The F-theory geometry with most flux vacua
Applying the Ashok-Denef-Douglas estimation method to elliptic Calabi-Yau fourfolds suggests that a single elliptic fourfold M max gives rise to O(10 272,000 ) F-theory flux vacua, and that the sum total of the numbers of flux vacua from all other F-theory geometries is suppressed by a relative factor of O(10 –3000 ). The fourfold M max arises from a generic elliptic fibration over a specific toric threefold base B max , and gives a geometrically non-Higgsable gauge group of E 8 9 × F 4 8 × (G 2 × SU(2)) 16 , of which we expect some factors to be broken by G-flux to smaller groups. It is not possible to tune an SU(5) GUT group on any further divisors in M max , or even an SU(2) or SU(3), so the standard model gauge group appears to arise in this context only from a broken E 8 factor. Furthermore, the results of this paper can either be interpreted as providing a framework for predicting how the standard model arises most naturally in F-theory and the types of dark matter to be found in a typical F-theory compactification, or as a challenge to string theorists to explain why other choices of vacua are not exponentially unlikely compared to F-theory compactifications on M max .