Convexity of Charged Operators in CFTs with Multiple Abelian Symmetries

Understand

Motivated by the Weak Gravity Conjecture in the context of holography in AdS, it has been proposed that operators charged under global symmetries in CFTs, in three dimensions or higher, should satisfy certain convexity properties on their spectrum.

• A key element of this proposal is the charge at which convexity must appear, which was proposed to never be parametrically large.
• In this paper, we develop this constraint in the context of multiple Abelian global symmetries.
• We propose the statement that the convex directions in the multi-dimensional charge space should generate a sub-lattice of the total lattice of charged operators, such that the index of this sub-lattice cannot be made parametrically large.