Weak Gravity Conjecture for EFTs with U(1) Gauge Fields Coupled to Gravity

Prove the Weak Gravity Conjecture by demonstrating that any effective field theory coupled to gravity and containing a U(1) gauge field admits a self‑repulsive charged state whose mass m and charge q satisfy the inequality m < sqrt(2) g q M_p, where g is the gauge coupling and M_p is the Planck mass.

Background

Within the Swampland program, general constraints are proposed to delineate which low‑energy effective field theories can arise from a consistent quantum gravity. The Weak Gravity Conjecture (WGC) is a central example positing that gravity must be the weakest force, formulated as the existence of a charged state lighter than its extremal bound. The authors highlight its role and present the canonical inequality form.

Establishing or refuting the WGC has far‑reaching implications for model building, compactifications, and the spectrum of states in quantum gravity. Although circumstantial evidence is extensive, the conjecture remains formally unproven and is a key open problem in the Swampland program.