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Calabi-Yau Volumes and Reflexive Polytopes

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arxiv 1704.03462 v1 pith:OE2ZCNYX submitted 2017-04-11 hep-th math.AG

Yang-Hui He , Rak-Kyeong Seong , Shing-Tung Yau This is my paper · ORCID
classification hep-thmath.AG
keywords varietiescalabi-yaupolytopesreflexivevariousboundscorrespondingquantities
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We study various geometrical quantities for Calabi-Yau varieties realized as cones over Gorenstein Fano varieties, obtained as toric varieties from reflexive polytopes in various dimensions. Focus is made on reflexive polytopes up to dimension 4 and the minimized volumes of the Sasaki-Einstein base of the corresponding Calabi-Yau cone are calculated. By doing so, we conjecture new bounds for the Sasaki-Einstein volume with respect to various topological quantities of the corresponding toric varieties. We give interpretations about these volume bounds in the context of associated field theories via the AdS/CFT correspondence.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Abelian Orbifolds for Brane Brick Models

    hep-th 2026-06 unverdicted novelty 7.0 of 10

    A construction procedure that induces an abelian orbifold action on the fields and J/E-terms of a parent brane brick model for a toric CY4, yielding explicit orbifolded theories that preserve consistency conditions.

  2. Birational Transformations and 2d (0,2) Quiver Gauge Theories beyond Toric Fano 3-folds

    hep-th 2025-02 conditional novelty 5.0 of 10

    Mass deformations of 2d (0,2) brane brick models are shown in four explicit examples to implement birational transformations of toric Calabi-Yau 4-folds, including non-reflexive toric diagrams.

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