Evidence for a Lattice Weak Gravity Conjecture

TL;DR

This work refines the Weak Gravity Conjecture by proposing the Sublattice Weak Gravity Conjecture (sLWGC), which requires a superextremal state on a finite-index sublattice of the charge lattice rather than at every lattice site. It provides bottom-up KK arguments, top-down string-theory evidence via modular invariance, and explicit toroidal-orbifold examples showing the LWGC can fail while the sLWGC holds. In AdS5 contexts, particularly with N=4 theories, the sLWGC remains satisfiable, underscoring its robustness across contexts. A key implication is that a very small gauge coupling implies a relatively low gravitational cutoff, shaping EFT validity and phenomenology, including inflationary models. The work highlights modular invariance as a powerful constraint for spectrum structure and motivates further exploration of sLWGC variants, coarse-graining of lattices, and UV/IR connections in quantum gravity.

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 $\sim e^{1/3} M_{\rm Pl}$.