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

Phys Rev Lett. 2019 Sep 6;123(10):101601. doi: 10.1103/PhysRevLett.123.101601.


We present O(10^{15}) 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(10^{15}) bases, each of which defines a distinct compactification.