$\mathcal{N}=4$ Super-Yang-Mills Correlators at Strong Coupling from String Theory and Localization

Abstract

We compute $1/\lambda$ 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 $\lambda =g_{\text{YM}}^{2}N$ 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 $Ad{S}_5\times S^5$, 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 arXiv:1809.10670, 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 $g_{\mathrm{YM}}$ 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.

arXiv comment33 pages plus appendices, v2 fixed minor typos, version submitted to journal

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