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) x F-4(8) x (G(2) x 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. 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.