Viscosity bound violation in higher derivative gravity

Motivated by the vast string landscape, we consider the shear viscosity to entropy density ratio in conformal field theories dual to Einstein gravity with curvature square corrections. After field redefinitions these theories reduce to Gauss-Bonnet gravity, which has special properties that allow us to compute the shear viscosity nonperturbatively in the Gauss-Bonnet coupling. By tuning of the coupling, the value of the shear viscosity to entropy density ratio can be adjusted to any positive value from infinity down to zero, thus violating the conjectured viscosity bound. At linear order in the coupling, we also check consistency of four different methods to calculate the shear viscosity, and we find that all of them agree. We search for possible pathologies associated with this class of theories violating the viscosity bound.

Figure 1

$c_g^2(z)$ (vertical axis) as a function of $z$ (horizontal axis) for ${\lambda }_{\mathrm{GB}}=0.08$ (left panel) and ${\lambda }_{\mathrm{GB}}=0.1$ (right panel). For ${\lambda }_{\mathrm{GB}}<\frac{9}{100}$, $c_g^2$ is a monotonically increasing function of $z$. When ${\lambda }_{\mathrm{GB}}>\frac{9}{100}$, as one decreases $z$ from infinity, $c_g^2$ increases from 1 to a maximum value at some $z>1$ and then decreases to 0 as $z\to 1$ (horizon).

Figure 2

$V(z)-q^2$ (vertical axis) as a function of $z$ (horizontal axis) for ${\lambda }_{\mathrm{GB}}=0.08$ and $\tilde{q}=500$ (left panel) and for ${\lambda }_{\mathrm{GB}}=0.1$ and $\tilde{q}=500$ (right panel). $V(z)$ is a monotonically increasing function of $z$ for ${\lambda }_{\mathrm{GB}}\le \frac{9}{100}$, but develops a local minimum for ${\lambda }_{\mathrm{GB}}>\frac{9}{100}$ with large enough $\tilde{q}$.