### 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/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}.

Original language | English (US) |
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Article number | 34 |

Journal | Journal of High Energy Physics |

Volume | 2020 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2020 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Keywords

- 1/N Expansion
- AdS-CFT Correspondence
- Conformal Field Theory
- M-Theory

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## Cite this

_{4}/CFT

_{3}from weak to strong string coupling.

*Journal of High Energy Physics*,

*2020*(1), [34]. https://doi.org/10.1007/JHEP01(2020)034