Sensitivity of holographic $\mathcal{N}=4$ SYM plasma hydrodynamics to finite coupling corrections

Gauge theory/string theory holographic correspondence for $\mathcal{N}=4$ supersymmetric Yang-Mills theory is well under control in the planar limit, and for large (infinitely large) 't Hooft coupling, $\lambda \to \mathrm{\infty }$. Certain aspects of the correspondence can be extended including ${\cal O}(\lambda^{-3/2})$ corrections. There are no reliable first principle computations of the $\mathcal{N}=4$ plasma non-equilibrium properties beyond the stated order. We show extreme sensitivity of the non-hydrodynamic spectra of holographic $\mathcal{N}=4$ SYM plasma to $\mathcal{O}({\lambda }^{-3})$ corrections, challenging any conclusions reached from ‘resummation’ of ${\cal O}(\lambda^{-3/2})$ corrections.