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

Abstract

Quantum gravity (QG) has a natural cutoff given by the Planck scale $M_{\mathrm{pl}}$. However, it is known that the EFT of gravity can break down at a lower scale, the species scale ${\Lambda }_s\lesssim M_{\mathrm{pl}}$, if there are light species of particles. Here we point out that there is a third scale ${\Lambda }_{\mathrm{BH}}\lesssim {\Lambda }_s\lesssim M_{\mathrm{pl}}$, 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 ${\Lambda }_{\mathrm{BH}}$ 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 ${\Lambda }_{\mathrm{BH}}$ 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 ${\Lambda }_{\mathrm{BH}}$ is close to the mass scale of the lightest tower but deviates from it as we move inwards in the moduli space.

8+1 pages, 2 figures, added appendix for clarification

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