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

TL;DR

This work combines supersymmetric localization and AdS/CFT to determine 1/λ corrections to four-point functions of half-BPS operators in N=4 SYM at large N and strong coupling, exposing the first subleading higher-derivative bulk couplings (R^4 and D^4R^4) via a Mellin-space bootstrap constrained by Ward identities and crossing. Localization bounds the integrated correlators by derivatives of the S^4 partition function with mass and Coulomb-branch deformations, while flat-space string amplitudes fix the corresponding Mellin structures; together they yield exact leading corrections and consistent subleading data, including one-loop implications through Alday’s framework. The results reproduce the expected R^4 coefficient through AdS/CFT as nontrivial evidence beyond supergravity and predict the Eisenstein-series structure governing very strong coupling (finite g_YM) behavior, tying nonperturbative instanton effects to the holographic correlators. The paper thus forges a concrete bridge between localization, holography, and string-theoretic amplitudes to pin down CFT data at tree and 1-loop levels and outlines a program to extend to higher-derivative terms and nonperturbative regimes.

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 $λ=g_\text{YM}^2 N$ 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 $1/λ$ 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 $AdS_5\times S^5$, 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 $D^4R^4$ order. Combined with constraints from arXiv:1809.10670, our results can be used to derive CFT data to one-loop $D^4R^4$ order. Finally, we use AdS/CFT to fix these correlators in the limit where $N$ is taken to be large while $g_{\rm YM}$ 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.