AdS Virasoro-Shapiro amplitude with KK modes

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 $⟨{\mathcal{O}}_2{\mathcal{O}}_2{\mathcal{O}}_p{\mathcal{O}}_p⟩$ 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.

28 pages, 1 figure