Heterotic Models from Vector Bundles on Toric Calabi-Yau Manifolds

Understand

We systematically approach the construction of heterotic E_8 X 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.