Beschreibung:
<jats:p>We briefly review an algorithmic strategy to explore the landscape of heterotic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>E</mml:mi><mml:mn>8</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi>E</mml:mi><mml:mn>8</mml:mn></mml:msub></mml:math>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.</jats:p>