  The promising solution to the strong CP problem by a Peccei-Quinn (PQ)
symmetry may introduce quality and hierarchy problems, which are both relevant
to Planck physics. In this paper, we study whether both problems can be
explained by introducing a simple hidden gauge group that satisfies a weak
gravity conjecture (WGC) or its variant. As a concrete example, we point out
that a weakly-coupled hidden $SU(N)$ gauge symmetry, which is broken down to
$SO(N)$, can do this job in the context of a Tower/sub-Lattice WGC. Cosmology
is discussed.
