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

Understand

Gauge theory/string theory holographic correspondence for ${\cal N}=4$ supersymmetric Yang-Mills theory is well under control in the planar limit, and for large (infinitely large) 't Hooft coupling, $\lambda\to \infty$.

• Certain aspects of the correspondence can be extended including ${\cal O}(\lambda^{-3/2})$ corrections.
• There are no reliable first principle computations of the ${\cal N}=4$ plasma non-equilibrium properties beyond the stated order.
• We show extreme sensitivity of the non-hydrodynamic spectra of holographic ${\cal N}=4$ SYM plasma to ${\cal O}(\lambda^{-3})$ corrections, challenging any conclusions reached from 'resummation' of ${\cal O}(\lambda^{-3/2})$ corrections.