A Quadrillion Standard Models from F-theory

Abstract

We present an explicit construction of $\mathcal{O}(10^{15})$ 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 $\mathcal{O}(10^{15})$ bases, each of which defines a distinct compactification.

7 pages, double column; v3: improved and expanded discussion, technical details deferred to an added appendix