The type IIA Virasoro-Shapiro amplitude in AdS4 × CP3 from ABJM theory

Abstract

We consider tree level scattering of gravitons in type IIA string theory on AdS₄ × ${\mathbb{CP}}^3$ to all orders in α^′, which is dual to the stress tensor correlator in U(N)_k × U(N)_−k ABJM theory in the planar large N limit and to all orders in large λ ~ 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 R⁴ 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 D⁴R⁴ correction at finite AdS curvature, and to give many predictions for future integrability studies.