AdS Virasoro-Shapiro amplitude with KK modes

TL;DR

This paper computes the first curvature correction to the AdS Virasoro-Shapiro amplitude involving KK modes, providing new strong-coupling OPE data for operators in N=4 SYM and confirming results through multiple methods.

Contribution

It introduces a novel calculation of the curvature correction to the string amplitude with KK modes in AdS, connecting it to OPE data and integrability results.

Findings

Determined the curvature correction integral form involving polylogarithms.

Fixed OPE data for operators with non-zero R-charge and odd spin.

Validated results against integrability, localisation, and effective action.

Abstract

We determine the first curvature correction for the string amplitude of two supergravity states and two Kaluza-Klein modes on $\text{AdS}_5 \times \text{S}^5$, which is dual to the correlator $\langle \mathcal{O}_2 \mathcal{O}_2 \mathcal{O}_p \mathcal{O}_p \rangle$ of half-BPS operators in $\mathcal{N}=4$ SYM theory. The result has the form of an integral over the Riemann sphere as for the usual Virasoro-Shapiro amplitude, with the insertion of single-valued multiple polylogarithms of weight three. The result fixes OPE data of single-trace operators in $\mathcal{N}=4$ SYM theory at strong coupling, including operators with non-zero $R$-charge and odd spin. We successfully check our results by comparing to data available from integrability, localisation and consistency with a $10d$ effective action.