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 M ₏₋. However, it is known that the EFT of gravity can break down at a lower scale, the species scale ₛ M ₏₋, if there are light species of particles. Here we point out that there is a third scale ₁₇ ₛ M ₏₋, 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 ₁₇ 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 ₁₇ 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 ₁₇ is close to the mass scale of the lightest tower but deviates from it as we move inwards in the moduli space.