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Combinatorics in N = 1 Heterotic Vacua

Abstract

We briefly review an algorithmic strategy to explore the landscape of heterotic E8 \times E8 vacua, in the context of compactifying smooth Calabi-Yau three-folds with vector bundles. The Calabi-Yau three-folds are algebraically realised as hypersurfaces in toric varieties and a large class of vector bundles are constructed thereon as monads. In the spirit of searching for Standard-like heterotic vacua, emphasis is placed on the integer combinatorics of the model-building programme.Comment: 14 pages. An introductory review prepared for the special issue "Computational Algebraic Geometry in String and Gauge Theory" of Advances in High Energy Physic

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