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 (SYM) 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 $\mathcal{O}({\lambda }^{-3/2})$ corrections. There are no reliable first principle computations of the $\mathcal{N}=4$ plasma nonequilibrium properties beyond the stated order. We show extreme sensitivity of the nonhydrodynamic spectra of holographic $\mathcal{N}=4$ SYM plasma to $\mathcal{O}({\lambda }^{-3})$ corrections, challenging any conclusions reached from “resummation” of $\mathcal{O}({\lambda }^{-3/2})$ corrections.

Figure 1

Left panel: The lowest QNM frequencies ${\mathfrak{w}}_{\mathcal{O}(\gamma )}^{[1]}$ computed with (1.10) (solid blue curve) and the lowest QNM frequencies ${\mathfrak{w}}_{\mathcal{O}({\gamma }^2)}^{[1]}$ computed with (1.11) with $\alpha =0$ (dashed red curve). Right panel: Log-comparison of the lowest QNM frequencies for different orders of the approximation of the gravitational effective action.

Figure 2

The lowest QNM frequencies ${\mathfrak{w}}_{\mathcal{O}({\gamma }^2)}^{[1]}$ computed with (1.11) at $\gamma ={10}^{-3}$ as a function of the phenomenological parameter $\alpha$.