Higher Derivative Corrections to Shear Viscosity from Graviton's Effective Coupling

TL;DR

This work addresses how higher-derivative bulk terms in gravity modify the holographic shear viscosity of the boundary fluid. The authors construct an effective graviton action in canonical form to first order in the higher-derivative coupling $\mu$, ensuring its equation of motion matches the original theory to that order, and show that the shear viscosity is determined by the horizon value of the graviton's effective coupling $K_{\mathrm{eff}}(r)$. They provide a concrete procedure to compute the corrections, including fixing a normalization $\Gamma=0$, deriving a radial flow relation, and connecting to the membrane paradigm. The method is validated on two nontrivial cases: a general four-derivative bulk action and the Weyl^4 eight-derivative term from string theory, with results agreeing with existing literature. The approach offers a systematic way to obtain transport coefficients in generic higher-derivative gravity and emphasizes the near-horizon data as the key driver of boundary hydrodynamics.

Abstract

The shear viscosity coefficient of strongly coupled boundary gauge theory plasma depends on the horizon value of the effective coupling of transverse graviton moving in black hole background. The proof for the above statement is based on the canonical form of graviton's action. But in presence of generic higher derivative terms in the bulk Lagrangian the action is no longer canonical. We give a procedure to find an effective action for graviton (to first order in coefficient of higher derivative term) in canonical form in presence of any arbitrary higher derivative terms in the bulk. From that effective action we find the effective coupling constant for transverse graviton which in general depends on the radial coordinate $r$. We also argue that horizon value of this effective coupling is related to the shear viscosity coefficient of the boundary fluid in higher derivative gravity. We explicitly check this procedure for two specific examples: (1) four derivative action and (2) eight derivative action ($Weyl^4$ term). For both cases we show that our results for shear viscosity coefficient (up to first order in coefficient of higher derivative term) completely agree with the existing results in the literature.