Evidence for a Lattice Weak Gravity Conjecture

TL;DR

The paper provides evidence supporting a stronger version of the Weak Gravity Conjecture, proposing that an infinite sublattice of superextremal particles exists in known theories, with implications for quantum gravity and fundamental physics.

Contribution

It demonstrates that the Sublattice Weak Gravity Conjecture holds in effective theories and string vacua, and presents counterexamples to the stronger conjecture that particles exist at every lattice site.

Findings

Effective theories and string vacua respect the Sublattice Weak Gravity Conjecture.

Modular invariance in string theory implies the conjecture.

Counterexamples show the strongest form of the conjecture does not always hold.

Abstract

The Weak Gravity Conjecture postulates the existence of superextremal charged particles, i.e. those with mass smaller than or equal to their charge in Planck units. We present further evidence for our recent observation that in known examples a much stronger statement is true: an infinite tower of superextremal particles of different charges exists. We show that effective Kaluza-Klein field theories and perturbative string vacua respect the Sublattice Weak Gravity Conjecture, namely that a finite index sublattice of the full charge lattice exists with a superextremal particle at each site. In perturbative string theory we show that this follows from modular invariance. However, we present counterexamples to the stronger possibility that a superextremal particle exists at every lattice site, including an example in which the lightest charged particle is subextremal. The Sublattice Weak Gravity Conjecture has many implications both for abstract theories of quantum gravity and for real-world physics. For instance, it implies that if a gauge group with very small coupling $e$ exists, then the fundamental gravitational cutoff energy of the theory is no higher than $\sim e^{1/3} M_{\rm Pl}$.