Quantum gravity (QG) has a natural cutoff given by the Planck scale $M_{\rm pl}$. However, it is known that the EFT of gravity can break down at a lower scale, the species scale $Λ_s\lesssim M_{\rm pl}$, if there are light species of particles. Here we point out that there is a third scale $Λ_{\rm BH}\lesssim Λ_s\lesssim M_{\rm pl}$, 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 $Λ_{\rm BH}$ 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 $Λ_{\rm BH}$ 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 $Λ_{\rm BH}$ is close to the mass scale of the lightest tower but deviates from it as we move inwards in the moduli space.
Probing Planck-Scale Physics with High-Frequency Gravitational Waves
University of California, Santa Cruz（加州大学圣克鲁兹分校）；Santa Cruz Institute for Particle Physics, University of California, Santa Cruz（加州大学圣克鲁兹分校圣克鲁兹粒子物理研究所）
