# Calabi-Yau Volumes and Reflexive Polytopes

## TL;DR

This paper investigates the volumes of Calabi-Yau cones derived from reflexive polytopes, providing new bounds and interpretations within the context of toric geometry and the AdS/CFT correspondence.

## Contribution

It introduces new volume bounds for Calabi-Yau cones from reflexive polytopes and explores their implications in field theory via the AdS/CFT correspondence.

## Key findings

- Calculated minimized volumes for reflexive polytopes up to dimension 4.
- Conjectured new bounds for Sasaki-Einstein volumes based on topological data.
- Provided field theory interpretations of geometric volume bounds.

## 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.