The F-theory geometry with most flux vacua release_zr5rp65utrasbmwmyb4st6gktm

Abstract

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. 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.
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