The Ftheory geometry with most flux vacua
Abstract
Applying the AshokDenefDouglas estimation method to elliptic CalabiYau fourfolds suggests that a single elliptic fourfold {M}_{max } gives rise to O({10}^{272,000}) Ftheory flux vacua, and that the sum total of the numbers of flux vacua from all other Ftheory 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 nonHiggsable gauge group of E _{8} ^{9} × F _{4} ^{8} × ( G _{2} × SU(2))^{16}, of which we expect some factors to be broken by Gflux 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 Ftheory and the types of dark matter to be found in a typical Ftheory compactification, or as a challenge to string theorists to explain why other choices of vacua are not exponentially unlikely compared to Ftheory compactifications on {M}_{max }.
 Publication:

Journal of High Energy Physics
 Pub Date:
 December 2015
 DOI:
 10.1007/JHEP12(2015)164
 arXiv:
 arXiv:1511.03209
 Bibcode:
 2015JHEP...12..164T
 Keywords:

 Flux compactifications;
 FTheory;
 Superstring Vacua;
 High Energy Physics  Theory
 EPrint:
 19 pages, 2 figures, v3: minor corrections, clarifications, references added