Shear Viscosity from Effective Couplings of Gravitons

TL;DR

This paper calculates the shear viscosity of strongly coupled field theories with gravity duals, showing it depends on the effective coupling of transverse gravitons at the horizon, and explores how higher curvature and matter field corrections influence this ratio.

Contribution

It derives a universal formula linking shear viscosity to effective graviton couplings and applies it to Einstein and Gauss-Bonnet gravities with matter corrections.

Findings

Shear viscosity is determined by the effective coupling of transverse gravitons.

Higher curvature and matter field corrections modify the viscosity-to-entropy ratio.

The formula is validated for Einstein and Gauss-Bonnet gravity models.

Abstract

We calculate the shear viscosity of field theories with gravity duals using Kubo-formula by calculating the Green function of dual transverse gravitons and confirm that the value of the shear viscosity is fully determined by the effective coupling of transverse gravitons on the horizon. We calculate the effective coupling of transverse gravitons for Einstein and Gauss-Bonnet gravities coupled with matter fields, respectively. Then we apply the resulting formula to the case of AdS Gauss-Bonnet gravity with $F^4$ term corrections of Maxwell field and discuss the effect of $F^4$ terms on the ratio of the shear viscosity to entropy density.