Grozdanov, SasoKovtun, PavelStarinets, Andrei O.Tadic, Petar2020-11-102020-11-1020192019Grozdanov, S., Kovtun, P. K., Starinets, A. O., & Tadić, P. (2019) The complex life of hydrodynamic modes. Journal of High Energy Physics, 2019(97). https://doi.org/10.1007/JHEP11(2019)097https://doi.org/10.1007/JHEP11(2019)097http://hdl.handle.net/1828/12333We 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 N = 4 supersymmetric Yang-Mills theory in 3+1 dimensions, in a holographic model with broken translation symmetry in 2+1 dimensions, and in con- formal field theory in 1+1 dimensions. We comment on the pole-skipping phenomenon in thermal correlation functions, and show that it is not specific to energy density correlations.enBlack Holes in String TheoryEffective Field TheoriesGauge-gravity correspondenceHolography and quark-gluon plasmasArticleDepartment of Physics and Astronomy