The type IIA Virasoro-Shapiro amplitude in AdS4 × CP3 from ABJM theory
Shai M. Chester, Tobias Hansen, De-liang Zhong
Abstract
A bstract We consider tree level scattering of gravitons in type IIA string theory on AdS 4 × $$ {\mathbbm{CP}}^3 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>CP</mml:mi> <mml:mn>3</mml:mn> </mml:msup> </mml:math> 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 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.