Hydrodynamic dispersion relations at finite coupling

Understand

By using holographic methods, the radii of convergence of the hydrodynamic shear and sound dispersion relations were previously computed in the ${\cal N} = 4$ supersymmetric Yang-Mills theory at infinite 't Hooft coupling and infinite number of colours.

• Here, we extend this analysis to the domain of large but finite 't Hooft coupling.
• To leading order in the perturbative expansion, we find that the radii grow with increasing inverse coupling, contrary to naive expectations.
• However, when the equations of motion are solved using a qualitative non-perturbative resummation, the dependence on the coupling becomes piecewise continuous and the initial growth is followed by a decrease.