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We review lessons from the AdS/CFT correspondence that indicate that theemergence of locality in quantum gravity is contingent on consideringobservables with a small number of insertions. Correlation functions where thenumber of insertions scales with a power of the central charge of the CFT aresensitive to nonlocal effects in the bulk theory, which arise from acombination of the effects of the bulk Gauss law and a breakdown ofperturbation theory. To examine whether a similar effect occurs in flat space,we consider the scattering of massless particles in the bosonic string and thesuperstring in the limit where the number of external particles, n, becomesvery large. We use estimates of the volume of the Weil-Petersson moduli spaceof punctured Riemann surfaces to argue that string amplitudes grow factoriallyin this limit. We verify this factorial behaviour through an extensivenumerical analysis of string amplitudes at large n. Our numerical calculationsrely on the observation that, in the large n limit, the string scatteringamplitude localizes on the Gross-Mende saddle points, even though individualparticle energies are small. This factorial growth implies the breakdown ofstring perturbation theory for $n \sim (M_{pl}/E)^{d-2}$ in d dimensions whereE is the typical individual particle energy. We explore the implications ofthis breakdown for the black hole information paradox. We show that the loss oflocality suggested by this breakdown is precisely sufficient to resolve thecloning and strong subadditivity paradoxes.

Loss of locality in gravitational correlators with a large number of insertions