The type IIA Virasoro-Shapiro amplitude in AdS$_4$ $\times$ CP$^3$ from ABJM theory

Abstract

We consider tree level scattering of gravitons in type IIA string theory on $AdS_4\times \mathbb{CP}^3$ to all orders in $\alpha'$, which is dual to the stress tensor correlator in $U(N)_k\times U(N)_{-k}$ ABJM theory in the planar large $N$ limit and to all orders in large $\lambda\sim N/k$. The small curvature expansion of this correlator, defined via a Borel transform, is given by the flat space Virasoro-Shapiro amplitude plus AdS curvature corrections. We fix curvature corrections by demanding that their resonances are consistent with the superconformal block expansion of the correlator and with a worldsheet ansatz in terms of single-valued multiple polylogarithms. The first correction is fully fixed in this way, and matches independent results from integrability, as well as the $R^4$ correction at finite AdS curvature that was previously fixed using supersymmetric localization. We are also able to fix the second curvature correction by using a few additional assumptions, and find that it also satisfies various non-trivial consistency checks. We use our results to fix the tree level $D^4R^4$ correction at finite AdS curvature, and to give many predictions for future integrability studies.