Non-toric bases for elliptic Calabi-Yau threefolds and 6D F-theory vacua

Abstract

We develop a combinatorial approach to the construction of general smooth compact base surfaces that support elliptic Calabi-Yau threefolds. This extends previous analyses that have relied on toric or semi-toric structure. The resulting algorithm is used to construct all classes of such base surfaces $S$ with $h^{1,1}(S)<8$ and all base surfaces over which there is an elliptically fibered Calabi-Yau threefold $X$ with Hodge number $h^{2,1}(X)\ge 150$. These two sets can be used todescribe all 6D F-theory models that have fewer than seven tensor multiplets or more than 150 neutral scalar fields respectively in their maximally Higgsed phase. Technical challenges to constructing the complete list of base surfaces for all Hodge numbers are discussed.

51 pages, 10 figures

References in corpus (7)

• Les Houches Lectures on Constructing String Vacua
• Global aspects of the space of 6D N = 1 supergravities
• A Calabi-Yau Database: Threefolds Constructed from the Kreuzer-Skarke List
• TASI Lectures on Supergravity and String Vacua in Various Dimensions
• Topological Invariants and Fibration Structure of Complete Intersection Calabi-Yau Four-Folds
• Calabi-Yau threefolds with large h^{2, 1}
• 6D SCFTs and Gravity

Cited by in corpus (6)

• On Algorithmic Universality in F-theory Compactifications
• ${\mathbb{P}}^1$-bundle bases and the prevalence of non-Higgsable structure in 4D F-theory models
• The Calabi-Yau Landscape: from Geometry, to Physics, to Machine-Learning
• Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds
• On Instanton Superpotentials, Calabi-Yau Geometry, and Fibrations
• Tuned and Non-Higgsable U(1)s in F-theory