More on the Weak Gravity Conjecture via Convexity of Charged Operators

Understand

The Weak Gravity Conjecture has recently been re-formulated in terms of a particle with non-negative self-binding energy.

• Because of the dual conformal field theory (CFT) formulation in the anti-de Sitter space the conformal dimension $\Delta (Q)$ of the lowest-dimension operator with charge Q under some global U(1) symmetry must be a convex function of Q.
• This property has been conjectured to hold for any (unitary) conformal field theory and generalized to larger global symmetry groups.
• Here we refine and further test the convex charge conjecture via semiclassical computations for fixed charge sectors of different theories in different dimensions.