Axion species scale and axion weak gravity conjecture-like bound

As a cutoff scale of quantum gravity, the species scale can be defined by the scale at which the perturbativity of the non-renormalizable gravitational interaction begins to break down. Since it is determined by the number of species in the effective field theory, we can find the close connection to the distance conjecture, which predicts the lowering of the cutoff at the asymptotic limit of the moduli space caused by the descent of a tower of states from UV. Meanwhile, the same kind of the cutoff scale can be obtained from any non-renormalizable interaction, in particular the interaction between the axion and the gauge field through the $\theta F\wedge F$ term. Demanding this `axion species scale' not to exceed the gravitational species scale, we obtain the bound $(8\pi^2/g^2)f \lesssim M_{\rm Pl}$. This is quite similar to the axion weak gravity conjecture bound, but can be applied to any gauge as well as the string interactions which are relevant to towers of states. We also investigate the implications of the (axion) species scale and the axion weak gravity conjecture-like bound by considering the Peccei-Quinn charge reduction of black hole through the interaction between black hole and the string or wormhole.