Does the weak gravity conjecture hold in all quantum gravity theories
In plain words
The conjecture says gravity must be the weakest force: some particle must feel electric repulsion stronger than its gravitational attraction. Whether this is a law of all quantum gravity theories is unproven.
Precise statement
Weak gravity conjecture (Arkani-Hamed, Motl, Nicolis, Vafa 2006): every U(1) gauge theory coupled to gravity has a state with charge-to-mass ratio at least that of extremal black holes. Determine whether this holds in every consistent quantum gravity theory, and whether the sublattice or tower versions hold.
What would settle it
A derivation from general principles (black hole thermodynamics, unitarity, holography), or a consistent theory violating it.
Status in the literature
Shown in perturbative string settings and supported by black-hole arguments; the strongest lattice version fails in some compactifications (2016), leaving sublattice and tower versions.