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

## TL;DR

This paper investigates how the emergence of locality in quantum gravity breaks down with many insertions, showing factorial growth in string amplitudes at large n, which impacts the black hole information paradox.

## Contribution

It demonstrates that string scattering amplitudes grow factorially with many external particles, indicating a loss of locality and a breakdown of perturbation theory in high-insertion regimes.

## Key findings

- String amplitudes grow factorially at large n.
- Locality breaks down when n exceeds a certain threshold.
- Loss of locality helps resolve black hole information paradoxes.

## Abstract

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