Abstract
We study the geometric requirements on a threefold base for the corresponding F-theory compactification to admit a weakly-coupled type IIB limit. We examine both the standard Sen limit and a more restrictive limit, and determine conditions sufficient for their non-existence for both toric bases and more general algebraic bases. In a large ensemble of geometries generated by base changing resolutions we derive an upper bound on the frequency with which a weak-coupling limit may occur, and find that such limits are extremely rare. Our results sharply quantify the widely held notion that the vast number of weakly-coupled IIB vacua is but a tiny fraction of the landscape.
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Halverson, J., Long, C. & Sung, B. On the scarcity of weak coupling in the string landscape. J. High Energ. Phys. 2018, 113 (2018). https://doi.org/10.1007/JHEP02(2018)113
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DOI: https://doi.org/10.1007/JHEP02(2018)113