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 pl . However, it is known that the effective field theory (EFT) of gravity can break down at a lower scale, the species scale Λ s ≲ M pl , if there are light species of particles. Here we point out that there is a third scale Λ BH ≲ Λ s ≲ M pl , which marks the inverse length (or the temperature) of the smallest black hole where the EFT gives a correct description of its entropy and free energy. This latter scale is hard to detect from the viewpoint of EFT as it represents a phase transition to a state with lower free energy. We illustrate this using examples drawn from consistent QG landscape. In particular Λ BH 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 Λ BH 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 Λ BH is close to the mass scale of the lightest tower but deviates from it as we move inwards in the moduli space.