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Standard-Model Bundles on Non-Simply Connected Calabi--Yau Threefolds
High Energy Physics - Theory · Submitted 1 Aug 2000
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We give a proof of the existence of $G=SU(5)$, stable holomorphic vector bundles on elliptically fibered Calabi--Yau threefolds with fundamental group $\bbz_2$.
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The abstract, sentence by sentence
We give a proof of the existence of $G=SU(5)$, stable holomorphic vector bundles on elliptically fibered Calabi--Yau threefolds with fundamental group $\bbz_2$. The bundles we construct have Euler characteristic 3 and an anomaly that can be absorbed by M-theory five-branes. Such bundles provide the basis for constructing the standard model in heterotic M-theory. They are also applicable to vacua of the weakly coupled heterotic string. We explicitly present a class of three family models with gauge group $SU(3)_C\times SU(2)_L\times U(1)_Y$.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We give a proof of the existence of $G=SU(5)$, stable holomorphic vector bundles on elliptically fibered Calabi--Yau threefolds with fundamental group $\bbz_2$. | contribution 0.78 | 0.95 | 0.81 | asserted 1.00 |
| s1 | The bundles we construct have Euler characteristic 3 and an anomaly that can be absorbed by M-theory five-branes. | result 0.99 | 0.91 | 0.12 | asserted 1.00 |
| s2 | Such bundles provide the basis for constructing the standard model in heterotic M-theory. | interpretation 1.00 | 0.32 | 0.34 | asserted 0.94 |
| s3 | They are also applicable to vacua of the weakly coupled heterotic string. | interpretation 0.87 | 0.41 | 0.06 | asserted 0.96 |
| s4 | We explicitly present a class of three family models with gauge group $SU(3)_C\times SU(2)_L\times U(1)_Y$. | contribution 0.60 | 0.94 | 0.21 | asserted 1.00 |
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Original abstract
We give a proof of the existence of $G=SU(5)$, stable holomorphic vector bundles on elliptically fibered Calabi--Yau threefolds with fundamental group $\bbz_2$. The bundles we construct have Euler characteristic 3 and an anomaly that can be absorbed by M-theory five-branes. Such bundles provide the basis for constructing the standard model in heterotic M-theory. They are also applicable to vacua of the weakly coupled heterotic string. We explicitly present a class of three family models with gauge group $SU(3)_C\times SU(2)_L\times U(1)_Y$.
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How the literature uses it
12 arXiv papers cite this in 16 sentences
Papers citing it · 10 sentences without a confident label
Compares with it 1 paper
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This manifold is an elliptic fibration and it would seem to be analogous in a number of ways to $X^19,19$ which is at the heart of the heterotic model propounded by the School at the University of Pennsylvania [ref] .
New Calabi-Yau Manifolds with Small Hodge Numbers · Webs of CICY's with freely acting symmetries · 0.88
Cites it as background 5 papers
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The Schoen manifold $X$ was first introduced in [ref] ; here we follow the description of this manifold given e.g. in [ref] .
Schoen manifold with line bundles as resolved magnetized orbifolds · Schoen manifold · 0.99
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The Schoen threefold is constructed with fiber products of rational elliptic surfaces with section [ref] , and its quotient with $ℤ_3 ×ℤ_3$ fundamental group were utilized in constructing heterotic standard model [ref] .
Self-mirror Large Volume Scenario with de Sitter · Introduction · 0.84
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Since the literature on this topic is vast (see for example [ref] ) and applications [ref] , we make no attempt at a comprehensive review, but instead aim for a curated survey of some of the tools that will prove most useful in later Sections.
Extending the Geometry of Heterotic Spectral Cover Constructions · A review of vector bundles over Weierstrass elliptic fibrations and Fourier-Mukai Transforms · 1.00
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