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.
Highlights
Introduction and summaryEven though holographic correlators have been a subject of study since the early days of the AdS/CFT correspondence [1,2,3], they are in many cases hard or even impossible to compute directly
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
In this paper we focus on tree-level Witten diagrams, and in the rest of this section we aim to determine a basis of Mellin amplitudes that can be used to write the contribution from contact Witten diagrams with small numbers of derivatives
Summary
Even though holographic correlators have been a subject of study since the early days of the AdS/CFT correspondence [1,2,3] (see for example [4,5,6,7,8,9,10,11,12] for early work on four-point functions), they are in many cases hard or even impossible to compute directly. [21, 23, 25] showed that the tree-level Witten diagram corresponding to an R4 contact interaction, which is the first correction to supergravity in both 10d and 11d, can be completely determined using either supersymmetric localization or the flat space scattering amplitudes. (As shown in [49], cT is exactly calculable in ABJM theory using the supersymmetric localization results of [50] and [51] It behaves as cT ∝ k1/2N 3/2 at large N .) The Mellin amplitudes in (1.2) can be related to the 4-point scattering amplitudes of supergravitons in 11d and 10d flat space using the relation proposed in [36]: M-theory: type IIA, small gs: type IIA, finite gs: A11 = A1S1G.
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