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

We compute 1/lambda 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 lambda = g(YM)(2)N 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/lambda using supersymmetric localization. Secondly, we use AdS/CFT to relate these 1/lambda corrections to higher derivative corrections to supergravity for scattering amplitudes of Kaluza-Klein scalars in IIB string theory on AdS(5) x 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 (DR4)-R-4 order. Combined with constraints from [1], our results can be used to derive CFT data to one-loop (DR4)-R-4 order. Finally, we use AdS/CFT to fix these correlators in the limit where N is taken to be large while g(YM) 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.