The complex life of hydrodynamic modes

Understand

We study analytic properties of the dispersion relations in classical hydrodynamics by treating them as Puiseux series in complex momentum.

• The radii of convergence of the series are determined by the critical points of the associated complex spectral curves.
• For theories that admit a dual gravitational description through holography, the critical points correspond to level-crossings in the quasinormal spectrum of the dual black hole.
• We illustrate these methods in ${\cal N}=4$ supersymmetric Yang-Mills theory in 3+1 dimensions, in a holographic model with broken translation symmetry in 2+1 dimensions, and in conformal field theory in 1+1 dimensions.