Second-order transport, quasinormal modes and zero-viscosity limit in the Gauss-Bonnet holographic fluid

Gauss-Bonnet holographic fluid is a useful theoretical laboratory to study the effects of curvature-squared terms in the dual gravity action on transport coefficients, quasinormal spectra and the analytic structure of thermal correlators at strong coupling. To understand the behavior and possible pathologies of the Gauss-Bonnet fluid in $3+1$ dimensions, we compute (analytically and non-perturbatively in the Gauss-Bonnet coupling) its second-order transport coefficients, the retarded two- and three-point correlation functions of the energy-momentum tensor in the hydrodynamic regime as well as the relevant quasinormal spectrum. The Haack-Yarom universal relation among the second-order transport coefficients is violated at second order in the Gauss-Bonnet coupling. In the zero-viscosity limit, the holographic fluid still produces entropy, while the momentum diffusion and the sound attenuation are suppressed at all orders in the hydrodynamic expansion. By adding higher-derivative electromagnetic field terms to the action, we also compute corrections to charge diffusion and identify the non-perturbative parameter regime in which the charge diffusion constant vanishes.