AdS4/CFT3 from weak to strong string coupling

Abstract

A bstract 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/k 5 is held fixed. In this limit, ABJM theory is holographically dual to type IIA string theory on AdS 4 × ℂℙ 3 at finite string coupling g s ∼ ( N/k 5 ) 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 R 4 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 R 4 correction as a function of N/k 5 . Taking its flat space limit, we recover the known R 4 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 AdS 4 × ℂℙ 3 at small string coupling and M-theory on AdS 4 × S 7 / ℤ k .