Causality violation in the holographic approach to N=4 SYM theory at finite 't Hooft coupling

In the AdS/CFT correspondence, correlation functions of the energy-momentum tensor in N=4 supersymmetric Yang-Mills theory at large but finite 't Hooft coupling can be studied using higher-derivative corrections to supergravity. We show that the commonly used holographic prescription for correlation functions which is obtained by truncating the equations of motion at order $({\alpha }^{\mathrm{\prime }}{)}^3$ implies that the thermal equilibrium state of N=4 SYM theory in the planar limit is dynamically unstable at arbitrarily large finite 't Hooft coupling. The instability is a reflection of the unphysical causality violation brought about by treating perturbatively-derived equations as if they were non-perturbative, analogous to the instability of AdS black branes in five-dimensional Gauss-Bonnet gravity. While other holographic prescriptions for treating the $O({\alpha }^{\mathrm{\prime }3})$ corrections to supergravity may alleviate the pathology introduced by the truncation, the validity regime of the results obtained by any prescription at $O({\alpha }^{\mathrm{\prime }3})$ must be limited to the strict perturbative treatment of the $O({\alpha }^{\mathrm{\prime }3})$ effects on N=4 SYM observables.