In this work we will study it as the first nontrivial local Calabi-Yau geometries for which we try to establish local mirror symmetry in the new formalism of the local B-theory [ref] , which involves open string invariants.

    Open string amplitudes and large order behavior in topological string theory · Introduction · 0.89

  • In this work we will study it as the first nontrivial local Calabi-Yau geometries for which we try to establish local mirror symmetry in the new formalism of the local B-theory [ref] , which involves open string invariants.

    Remodeling the B-model · Introduction · 0.89

Compares with 1 paper
Cites as background 10 papers
  • For open string, Aganagic and Vafa [ref] conjectured a relationship between genus $0$ open string invariants and the equation for the mirror curve given by the Hori-Iqbal-Vafa construction [ref] .

    D-Branes And Mirror Symmetry · Introduction · 0.87

  • For open string, Aganagic and Vafa [ref] conjectured a relationship between genus $0$ open string invariants and the equation for the mirror curve given by the Hori-Iqbal-Vafa construction [ref] .

    Mirror Symmetry, D-Branes and Counting Holomorphic Discs · Introduction · 0.87

  • Extending results in the theory of matrix models, Eynard-Orantin [ref] developed a formalism that recursively defines some differentials from a plane algebraic curve.

    Invariants of algebraic curves and topological expansion · Introduction · 0.82

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