More on the weak gravity conjecture via convexity of charged operators

The Weak Gravity Conjecture has recently been re-formulated in terms of a particle with non-negative self-binding energy. Because the dual conformal field theory (CFT) formulation anti-de Sitter space dimension $\Delta (Q)$ lowest-dimension operator charge Q under some global U(1) symmetry must be convex function Q. This property conjectured to hold for any (unitary) and generalized larger groups. Here we refine further test conjecture via semiclassical computations fixed sectors different theories dimensions. We analyze convexity properties leading next-to-leading order stemming from computation, de facto, extending previous tests beyond perturbative contributions arbitrary charges. In particular, contribution is sufficient computations. also consider intriguing cases which models feature transition real complex dimensions either as or number matter fields. As relevant example first kind, investigate $O(N)$ model $4+\epsilon$ an second type $U(N)\times U(M)$ $4-\epsilon$ Both display rich dynamics where, by changing fields and/or charge, one can achieve dramatically physical regimes. discover that whenever appears, part satisfies property.