2017/04/11 by Yang-Hui He, Rak-Kyeong Seong, Shing-Tung Yau · 26 citations
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Base (topology) #Cone (formal languages) #Conjecture #Context (archaeology) #Dimension (graph theory) #Fano plane #Geometry and complex manifolds #Polytope #Reflexivity #hep-th #math.AG
paper · pdf · doi:10.1007/s00220-018-3128-6
published in Communications in Mathematical Physics 361(1), 155-204 (Springer Science+Business Media) · 70 pages, 22 figures, 6 tables
arxiv created 2017/04/11 · openalex created_date 2017/04/28 · openalex publication_date 2018/04/02 · arxiv updated 2018/04/04 · openalex updated_date 2026/08/06
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.