Calabi-Yau Volumes and Reflexive Polytopes
arXiv:1704.03462 · doi:10.1007/s00220-018-3128-6
Abstract
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.
70 pages, 22 figures, 6 tables
References in corpus (16)
- N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
- Algebraic structures on parallel M2-branes
- Modeling Multiple M2's
- Counting Gauge Invariants: the Plethystic Program
- Sasaki-Einstein Manifolds and Volume Minimisation
- Moduli spaces of Chern-Simons quiver gauge theories and AdS_4/CFT_3
- Brane Tilings and M2 Branes
- A Calabi-Yau Database: Threefolds Constructed from the Kreuzer-Skarke List
- Brane Tilings and Reflexive Polygons
- 2d (0,2) Quiver Gauge Theories and D-Branes
- Topological Invariants and Fibration Structure of Complete Intersection Calabi-Yau Four-Folds
- Brane Brick Models and 2d (0,2) Triality
- Calabi-Yau threefolds with large h^{2, 1}
- Brane Brick Models, Toric Calabi-Yau 4-Folds and 2d (0,2) Quivers
- Heavy Tails in Calabi-Yau Moduli Spaces
- Multiple Fibrations in Calabi-Yau Geometry and String Dualities
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- Standard Model Plethystics
- Some Open Questions in Quiver Gauge Theory
- Futaki Invariants and Reflexive Polygons
- Quiver Gauge Theories: Beyond Reflexivity
- Birational Transformations and 2d (0,2) Quiver Gauge Theories beyond Toric Fano 3-folds
- Classification and Birational Equivalence of Dimer Integrable Systems for Reflexive Polygons
- Machine Learning Clifford invariants of ADE Coxeter elements
- Reflexions on Mahler: Dessins, Modularity and Gauge Theories
- Metaheuristic Generation of Brane Tilings