Weak Gravity Conjecture in AdS/CFT

TL;DR

This paper explores how the weak gravity conjecture extends to AdS/CFT, deriving inequalities for CFT operators and testing their universality, revealing exceptions in certain supersymmetric theories.

Contribution

It generalizes the weak gravity conjecture to AdS spacetime and translates it into CFT inequalities, analyzing their validity across different theories.

Findings

Certain CFTs violate the derived inequalities.

Violations occur in supersymmetric QCDs at large N.

Violations do not contradict the conjecture in AdS due to weakly coupled gravity limitations.

Abstract

We study implications of the weak gravity conjecture in the AdS/CFT correspondence. Unlike in Minkowski spacetime, AdS spacetime has a physical length scale, so that the conjecture must be generalized with an additional parameter. We discuss possible generalizations and translate them into the language of dual CFTs, which take the form of inequalities involving the dimension and charge of an operator as well as the current and energy-momentum tensor central charges. We then test these inequalities against various CFTs to see if they are universally obeyed by all the CFTs. We find that certain CFTs, such as supersymmetric QCDs, do not satisfy them even in the large $N$ limit. This does not contradict the conjecture in AdS spacetime because the theories violating them are either unlikely or unclear to have weakly coupled gravitational descriptions, but it suggests that the CFT inequalities obtained here by naive translations do not apply beyond the regime in which weakly coupled gravitational descriptions are available.