Open Access
August 2006 Vector bundle extensions, sheaf cohomology, and the heterotic standard model
Volker Braun, Yang-Hui He, Burt A. Ovrut, Tony Pantev
Adv. Theor. Math. Phys. 10(4): 525-589 (August 2006).


Stable, holomorphic vector bundles are constructed on a torus fibered, non-simply connected Calabi–Yau three-fold using the method of bundle extensions. Since the manifold is multiply connected, we work with equivariant bundles on the elliptically fibered covering space. The cohomology groups of the vector bundle, which yield the low energy spectrum, are computed using the Leray spectral sequence and fit the requirements of particle phenomenology. The physical properties of these vacua were discussed previously. In this paper, we systematically compute all relevant cohomology groups and explicitly prove the existence of the necessary vector bundle extensions. All mathematical details are explained in a pedagogical way, providing the technical framework for constructing heterotic standard model vacua.


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Volker Braun. Yang-Hui He. Burt A. Ovrut. Tony Pantev. "Vector bundle extensions, sheaf cohomology, and the heterotic standard model." Adv. Theor. Math. Phys. 10 (4) 525 - 589, August 2006.


Published: August 2006
First available in Project Euclid: 5 April 2007

zbMATH: 1101.81086
MathSciNet: MR2259689

Primary: 14J81
Secondary: 14J60 , 81T30 , 81V22

Rights: Copyright © 2006 International Press of Boston

Vol.10 • No. 4 • August 2006
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