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Heterotic models from vector bundles on toric Calabi-Yau manifolds. (English) Zbl 1287.81094
Summary: We systematically approach the construction of heterotic \(E_{8}\times E_{8}\) Calabi-Yau models, based on compact Calabi-Yau three-folds arising from toric geometry and vector bundles on these manifolds. We focus on a simple class of 101 such three-folds with smooth ambient spaces, on which we perform an exhaustive scan and find all positive monad bundles with SU(\(N\)), \(N\) = 3; 4; 5 structure groups, subject to the heterotic anomaly cancellation constraint. We find that anomaly-free positive monads exist on only 11 of these toric three-folds with a total number of bundles of about 2000. Only 21 of these models, all of them on three-folds realizable as hypersurfaces in products of projective spaces, allow for three families of quarks and leptons. We also perform a preliminary scan over the much larger class of semi-positive monads which leads to about 44000 bundles with 280 of them satisfying the three-family constraint. These 280 models provide a starting point for heterotic model building based on toric three-folds.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
81V25 Other elementary particle theory in quantum theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory)
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