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Title: Does the weak gravity conjecture hold in all quantum gravity theories
Plain: 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: 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.
Settled by: A derivation from general principles (black hole thermodynamics, unitarity, holography), or a consistent theory violating it.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: partially-resolved
Status note: 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.
Posed since: 2006