Heterotic models from vector bundles on toric Calabi-Yau manifolds

• Published in: The journal of high energy physics Vol. 2010; no. 5
• Main Authors: He, Yang-Hui, Lee, Seung-Joo, Lukas, André
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01.05.2010; Springer Nature B.V
• Subjects: Bundles; Bundling; Classical and Quantum Gravitation; Constraint modelling; Elementary Particles; High energy physics; Hyperspaces; Leptons; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Relativity Theory; String Theory; Superstring Vacua; Superstrings and Heterotic Strings
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP05(2010)071

We systematically approach the construction of heterotic E 8 × 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.