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 $Ad{S}_4\times {\mathbb{CP}}^3$ to all orders in ${\alpha }^{\prime }$, 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 $D^4{R}^4$ correction at finite AdS curvature, and to give many predictions for future integrability studies.

arXiv comment35 pages, 1 figure, v2: JHEP version, v3: fix typo in (A.8)

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