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Refined Topological Strings on Local $\mathbb{P}^2$

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Amer Iqbal, Can Kozcaz

High Energy Physics - Theory · Submitted 10 Oct 2012

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

The authors' main claim We calculate the refined topological string partition function of the Calabi-Yau threefold which is the total space of the canonical bundle on $\mathbb{P}^2$ (the local $\mathbb{P}^2$).

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arXiv ID1210.3016 (version 2)
Pith IDX2M32VVQ, Pith's permanent record of this paper and its review
CitationAmer Iqbal, Can Kozcaz. "Refined Topological Strings on Local $\mathbb{P}^2$." arXiv:1210.3016 (2012). https://pith.science/paper/X2M32VVQ
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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, 2,438 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.71 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.23 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We calculate the refined topological string partition function of the Calabi-Yau threefold which is the total space of the canonical bundle on $\mathbb{P}^2$ (the local $\mathbb{P}^2$). The refined topological vertex formalism can not be directly applied to local $\mathbb{P}^2$ therefore we use the properties of the refined Hopf link to define a new two legged vertex which together with the refined vertex gives the partition function of the local $\mathbb{P}^2$.

background contribution method result interpretation main claim

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We calculate the refined topological string partition function of the Calabi-Yau threefold which is the total space of the canonical bundle on $\mathbb{P}^2$ (the local $\mathbb{P}^2$). contribution 0.83 0.96 0.51 asserted 1.00
s1 The refined topological vertex formalism can not be directly applied to local $\mathbb{P}^2$ therefore we use the properties of the refined Hopf link to define a new two legged vertex which together with the refined vertex gives the partition function of the local $\mathbb{P}^2$. method 0.89 0.89 0.31 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.76 · evidence from proof or derivation 0.98.

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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 calculate the refined topological string partition function of the Calabi-Yau threefold which is the total space of the canonical bundle on $\mathbb{P}^2$ (the local $\mathbb{P}^2$). The refined topological vertex formalism can not be directly applied to local $\mathbb{P}^2$ therefore we use the properties of the refined Hopf link to define a new two legged vertex which together with the refined vertex gives the partition function of the local $\mathbb{P}^2$.

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References
How the literature uses it

22 arXiv papers cite this in 38 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 · 19 sentences without a confident label

Uses its method or tool 9 papers
  • The combinatorial formula used in Theorem [ref] is assembled from the rank-two refined-vertex–Nekrasov fixed-point partition identity of Taki and Awata–Kanno [ref] and the local-\(𝔽_1\)-to-local-\(ℙ^2\) transition of Iqbal–Kozçaz [ref] .

    Topological String Blowup Equations via Stable Pairs · The contraction to local P2 · 0.81

  • The same web diagram specifies the toric Calabi–Yau 3-fold of the compactified M-theory dual to the 5-brane web, and then we calculate the 5d Nekrasov partition function [ref] using the topological string method [ref] known as the topological vertex [ref] through geometric engineering [ref] .

    Tao Probing the End of the World · Introduction · 0.98

  • A trick is that when we divide it by partition function of the resolved conifold, namely Z̃_(3)(Q_B, Q̃_1, Q̃_2) = Z_(3)(Q_B^-1, Q̃_1Q_B, Q̃_2Q_B) /ℋ(Q_B^-1)^-1 then the terms with negative power of $Q_B$ disappears [ref] .

    5d/6d DE instantons from trivalent gluing of web diagrams · $𝒪(-3)$ model · 0.93

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Cites it as background 5 papers

What it cites · 15 sentences without a confident label

Uses the method or tool of 1 paper
  • Since the two Schur functions in the summation above have the same argument we can use s_λ(x) s_μ(x)=∑_ηN^η_λ μs_η(x), to write the normalized open amplitude as [equation] Following [ref] , we express the Schur function in terms of Macdonald function to obtain H_η(Q,t,q) = ∑_σU_η σ(q,t)J_σ(Q,t,q) J_σ(Q,t,q) ∑_ν (-Q)^|ν| q^ν^2/2 t^ν^t^2/2 Z_ν(t,q) Z_ν^t(q,t) P_σ(t^-ρq^-ν;q,t), where the $U_η σ(q,t)$ are the previously defined matrices which take Macdonald functions to Schur functions.

    Macdonald operators and homological invariants of the colored Hopf link · Derivation of the two-legged new vertex · 0.99

Cites as background 7 papers

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