The Asymptotic Weak Gravity Conjecture for Open Strings

TL;DR

This paper examines the asymptotic Tower Weak Gravity Conjecture in open string theories with minimal supersymmetry, revealing that only emergent string limits satisfy the conjecture, while others lead to decompactification or decoupled theories.

Contribution

It classifies weak coupling limits in F-theory and shows that the Tower Weak Gravity Conjecture holds only in emergent string limits, providing a geometric framework for these classifications.

Findings

Weak coupling limits are classified into three classes based on EFT string limits.

The Tower Weak Gravity Conjecture is satisfied only in emergent string limits with critical heterotic strings.

Other limits lead to decompactification or decoupled gauge theories, lacking super-extremal towers.

Abstract

We investigate the asymptotic Tower Weak Gravity Conjecture in weak coupling limits of open string theories with minimal supersymmetry in four dimensions, focusing for definiteness on gauge theories realized on 7-branes in F-theory. Contrary to expectations, we find that not all weak coupling limits contain an obvious candidate for a tower of states marginally satisfying the super-extremality bound. The weak coupling limits are classified geometrically in the framework of EFT string limits and their generalizations. We find three different classes of weak coupling limits, whose physics is characterized by the ratio of the magnetic weak gravity scale and the species scale. The four-dimensional Tower Weak Gravity Conjecture is satisfied by the (non-BPS) excitations of the weakly coupled EFT string only in emergent string limits, where the EFT string can be identified with a critical (heterotic) string. All other weak coupling limits lead to a decompactification either to an in general strongly coupled gauge theory coupled to gravity or to a defect gauge theory decoupling from the gravitational bulk, in agreement with the absence of an obvious candidate for a marginally super-extremal tower of states.