The AdS$_3\times $S$^3$ Virasoro-Shapiro amplitude with RR flux

TL;DR

This paper calculates the all-order curvature corrections to the AdS$_3$ Virasoro-Shapiro amplitude with RR flux, linking string theory scattering amplitudes to dual CFT data and providing insights for integrability at strong coupling.

Contribution

It introduces a method to compute the AdS$_3$ Virasoro-Shapiro amplitude with RR flux to all orders in $'$ using a worldsheet integral ansatz and flat space limit matching, fixing the first curvature correction.

Findings

First curvature correction fully determined and consistent with high energy limits.

Provides infinite predictions for CFT data at strong coupling.

Establishes a framework for future integrability studies in AdS$_3$/CFT$_2$.

Abstract

We compute the AdS Virasoro-Shapiro amplitude for scattering of dilatons in type IIB string theory with pure RR flux on $AdS_3\times S^3\times M_4$ for $M_4=T^4$ or $K3$, to all orders in $\alpha'$ in a small AdS curvature expansion. This is achieved by comparing the flat space limit of the dual D1D5 CFT correlator to an ansatz for the amplitude as a worldsheet integral in terms of single valued multiple polylogarithms. The first curvature correction is fully fixed in this way, and satisfies consistency checks in the high energy limit, and by comparison of the energy of massive string operators to a semiclassical expansion. Our result gives infinite predictions for CFT data in the planar limit at strong coupling, which can guide future integrability studies.