The F-theory geometry with most flux vacua
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 }.
- 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;
- F-Theory;
- Superstring Vacua;
- High Energy Physics - Theory
- E-Print:
- 19 pages, 2 figures, v3: minor corrections, clarifications, references added