This note summarizes a proposed proof that a version of the Weak Gravity Conjecture (WGC) holds in perturbative string theory. The work gives a proof‑of‑concept using the bosonic string. The authors show how general features of string models force the existence of charged states that are sufficiently “strongly charged” compared with their mass. They argue this prevents certain problematic stable black hole remnants and so supports the WGC from a top‑down perspective.

The WGC is a theoretical idea that says gravity should be the weakest long‑range force. In practice it demands that a theory with a massless photon include charged particles whose charge‑to‑mass ratio is at least as large as that of an extremal black hole. There are several sharpenings of the idea. A lattice or sublattice version requires such charged states across an entire grid of possible charges. The authors aim at the Ooguri‑Vafa form of the sublattice WGC, meaning they find a regular sublattice of charges filled by particles that are superextremal (they beat the black hole bound) but do not saturate it.

The proof uses only general, model‑independent properties of string theory. First, modular invariance of the worldsheet theory — a symmetry of the two‑dimensional quantum field theory that defines the string — constrains the spectrum and guarantees charged states with known relations between mass and charge. Second, by coupling the low‑energy effective field theory (EFT) to the worldsheet description, the authors express scattering amplitudes as correlators in the worldsheet conformal field theory. From those correlators they compute the long‑range forces between identical charged states. Combining these steps they show a form of the Repulsive Force Conjecture (RFC) on a sublattice. The RFC is a related conjecture that requires identical charged particles to repel each other overall, once gravity and other long‑range forces are included.