Newton vs. Coulomb in AdS/CFT and the Weak Gravity Conjecture

Abstract

We study (near-)circular orbits of charged particles in the background of charged black holes in asymptotically Anti-de Sitter (AdS) spacetimes of arbitrary dimensionality. We calculate the energy and angular momentum of such particles in a large-radius limit. This allows us to compute the anomalous dimension of the dual charged double-twist operators in a large-spin expansion, making a prediction for the bootstrap analysis at large charge and spin. We relate our result to the Weak Gravity Conjecture (WGC) for AdS black holes of all sizes. We also discuss the relation of WGC with the existence of the innermost stable circular orbit (ISCO) in any dimension.