The Weak Gravity Conjecture in Asymptotically Safe Quantum Gravity

Abstract

The Weak Gravity Conjecture (WGC) posits that gravity must be the weakest force in any consistent theory of quantum gravity. Originally formulated to constrain the landscape of effective field theories arising from string theory, the WGC suggests the existence of states with a charge-to-mass ratio larger than that of extremal black holes. In this work, we revisit the WGC within the framework of Asymptotically Safe Quantum Gravity, a non-perturbative approach where gravitational and gauge couplings flow to a non-Gaussian ultraviolet (UV) fixed point. We construct a scale-dependent effective action, derive quantum-corrected Reissner--Nordstr\"om black hole solutions by incorporating position-dependent renormalization scale identification, and compute leading quantum corrections to the extremality condition. Our key finding is that the quantum correction to the extremal charge-to-mass ratio is dominantly governed by the running of the gauge coupling, characterized by a correction parameter $\delta \sim \epsilon_e (\ell_P/r_+)^{2\theta}$, where $\epsilon_e$ captures deviations from infrared behavior. We show that if the electromagnetic coupling grows in the UV ($\epsilon_e > \epsilon_G$), the WGC is dynamically strengthened, whereas if it decreases ($\epsilon_e < \epsilon_G$), large extremal black holes may violate the WGC unless additional light charged states exist. Our analysis demonstrates that Asymptotic Safety provides a concrete ultraviolet mechanism influencing low-energy swampland criteria, offering a deep UV/IR connection between quantum gravity consistency and effective field theory behavior.