Improved hydrodynamics from the AdS/CFT duality

We generalize (linearized) relativistic hydrodynamics by including all order gradient expansion of the energy-momentum tensor, parametrized by four momenta-dependent transport coefficients, one of which is the usual shear viscosity. We then apply the AdS/CFT duality for N=4 SUSY in order to compute the retarded correlators of the energy-momentum tensor. From these correlators we determine a large set of transport coefficients of third- and fourth-order hydrodynamics. We find that higher order terms have a tendency to reduce the effect of viscosity.