Calabi-Yau Volumes and Reflexive Polytopes
High Energy Physics - Theory
2018-04-04 v1 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1704.03462,
title = {Calabi-Yau Volumes and Reflexive Polytopes},
author = {Yang-Hui He and Rak-Kyeong Seong and Shing-Tung Yau},
journal= {arXiv preprint arXiv:1704.03462},
year = {2018}
}
Comments
70 pages, 22 figures, 6 tables