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Geometrical Aspects of Fivebranes in Heterotic/F-Theory Duality in Four Dimensions
High Energy Physics - Theory · Submitted 11 Mar 1999
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We find that some of these can be usefully described in terms of degenerations of the base of the elliptic fibrations of these fourfolds.
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The abstract, sentence by sentence
We use the method of stable degenerations to study the local geometry of Calabi-Yau fourfolds for F-theory compactifications dual to heterotic compactifications on a Calabi-Yau threefold with fivebranes wrapping holomorphic curves in the threefold. When fivebranes wrap intersecting curves, or when many fivebranes wrap the same curve, the dual fourfolds degenerate in interesting ways. We find that some of these can be usefully described in terms of degenerations of the base of the elliptic fibrations of these fourfolds. We use Witten's criterion to determine which of the fivebranes can lead to the generation of a non-perturbative superpotential.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We use the method of stable degenerations to study the local geometry of Calabi-Yau fourfolds for F-theory compactifications dual to heterotic compactifications on a Calabi-Yau threefold with fivebranes wrapping holomorphic curves in the threefold. | contribution 0.62 | 0.93 | 0.09 | asserted 0.98 |
| s1 | When fivebranes wrap intersecting curves, or when many fivebranes wrap the same curve, the dual fourfolds degenerate in interesting ways. | result 0.89 | 0.43 | 0.11 | asserted 0.99 |
| s2 | We find that some of these can be usefully described in terms of degenerations of the base of the elliptic fibrations of these fourfolds. | result 0.78 | 0.95 | 0.20 | asserted 0.82 |
| s3 | We use Witten's criterion to determine which of the fivebranes can lead to the generation of a non-perturbative superpotential. | method 0.73 | 0.92 | 0.15 | asserted 0.98 |
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The paper
Original abstract
We use the method of stable degenerations to study the local geometry of Calabi-Yau fourfolds for F-theory compactifications dual to heterotic compactifications on a Calabi-Yau threefold with fivebranes wrapping holomorphic curves in the threefold. When fivebranes wrap intersecting curves, or when many fivebranes wrap the same curve, the dual fourfolds degenerate in interesting ways. We find that some of these can be usefully described in terms of degenerations of the base of the elliptic fibrations of these fourfolds. We use Witten's criterion to determine which of the fivebranes can lead to the generation of a non-perturbative superpotential.
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How the literature uses it
7 arXiv papers cite this in 19 sentences
Papers citing it · 15 sentences without a confident label
Builds on it 1 paper
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However, since the essential point in the analysis is the trivial heterotic gauge bundle, the results of [ref] carry over to our situation immediately.
Five-Brane Superpotentials and Heterotic/F-theory Duality · The Five-Brane Dual: Blowing Up in F-Theory · 0.84
Cites it as background 2 papers
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For a certain type of heterotic compactifications, namely on elliptically fibered Calabi-Yau manifolds, the heterotic/F-theory duality is relatively well understood [ref] .
Dynamically SUSY Breaking SQCD on F-Theory Seven-Branes · Introduction · 0.94
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The duality between these theories has been extensively studied (see e.g. Refs. [ref] ) since the discovery of F-theory [ref] more than 20 years ago.
NS5-Branes and Line Bundles in Heterotic/F-Theory Duality · Introduction · 1.00
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