Toric Elliptic Fibrations and F-Theory Compactifications

TL;DR

This paper classifies and analyzes 102,581 flat toric elliptic fibrations over P^2 within Calabi-Yau hypersurfaces derived from reflexive 4-polytopes, detailing their structure and gauge groups in F-theory compactifications.

Contribution

It provides a detailed relation between lattice polytopes and elliptic fibrations, introduces the fiber-divisor-graph for visualization, and computes gauge groups for a large class of fibrations.

Findings

Identified 102,581 flat toric elliptic fibrations over P^2.

Computed discriminant loci and Kodaira fiber groups for all fibrations.

Found the maximal gauge group to be SU(27).

Abstract

The 102581 flat toric elliptic fibrations over P^2 are identified among the Calabi-Yau hypersurfaces that arise from the 473800776 reflexive 4-dimensional polytopes. In order to analyze their elliptic fibration structure, we describe the precise relation between the lattice polytope and the elliptic fibration. The fiber-divisor-graph is introduced as a way to visualize the embedding of the Kodaira fibers in the ambient toric fiber. In particular in the case of non-split discriminant components, this description is far more accurate than previous studies. The discriminant locus and Kodaria fibers groups of all 102581 elliptic fibrations are computed. The maximal gauge group is SU(27), which would naively be in contradiction with 6-dimensional anomaly cancellation.