On the Scarcity of Weak Coupling in the String Landscape

Understand

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.