  We search for a possible relation between weak gravity conjecture and
conformal field theory in the hyperscaling violating and Kerr-Newman-AdS black
holes. We deal with the critical points of the black hole systems through the
correlation function introduced in conformal field theory. We discuss the weak
gravity conjecture conditions by the imaginary part of the energy obtained from
the critical points and their poles. Under the assumptions $z=1$, $d=1$ and
$\theta\rightarrow0^{-}$, we link weak gravity conjecture to the hyperscaling
violating black holes due to the existence of $r_{H}$ larger and smaller than
one. As the second black hole system, we study the conditions of weak gravity
conjecture for the Kerr-Newman-AdS black hole by rotation and radius
parameters. Then, we show that the conditions of weak gravity conjecture are
satisfied when the charged particle near the hyperscaling violating and
Kerr-Newman black holes is $\frac{1}{a}$ with a ratio $\frac{a}{\ell}\ll 1$.

High Energy Physics - Theory;General Relativity and Quantum Cosmology