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The Tale of Three Scales: the Planck, the Species, and the Black Hole Scales
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abstract
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 $\Lambda_s\lesssim M_{\rm pl}$, if there are light species of particles. Here we point out that there is a third scale $\Lambda_{\rm BH}\lesssim \Lambda_s\lesssim M_{\rm pl}$, 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 $\Lambda_{\rm BH}$ 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 $\Lambda_{\rm BH}$ 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 $\Lambda_{\rm BH}$ is close to the mass scale of the lightest tower but deviates from it as we move inwards in the moduli space.
Forward citations
Cited by 14 Pith papers
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Tame Complexity of Effective Field Theories in the Quantum Gravity Landscape
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Quantum gravity EFT actions organize higher-curvature corrections into a field-theoretic expansion suppressed by the lightest new mass and a quantum-gravitational expansion suppressed by the species scale.
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String stars in $d\geq 7$
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Kaluza-Klein tower thresholds and scheme dependence of the species scale
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IR Black Hole Instabilities Trigger Species-Scale Particle Production
A mechanism is proposed in which black hole instability at the tower scale converts a fraction of the mass into particles at the species scale, with Hawking evaporation subdominant.
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Stochastic Survival near Swampland Boundaries
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Classical Black Hole Probes of UV Scales
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Phases of String Stars in the Presence of a Spatial Circle
String star phase diagrams on a spatial circle are computed: new d=2 solutions, a quartic-induced d=5 swallowtail, and an anomalous d=6 stability pattern.
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Moduli Space Quantum Mechanics
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A two-parameter fading dark sector model, with exponential dark energy potential and exponential dark matter mass, matches DESI DR2 plus supernova data and naturally yields apparent w<-1 phantom behavior.
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A short overview on the Black Hole-Tower Correspondence and Species Thermodynamics
A review of the black hole-tower correspondence and species thermodynamics, which aim to explain black hole entropy via towers of light states and to show only certain towers are allowed.
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