Gravitational S-matrix from CFT dispersion relations

TL;DR

This paper uses CFT dispersion relations to analyze four-point correlators in N=4 SYM, extracting one-loop supergravity effects and confirming the duality with IIB supergravity scattering amplitudes.

Contribution

It introduces two equivalent inversion methods to extract one-loop supergravity data from CFT correlators, connecting conformal field theory and flat-space scattering amplitudes.

Findings

Successful extraction of one-loop supergravity effects from CFT data.

Agreement between CFT-based calculations and IIB supergravity scattering amplitudes.

Validation of dispersion relation techniques in holographic duality context.

Abstract

We analyse the double-discontinuities of the four-point correlator of the stress-tensor multiplet in N=4 SYM at large t' Hooft coupling and at order $1/N^4$, as a way to access one-loop effects in the dual supergravity theory. From these singularities we extract CFT-data by using two inversion procedures: one based on a recently proposed Froissart-Gribov inversion integral, and the other based on large spin perturbation theory. Both procedures lead to the same results and are shown to be equivalent more generally. Our computation parallels the standard S-matrix reconstruction via dispersion relations. In a suitable limit, the result of the conformal field theory calculation is compared with the one-loop graviton scattering amplitude in ten-dimensional IIB supergravity in flat space, finding perfect agreement.