AdS₄/CFT₃ from weak to strong string coupling

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 g_s∼ (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 g_s from genus zero and genus one string worldsheets. This is the first check of AdS/CFT at finite g_s 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/ℤ_k.