Emergence of Species Scale Black Hole Horizons

Abstract: The scale at which quantum gravity becomes manifest, the species scale $\Lambda_s$, has recently been argued to take values parametrically lower than the Planck scale. We use black holes of vanishing horizon area (small black holes) in effective field theories coupled to quantum gravity to shed light on how the three different physical manifestations of the species scale $\Lambda_s$ relate to each other. (i) Near the small black hole core, a scalar field runs to infinite distance in moduli space, a regime in which the Swampland Distance Conjecture predicts a tower of exponentially light states, which lower $\Lambda_s$. (ii) We integrate out modes in the tower and generate via Emergence a set of higher derivative corrections, showing that $\Lambda_s$ is the scale at which such terms become relevant. (iii) Finally, higher derivative terms modify the black hole solution and grant it a non-zero, species scale sized stretched horizon of radius $\Lambda_s^{-1}$, showcasing the species scale as the size of the smallest possible black hole describable in the effective theory. We present explicit 4d examples of small black holes in 4d $\mathcal{N}=2$ supergravity, and the 10d example of type IIA D0-branes. The emergence of the species scale horizon for D0-branes requires a non-trivial interplay of different 8-derivative terms in type IIA and M-theory, providing a highly non-trivial check of our unified description of the different phenomena associated to the species scale.