Tale of three scales: The Planck, the species, and the black hole scales
Alek Bedroya (Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138, USA, Princeton Gravity Initiative, Princeton University, Princeton, New Jersey 08544, USA)
; Cumrun Vafa (Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138, USA); David H. Wu (Jefferson Physical Laboratory, Harvard University, Cambridge, Massachusetts 02138, USA)
Quantum gravity (QG) has a natural cutoff given by the Planck scale . However, it is known that the effective field theory (EFT) of gravity can break down at a lower scale, the species scale , if there are light species of particles. Here we point out that there is a third scale , 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 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 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 is close to the mass scale of the lightest tower but deviates from it as we move inwards in the moduli space.