Geometric Transitions, del Pezzo Surfaces and Open String Instantons

Antonella Grassi; Bogdan Florea; Duiliu-Emanuel Diaconescu

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Geometric Transitions, del Pezzo Surfaces and Open String Instantons

Duiliu-Emanuel Diaconescu, Bogdan Florea, Antonella Grassi

High Energy Physics - Theory · Submitted 18 Jun 2002

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

The authors' main claim This yields a striking conjecture relating the topological amplitudes of all genus of the local del Pezzo model to a system of coupled Chern-Simons theories.

how it is stated · speculative 0.89 read the record →

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arXiv IDhep-th/0206163 (version 6)

Pith ID7JSARZEN, Pith's permanent record of this paper and its review

CitationAntonella Grassi, Bogdan Florea, Duiliu-Emanuel Diaconescu. "Geometric Transitions, del Pezzo Surfaces and Open String Instantons." arXiv:hep-th/0206163 (2002). https://pith.science/paper/7JSARZEN

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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, 3,667 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.28 · mentions code or data availability 0.02.

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arXiv listing abstract v6. Results and the main claim are underlined; show every role.

We continue the study of a class of geometric transitions proposed by Aganagic and Vafa which exhibit open string instanton corrections to Chern-Simons theory. In this paper we consider an extremal transition for a local del Pezzo model which predicts a highly nontrivial relation between topological open and closed string amplitudes. We show that the open string amplitudes can be computed exactly using a combination of enumerative techniques and Chern-Simons theory proposed by Witten some time ago. This yields a striking conjecture relating the topological amplitudes of all genus of the local del Pezzo model to a system of coupled Chern-Simons theories.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We continue the study of a class of geometric transitions proposed by Aganagic and Vafa which exhibit open string instanton corrections to Chern-Simons theory.	background 0.97	0.32	0.04	asserted 0.89
s1	In this paper we consider an extremal transition for a local del Pezzo model which predicts a highly nontrivial relation between topological open and closed string amplitudes.	contribution 0.98	0.56	0.18	asserted 0.75
s2	We show that the open string amplitudes can be computed exactly using a combination of enumerative techniques and Chern-Simons theory proposed by Witten some time ago.	method 0.78	0.90	0.15	asserted 1.00
s3	This yields a striking conjecture relating the topological amplitudes of all genus of the local del Pezzo model to a system of coupled Chern-Simons theories.	result 0.66	0.67	0.75	speculative 0.89

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.93.

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arXiv listing abstract v6

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full text
figures and tables
references and citing sentences
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P abstract

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S sections
T body sentences
C citations
R cross-paper relations

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The paper

Original abstract

We continue the study of a class of geometric transitions proposed by Aganagic and Vafa which exhibit open string instanton corrections to Chern-Simons theory. In this paper we consider an extremal transition for a local del Pezzo model which predicts a highly nontrivial relation between topological open and closed string amplitudes. We show that the open string amplitudes can be computed exactly using a combination of enumerative techniques and Chern-Simons theory proposed by Witten some time ago. This yields a striking conjecture relating the topological amplitudes of all genus of the local del Pezzo model to a system of coupled Chern-Simons theories.

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References

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Matrix Models, Topological Strings, and Supersymmetric Gauge Theories
hep-th 2002-06 accept novelty 8.0 of 10

The planar limit of a one-matrix model with potential W(x) reproduces the special geometry of the B-model topological string on the local Calabi-Yau uv + y^2 + W'(x)^2 + f(x) = 0, with the matrix filling fractions ide...
Matrix Models, Geometric Engineering and Elliptic Genera
hep-th 2003-10 accept novelty 7.0 of 10

For N=2* theory compactified from six to four dimensions on a torus, matrix models, geometric engineering via the topological vertex, and elliptic-genus instanton calculus all yield the same prepotential, encoded in a...

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2 arXiv papers cite this in 3 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

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Cites it as background 2 papers

Typical examples of compact complex surfaces $S$ which have been considered in F-Theory GUT literature are given by the del Pezzo surfaces dP$_n$ with $n=0,1,...,8$ obtained by preforming up to eight blow ups in the projective plane $ℙ^2$ [ref] .Later on we develop a class of models based on toric manifold involving the complex tetrahedral surface of figure ([ref]) and its blown ups [ref] .

Quiver Gauge Models in F-Theory on Local Tetrahedron · Engineering F-theory GUT model · 0.89
These complex surfaces are obtained by preforming up to eight blow ups at isolated points of the projective plane $CP^2=dP_0$ by complex projective lines [ref] ; see also section 2 for technical details.Motivated by the study of the geometric engineering of the F-theory GUT models building à la BHV, we aim in this paper to contribute to this matter by constructing a family of backgrounds for F-theory compactification based on the tetrahedron geometry $𝒯$ and its blow ups.

Tetrahedron in F-theory Compactification · Introduction · 0.82

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