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.
Highlights
While corrections in 1/N come from bulk loop diagrams with internal 10d supergravitons
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
Despite the lack of knowledge of the precise 10d bulk interaction vertices that contribute to the four-point functions, we will use a combination of recent techniques to determine the first three terms in the 1/λ expansion of these correlation functions
Summary
Let us begin by discussing the large N , strong coupling expansion of the four-point function. The superconformal Ward identities relating the Spi to one another [31], given in appendix B, are identical for any p Quite remarkably, they can be solved in terms of a single unconstrained function Tp of U, V by writing Spi as [31]: Spi (U, V ) = Θi(U, V )Tp(U, V ) + Spi,free(U, V ) , Θi(U, V ) ≡ VUVUU (U − V − 1) 1 − U − V V (V − U − 1). Does this function determine S2S2SpSp , but through the superconformal Ward identities it (along with c) uniquely determines all other correlators related to it through supersymmetry. In the appendix B we discuss these superconformal Ward identities in more detail
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