Weak Gravity Conjecture in AdS/CFT

TL;DR

The paper extends the weak gravity conjecture to AdS/CFT by proposing AdS-specific generalizations and translating them into CFT data via operator dimensions and central charges. It derives three families of inequalities—simple kinematic, dynamical, and large-black-hole bounds—that relate Δ, q, C_T, and C_V, and then tests them across known AdS/CFT examples, free theories, and large-N SUSY QCDs. The results show the proposed bounds are not universal across all CFTs, particularly failing for theories without a clear weakly coupled gravity dual, though they hold in several known holographic cases. The authors discuss possible universal refinements or bootstrap-based constraints and emphasize the regime dependence of these bounds in AdS/CFT.

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.