Quadrillion F -Theory Compactifications with the Exact Chiral Spectrum of the Standard Model

Abstract

We present O(1015) string compactifications with the exact chiral spectrum of the standard model of particle physics. This ensemble of globally consistent F-theory compactifications automatically realizes gauge coupling unification. 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 O(1015) bases, each of which defines a distinct compactification.