Density of states, black holes and the Emergent String Conjecture

We study universal features of the density of one-particle states rho(E) in weakly coupled theories of gravity at energies above the quantum gravity cutoff Lambda, 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 rho(E) above the black hole threshold Mmin 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 Lambda. Combining this with thermodynamic arguments we demonstrate that rho(E) has to grow exponentially for energies Lambda << E << Mmin. Furthermore we show that the tension of any weakly coupled p-brane with p >= 1 is bounded from below by Lambda p+1. We use this to argue that any tower of weakly coupled states with mass below Lambda 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.