Shear Viscosity from Gauss-Bonnet Gravity with a Dilaton Coupling

TL;DR

The paper investigates how a nontrivial dilaton coupled to Gauss-Bonnet gravity in AdS/CFT modifies the shear viscosity to entropy density ratio $\frac{\eta}{s}$. Using an effective action for transverse gravitons and horizon data, the authors derive an explicit η/s formula that depends on the horizon value of the dilaton and demonstrate how causticity constraints enforce a bound on GB parameters, with the potential for a small violation of the bound $\frac{4}{25\pi}$ in certain dilaton configurations. They show the violation is of order $O(\lambda)$, contrasting with perturbative scalar effects reported in other works. The results illuminate how nonminimal dilaton couplings alter holographic transport and point to future work on bulk viscosity in these backgrounds.

Abstract

We calculate the shear viscosity of field theories with gravity duals of Gauss-Bonnet gravity with a non-trivial dilaton using AdS/CFT. We find that the dilaton filed has a non-trivial contribution to the ratio of shear viscosity over entropy density and after imposing causal constraint for the boundary field theory, the new lower bound $4/25π$, obtained from pure Gauss-Bonnet gravity, may have a small violation.