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

Abstract

We compute 1/λ corrections to the four-point functions of half-BPS operators in SU(N) mathcal{N} = 4 super-Yang-Mills theory at large N and large ’t Hooft coupling λ = {g}_{mathrm{YM}}^2N 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.