Nonlinear Hydrodynamics from Flow of Retarded Green's Function

TL;DR

This paper analytically solves nonlinear flow equations for retarded Green's functions in holography, deriving second order transport coefficients for dual gauge theories with higher derivative corrections, including effects of chemical potentials.

Contribution

It provides an analytical method to compute second order transport coefficients from nonlinear flow equations in holography, including higher derivative and chemical potential effects.

Findings

Analytical solutions to nonlinear Riccati flow equations.

Explicit expressions for second order transport coefficients.

Higher derivative corrections and chemical potential effects included.

Abstract

We study the radial flow of retarded Green's function of energy-momentum tensor and $R$-current of dual gauge theory in presence of generic higher derivative terms in bulk Lagrangian. These are first order non-linear Riccati equations. We solve these flow equations analytically and obtain second order transport coefficients of boundary plasma. This way of computing transport coefficients has an advantage over usual Kubo approach. The non-linear equation turns out to be a linear first order equation when we study the Green's function perturbatively in momentum. We consider several examples including $Weyl^4$ term and generic four derivative terms in bulk. We also study the flow equations for $R$-charged black holes and obtain exact expressions for second order transport coefficients for dual plasma in presence of arbitrary chemical potentials. Finally we obtain higher derivative corrections to second order transport coefficients of boundary theory dual to five dimensional gauge supergravity.