The complex life of hydrodynamic modes

Transport properties of liquids and gases in the regime of weak coupling can be determined from relevant kinetic equations for particles or quasiparticles, with transport coefficients typically proportional to the minimal eigenvalue of the linearized kinetic operator. At strong coupling, the same physical quantities can in principle (for some QFTs) be found from dual gravity, where quasinormal spectra enter as eigenvalues of the linearized Einstein’s equations. We discuss the problem of interpolating between strong and weak coupling using the results from higher derivative gravity. We also consider the analytic structure of all-order hydrodynamic expansions arising from the associated complex analytic spectral curves and discuss how it is related to the phenomenon of level crossing in quasinormal spectra of dual black branes.