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arXiv · 1704.03462

Calabi-Yau Volumes and Reflexive Polytopes

Yang-Hui He·Rak-Kyeong Seong·Shing-Tung Yau
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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.

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Yang-Hui He, Rak-Kyeong Seong, Shing-Tung Yau. 2017-04-11. Calabi-Yau Volumes and Reflexive Polytopes. https://doi.org/10.1007/s00220-018-3128-6

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