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

TL;DR

This paper develops a method to determine the effective coupling of gravitons in higher derivative gravity theories, linking it to shear viscosity in boundary gauge theories, and confirms the method with known examples.

Contribution

It provides a systematic procedure to find the effective graviton action in the presence of arbitrary higher derivative terms, extending previous results to more general theories.

Findings

Effective coupling at the horizon determines shear viscosity.

Method validated for four and eight derivative actions.

Results agree with existing literature for specific higher derivative corrections.

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.