AdS4/CFT3 from weak to strong string coupling

Abstract

We consider the four-point function of operators in the stress tensor multiplet of the U(N)k× U(N)−k ABJM theory, in the limit where N is taken to infinity while N/k5 is held fixed. In this limit, ABJM theory is holographically dual to type IIA string theory on AdS4× ℂℙ3 at finite string coupling gs∼ (N/k5)1/4. While at leading order in 1/N, the stress tensor multiplet four-point function can be computed from type IIA supergravity, in this work we focus on the first subleading correction, which comes from tree level Witten diagrams with an R4 interaction vertex. Using superconformal Ward identities, bulk locality, and the mass deformed sphere free energy previously computed to all orders in 1/N from supersymmetric localization, we determine this R4 correction as a function of N/k5. Taking its flat space limit, we recover the known R4 contribution to the type IIA S-matrix and reproduce the fact that it only receives perturbative contributions in gs from genus zero and genus one string worldsheets. This is the first check of AdS/CFT at finite gs for local operators. Our result for the four-point correlator interpolates between the large N, large ’t Hooft coupling limit and the large N finite k limit. From the bulk perspective, this is an interpolation between type IIA string theory on AdS4× ℂℙ3 at small string coupling and M-theory on AdS4× S7/ℤk.