The Expanding Zoo of Calabi-Yau Threefolds

Abstract

This is a short review of recent constructions of new Calabi-Yau threefolds with small Hodge numbers and/or non-trivial fundamental group, which are of particular interest for model-building in the context of heterotic string theory. The two main tools are topological transitions and taking quotients by actions of discrete groups. Both of these techniques can produce new manifolds from existing ones, and they have been used to bring many new specimens to the previously sparse corner of the Calabi-Yau zoo where both Hodge numbers are small. Two new manifolds are also obtained here from hyperconifold transitions, including the first example with fundamental group S3, the smallest non-Abelian group.

24 pages, PDFLaTeX. To be published in the special issue "Computational Algebraic Geometry in String and Gauge Theory" of Advances in High Energy Physics. v2: Added reference, and data for four new manifolds constructed therein

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Cited by in corpus (15)

• On the Hodge structure of elliptically fibered Calabi-Yau threefolds
• Calabi-Yau threefolds with large h^{2, 1}
• The MSSM Spectrum from (0,2)-Deformations of the Heterotic Standard Embedding
• Calabi-Yau Threefolds With Small Hodge Numbers
• Formulae for Line Bundle Cohomology on Calabi-Yau Threefolds
• Hodge Numbers for CICYs with Symmetries of Order Divisible by 4
• 6D F-theory models and elliptically fibered Calabi-Yau threefolds over semi-toric base surfaces
• Non-toric bases for elliptic Calabi-Yau threefolds and 6D F-theory vacua
• Quantum black holes in Type-IIA String Theory
• Fibration structure in toric hypersurface Calabi-Yau threefolds
• Patterns in Calabi-Yau Distributions
• Heterotic String Models on Smooth Calabi-Yau Threefolds
• Classification and Properties of Hyperconifold Singularities and Transitions
• G${}_2$-Manifolds and M-Theory Compactifications
• On smooth Gorenstein polytopes