Abstract
Applying the Ashok-Denef-Douglas estimation method to elliptic Calabi-Yau fourfolds suggests that a single elliptic fourfold \( {\mathrm{\mathcal{M}}}_{\max } \) gives rise to \( \mathcal{O}\left({10}^{272,000}\right) \) 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 \( \mathcal{O}\left({10}^{-3000}\right) \). The fourfold \( {\mathrm{\mathcal{M}}}_{\max } \) arises from a generic elliptic fibration over a specific toric threefold base B max, and gives a geometrically non-Higgsable gauge group of E 98 × F 84 × (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 \( {\mathrm{\mathcal{M}}}_{\max } \), 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 \( {\mathrm{\mathcal{M}}}_{\max } \).
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Taylor, W., Wang, YN. The F-theory geometry with most flux vacua. J. High Energ. Phys. 2015, 1–21 (2015). https://doi.org/10.1007/JHEP12(2015)164
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DOI: https://doi.org/10.1007/JHEP12(2015)164