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

TL;DR

This paper computes the tree-level graviton scattering amplitude in type IIA string theory on AdS4×CP3, incorporating all orders in α' and curvature corrections, and matches these with integrability and localization results.

Contribution

It introduces a method to fix curvature corrections in the Virasoro-Shapiro amplitude in AdS4×CP3 using superconformal blocks and worldsheet ansatz, extending previous finite curvature results.

Findings

First correction matches integrability and localization results.

Second curvature correction fixed and passes consistency checks.

Results enable predictions for future integrability analyses.

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.