Density of states, black holes and the Emergent String Conjecture

A bstract We study universal features of the density of one-particle states ρ ( E ) in weakly coupled theories of gravity at energies above the quantum gravity cutoff Λ, defined as the scale suppressing higher-derivative corrections to the Einstein-Hilbert action. Using thermodynamic properties of black holes, we show that in asymptotically flat spacetimes, certain features of ρ ( E ) above the black hole threshold M min are an indicator for the existence of large extra dimensions, and cannot be reproduced by any lower-dimensional field theory with finitely many fields satisfying the weak energy condition. Based on the properties of gravitational scattering amplitudes, we argue that there needs to exist a (possibly higher-dimensional) effective description of gravity valid up to the cutoff Λ. Combining this with thermodynamic arguments we demonstrate that ρ ( E ) has to grow exponentially for energies Λ ≪ E ≪ M min . Furthermore we show that the tension of any weakly coupled p -brane with p ≥ 1 is bounded from below by Λ p +1 . We use this to argue that any tower of weakly coupled states with mass below Λ has to be a Kaluza-Klein (KK) tower. Altogether these results indicate that in gravitational weak-coupling limits the lightest tower of states is either a KK tower, or has an exponentially growing degeneracy thereby resembling a string tower. This provides evidence for the Emergent String Conjecture without explicitly relying on string theory or supersymmetry.