AdS Virasoro-Shapiro from dispersive sum rules

TL;DR

This paper derives dispersive sum rules for the AdS Virasoro-Shapiro amplitude in ${ m AdS}_5 imes S^5$, constraining its form and linking it to CFT data, with a unique solution consistent with integrability and localization.

Contribution

It introduces a new set of dispersive sum rules in Mellin space that determine the amplitude's coefficients from CFT data, extending the understanding of AdS amplitudes.

Findings

Sum rules strongly constrain the amplitude.

All coefficients are expressed in terms of heavy string operator data.

A unique solution matches integrability and localization results.

Abstract

We consider the four-point correlator of the stress-energy tensor in ${\cal N}=4$ SYM, to leading order in inverse powers of the central charge, but including all order corrections in $1/\lambda$. This corresponds to the AdS version of the Virasoro-Shapiro amplitude to all orders in the small $\alpha'$/low energy expansion. Using dispersion relations in Mellin space, we derive an infinite set of sum rules. These sum rules strongly constrain the form of the amplitude, and determine all coefficients in the low energy expansion in terms of the CFT data for heavy string operators, in principle available from integrability. For the first set of corrections to the flat space amplitude we find a unique solution consistent with the results from integrability and localisation.