Combinatorics in \({\mathcal N}=1\) heterotic vacua (Q765442)

Summary: We briefly review an algorithmic strategy to explore the landscape of heterotic \(E_8 \times E_8\) vacua, in the context of compactifying smooth Calabi-Yau threefolds with vector bundles. The Calabi-Yau threefolds 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.