On the Scarcity of Weak Coupling in the String Landscape

TL;DR

This paper investigates the geometric conditions necessary for F-theory compactifications to have weakly-coupled type IIB limits, revealing that such limits are exceedingly rare in the string landscape.

Contribution

It provides a detailed analysis of geometric criteria for weak coupling limits and quantifies their scarcity across a broad class of F-theory bases.

Findings

Weak coupling limits are extremely rare among studied geometries.

Derived an upper bound on the frequency of weak-coupling limits.

Quantified the scarcity of weakly-coupled IIB vacua in the string landscape.

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.