# A Quadrillion Standard Models from F-theory

## TL;DR

This paper constructs approximately one quadrillion globally consistent F-theory compactifications that realize the Standard Model spectrum, using algebraic geometry to simplify the global consistency conditions.

## Contribution

It provides an explicit method to generate an enormous number of Standard Model-like string vacua via a single geometric criterion on elliptically fibered Calabi--Yau fourfolds.

## Key findings

- Over 10^15 distinct compactifications identified
- Global consistency reduces to a single geometric criterion
- Criterion depends only on the associated polytope for toric bases

## Abstract

We present an explicit construction of ${\cal O}(10^{15})$ globally consistent string compactifications that realize the exact chiral spectrum of the Standard Model of particle physics with gauge coupling unification in the context of F-theory. Utilizing the power of algebraic geometry, all global consistency conditions can be reduced to a single criterion on the base of the underlying elliptically fibered Calabi--Yau fourfolds. For toric bases, this criterion only depends on an associated polytope and is satisfied for at least ${\cal O}(10^{15})$ bases, each of which defines a distinct compactification.