The Tale of Three Scales: the Planck, the Species, and the Black Hole Scales

Quantum gravity (QG) has a natural cutoff given by the Planck scale Mₚₗ. However, it is known that the EFT of gravity can break down at a lower scale, the species scale Λₛ Mₚₗ, if there are light species of particles. Here we point out that there is a third scale ΛBH Λₛ Mₚₗ, which marks the inverse length (or the temperature) of the smallest black hole where the EFT gives a correct description of its entropy. This latter scale is hard to detect from the viewpoint of EFT as it represents a phase transition to a state with higher entropy. We illustrate this using examples drawn from consistent QG landscape. In particular ΛBH gets related to Gregory--Laflamme transition in the decompactification limits of quantum gravity and to the Horowitz--Polchinski solution in the light perturbative string limits. We propose the existence of ΛBH marking the temperature at which neutral black holes undergo a phase transition, as a new Swampland condition for all consistent quantum theories of gravity. In the asymptotic regimes of field space ΛBH is close to the mass scale of the lightest tower but deviates from it as we move inwards in the moduli space.