A Monte Carlo exploration of threefold base geometries for 4d F-theory vacua

TL;DR

This paper employs Monte Carlo methods to explore the landscape of toric threefold bases supporting elliptic Calabi-Yau fourfolds in F-theory, revealing the distribution of gauge groups, matter, and geometric structures relevant for string compactifications.

Contribution

It introduces a Monte Carlo approach to systematically analyze the vast set of threefold bases and their associated gauge structures in F-theory compactifications, estimating their abundance and typical features.

Findings

Estimated number of bases: ~10^48.

Distribution peaks at h^{1,1} ~ 82.

76% of bases contain SU(3)×SU(2) gauge factors.

Abstract

We use Monte Carlo methods to explore the set of toric threefold bases that support elliptic Calabi-Yau fourfolds for F-theory compactifications to four dimensions, and study the distribution of geometrically non-Higgsable gauge groups, matter, and quiver structure. We estimate the number of distinct threefold bases in the connected set studied to be $\sim { 10^{48}}$. The distribution of bases peaks around $h^{1, 1}\sim 82$. All bases encountered after "thermalization" have some geometric non-Higgsable structure. We find that the number of non-Higgsable gauge group factors grows roughly linearly in $h^{1,1}$ of the threefold base. Typical bases have $\sim 6$ isolated gauge factors as well as several larger connected clusters of gauge factors with jointly charged matter. Approximately 76% of the bases sampled contain connected two-factor gauge group products of the form SU(3)$\times$SU(2), which may act as the non-Abelian part of the standard model gauge group. SU(3)$\times$SU(2) is the third most common connected two-factor product group, following SU(2)$\times$SU(2) and $G_2\times$SU(2), which arise more frequently.