Vector bundle extensions, sheaf cohomology, and the heterotic standard model. (English) Zbl 1101.81086

Summary: 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.


81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81V22 Unified quantum theories
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
32Q25 Calabi-Yau theory (complex-analytic aspects)
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