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Heterotic Bundles on Calabi-Yau Manifolds with Small Picard Number · Around

2011

Heterotic Bundles on Calabi-Yau Manifolds with Small Picard Number

He, Yang-Hui, Kreuzer, Maximilian, Lee, Seung-Joo et al.

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We undertake a systematic scan of vector bundles over spaces from the largest database of known Calabi-Yau three-folds, in the context of heterotic string compactification.

Specifically, we construct positive rank five monad bundles over Calabi-Yau hypersurfaces in toric varieties, with the number of Kahler moduli equal to one, two, and three and extract physically interesting models.
We select models which can lead to three families of matter after dividing by a freely-acting discrete symmetry and including Wilson lines.
About 2000 such models on two manifolds are found.

Built on

G. Horrocks and D. Mumford, “A rank 2 vector bundle on ℙ 4 \mathbb{P}^{4} with 15000 symmetries,” Topology, 12:63-81, (1973)
1973
Earlier work this paper cites.
R. Hartshorne, “Algebraic Geometry,” Springer, GTM52, Springer-Verlag, 1977
1977
Earlier work this paper cites.
A. Beilinson, “Coherent sheaves on ℙ n \mathbb{P}^{n} and problems in linear algebra,” Funktsional. Anal. i Prilozhen. 12 (1978), no. 3, 68-69
1978
Earlier work this paper cites.
M. Maruyama,” Moduli of stable sheaves, II ,” J. Math. Kyoto Univ. 18-3, 1978, 557-614
1978
Earlier work this paper cites.
P. Candelas, G. T. Horowitz, A. Strominger, E. Witten, “Vacuum Configurations for Superstrings,” Nucl. Phys. B258
1985
Earlier work this paper cites.
P. Candelas, A. M. Dale, C. A. Lutken and R. Schimmrigk, “Complete Intersection Calabi-Yau Manifolds,” Nucl. Phys. B 298
1988
Earlier work this paper cites.
C. Okonek, M. Schneider, H. Spindler, “Vector Bundles on Complex Projective Spaces,” Birkhauser Verlag, 1988
1988
Earlier work this paper cites.
J. Distler and B. R. Greene, “Aspects of (2,0) String Compactifications,” Nucl. Phys. B 304
1988
Earlier work this paper cites.
P. Candelas, C. A. Lutken and R. Schimmrigk, “Complete Intersection Calabi-Yau Manifolds 2. Tree Generation Manifolds,” Nucl. Phys. B 306
1988
Earlier work this paper cites.
B. McInnes, “Group Theoretic Aspects Of The Hosotani Mechanism,” J. Phys. A A22
1989
Earlier work this paper cites.
V. V. Batyrev, Dual polyhedra and mirror symmetry for Calabi-Yau hypersurfaces in toric varieties , J. Alg. Geom. 3
1994
Earlier work this paper cites.

Similar

S. Kachru, “Some Three Generation (0,2) Calabi-Yau Models,” Phys. Lett. B 349
1995
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M. Kreuzer, H. Skarke, “On the classification of reflexive polyhedra,” Commun. Math. Phys. 185
1997
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A. C. Avram, M. Kreuzer, M. Mandelberg, H. Skarke, “The Web of Calabi-Yau hypersurfaces in toric varieties,” Nucl. Phys. B505
1997
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R. Blumenhagen, “Target space duality for (0,2) compactifications,” Nucl. Phys. B 513
1997
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M. Kreuzer, H. Skarke, “Reflexive polyhedra, weights and toric Calabi-Yau fibrations,” Rev. Math. Phys. 14
2002
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M. Kreuzer, H. Skarke, “Complete classification of reflexive polyhedra in four-dimensions,” Adv. Theor. Math. Phys. 4

Then

L. B. Anderson, Y. -H. He, A. Lukas, “Heterotic Compactification, An Algorithmic Approach,” JHEP 0707
2007
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L. B. Anderson, Y. -H. He, A. Lukas, “Monad Bundles in Heterotic String Compactifications,” JHEP 0807
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2008
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M. Gabella, Y. -H. He, A. Lukas, “An Abundance of Heterotic Vacua,” JHEP 0812
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2008
Later among the works it cites.
P. Candelas, X. de la Ossa, Y. -H. He, B. Szendroi, “Triadophilia: A Special Corner in the Landscape,” Adv. Theor. Math. Phys. 12
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2008
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L. B. Anderson, J. Gray, A. Lukas, B. Ovrut, “Stability Walls in Heterotic Theories,” JHEP 0909
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