N = 4 Super-Yang-Mills correlators at strong coupling from string theory and localization

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 S⁴ 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 AdS₅× S⁵, which in the flat space limit are known from worldsheet calculations. These two methods match at the order corresponding to the tree level R⁴ 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 D⁴R⁴ order. Combined with constraints from [1], our results can be used to derive CFT data to one-loop D⁴R⁴ 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 S⁴ 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.