Stable Vector Bundles on Calabi-Yau Threefolds

Andreas, Bjorn; Gómez, Darío Sánchez

doi:10.1063/1.3089203

Cited by 4 publications

(6 citation statements)

References 18 publications

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“…× h k , we obtain a Courant extension of P , and hence a string algebroid, by applying Proposition 2.4. Explicit constructions of such bundles for X a compact Calabi-Yau threefold with k = 1, V 0 = T X and V 1 not isomorphic to V 0 can be found in [2,11,21,19,25] and references therein.…”

Section: )mentioning

confidence: 99%

Holomorphic string algebroids

Garcia-Fernandez

Rubio

Tipler

2020

Trans. Amer. Math. Soc.

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We introduce the category of holomorphic string algebroids, whose objects are Courant extensions of Atiyah Lie algebroids of holomorphic principal bundles, as considered by Bressler, and whose morphisms correspond to inner morphisms of the underlying holomorphic Courant algebroids in the sense ofŠevera. This category provides natural candidates for Atiyah Lie algebroids of holomorphic principal bundles for the (complexified) string group and their morphisms. Our main results are a classification of string algebroids in terms ofČech cohomology, and the construction of a locally complete family of deformations of string algebroids via a differential graded Lie algebra.

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Section: )mentioning

confidence: 99%

Holomorphic string algebroids

Garcia-Fernandez

Rubio

Tipler

2020

Trans. Amer. Math. Soc.

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“…The stable τ X -invariant SU(5) bundle V 5 on X will be constructed as a non-trivial extension. For this we will use the bundle construction of [9] which we will now briefly summarize.…”

Section: Outline Of the Bundle Constructionmentioning

confidence: 99%

“…satisfies rank(V ) = r and c 1 (V ) = 0. In [9] it is shown that the vector bundle V is (H + ǫD)-stable for each sufficiently small ǫ > 0 if the following three conditions hold:…”

Section: Outline Of the Bundle Constructionmentioning

confidence: 99%

“…The primary goal of this note is to construct a class of stable τ X -invariant SU (5) bundles on the class of manifolds of [5] which satisfy all of the above constraints. To construct the bundles we will apply the bundle construction method of [9]. The bundles are given by non-trivial extensions of τ X -invariant SU(4) bundles by τ X -invariant line bundles.…”

Section: Introductionmentioning

confidence: 99%

“…For more details and proofs we refer to [5] and [8]. In section 3, we give a broad outline of the bundle construction of [9] which we will apply to construct a class of stable τ X -invariant SU(5) bundles. In section 4…”

Section: Introductionmentioning

confidence: 99%

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SU(5) heterotic Standard Model bundles

Andreas

Hoffmann

2012

J. High Energ. Phys.

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Heterotic non-Kähler geometries via polystable bundles on Calabi–Yau threefolds

Andreas

Garcia-Fernandez

2012

Journal of Geometry and Physics

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In arXiv:1008.1018 it is shown that a given stable vector bundle V on a Calabi-Yau threefold X which satisfies c 2 (X) = c 2 (V ) can be deformed to a solution of the Strominger system and the equations of motion of heterotic string theory. In this note we extend this result to the polystable case and construct explicit examples of polystable bundles on elliptically fibered Calabi-Yau threefolds where it applies. The polystable bundle is given by a spectral cover bundle, for the visible sector, and a suitably chosen bundle, for the hidden sector. This provides a new class of heterotic flux compactifications via non-Kähler deformation of Calabi-Yau geometries with polystable bundles. As an application, we obtain examples of non-Kähler deformations of some three generation GUT models. 1 andreas@math.hu-berlin.de 2 mariogf@qgm.au.dk, Supported by QGM (Centre for Quantum Geometry of Moduli Spaces) funded by the Danish National Research Foundation.

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Stable Vector Bundles on Calabi-Yau Threefolds

Cited by 4 publications

References 18 publications

Holomorphic string algebroids

Holomorphic string algebroids

SU(5) heterotic Standard Model bundles

Heterotic non-Kähler geometries via polystable bundles on Calabi–Yau threefolds

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