The Asymptotic Weak Gravity Conjecture in M-theory

Abstract

The tower Weak Gravity Conjecture predicts infinitely many super-extremal states along every ray in the charge lattice of a consistent quantum gravity theory. We show this far-reaching claim in five-dimensional compactifications of M-theory on Calabi--Yau 3-folds for gauge groups with a weak coupling limit. We first characterize the possible weak coupling limits, building on an earlier classification of infinite distance limits in the Kähler moduli space of M-theory compactifications. We find that weakly coupled gauge groups are associated to curves on the compactification space contained in generic fibers or in fibers degenerating at finite distance in their moduli space. These always admit an interpretation as a Kaluza--Klein or winding U$(1)$ in a dual frame or as part of a dual perturbative heterotic gauge group, in agreement with the Emergent String Conjecture. Using the connection between Donaldson--Thomas invariants and Noether--Lefschetz theory, we then show that every ray in the associated charge lattice either supports a tower of BPS states or of non-BPS states, and prove that these satisfy the super-extremality condition, at least in the weak coupling regime.

v3: Added references, JHEP accepted, 50 pages

References in corpus (14)

• On the Geometry of the String Landscape and the Swampland
• The Swampland: Introduction and Review
• The Weak Gravity Conjecture in three dimensions
• The Dark Dimension and the Swampland
• Quantum Corrections in 4d N=1 Infinite Distance Limits and the Weak Gravity Conjecture
• The Emergence Proposal in Quantum Gravity and the Species Scale
• The M5-Brane Elliptic Genus: Modularity and BPS States
• EFT strings and emergence
• Elliptic K3 Surfaces at Infinite Complex Structure and their Refined Kulikov models
• Tameness, Strings, and the Distance Conjecture
• 4d strings at strong coupling
• Light Strings and Strong Coupling in F-theory
• The Weak Gravity Conjecture and BPS Particles
• Stability of BPS States and Weak Coupling Limits

Cited by in corpus (4)

• Minimal Black Holes and Species Thermodynamics
• Emergent Strings in Type IIB Calabi--Yau Compactifications
• Asymptotic Weak Gravity Conjecture in M-theory on K3 $\times$ K3
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme