  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.
