### Abstract

We compute 1/λ corrections to the four-point functions of half-BPS operators in SU(N) N = 4 super-Yang-Mills theory at large N and large ’t Hooft coupling λ = gYM2N using two methods. Firstly, we relate integrals of these correlators to derivatives of the mass deformed S^{4} free energy, which was computed at leading order in large N and to all orders in 1/λ using supersymmetric localization. Secondly, we use AdS/CFT to relate these 1/λ corrections to higher derivative corrections to supergravity for scattering amplitudes of Kaluza-Klein scalars in IIB string theory on AdS_{5}× S^{5}, which in the flat space limit are known from worldsheet calculations. These two methods match at the order corresponding to the tree level R^{4} interaction in string theory, which provides a precise check of AdS/CFT beyond supergravity, and allow us to derive the holographic correlators to tree level D^{4}R^{4} order. Combined with constraints from [1], our results can be used to derive CFT data to one-loop D^{4}R^{4} order. Finally, we use AdS/CFT to fix these correlators in the limit where N is taken to be large while gYM is kept fixed. In this limit, we present a conjecture for the small mass limit of the S^{4} partition function that includes all instanton corrections and is written in terms of the same Eisenstein series that appear in the study of string theory scattering amplitudes.

Original language | English (US) |
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Article number | 119 |

Journal | Journal of High Energy Physics |

Volume | 2019 |

Issue number | 12 |

DOIs | |

State | Published - Dec 1 2019 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Keywords

- 1/N Expansion
- AdS-CFT Correspondence
- Extended Supersymmetry

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## Cite this

*Journal of High Energy Physics*,

*2019*(12), [119]. https://doi.org/10.1007/JHEP12(2019)119