Viscosity Bound and Causality Violation

In recent work we showed that, for a class of conformal field theories (CFT) with Gauss-Bonnet gravity dual, the shear viscosity to entropy density ratio, $\eta /s$, could violate the conjectured Kovtun-Starinets-Son viscosity bound, $\eta /s\ge 1/4\pi$. In this Letter we argue, in the context of the same model, that tuning $\eta /s$ below $(16/25)(1/4\pi )$ induces microcausality violation in the CFT, rendering the theory inconsistent. This is a concrete example in which inconsistency of a theory and a lower bound on viscosity are correlated, supporting the idea of a possible universal lower bound on $\eta /s$ for all consistent theories.

Figure 1

Left: $c_g^2(z)$ as a function of $z$ for ${\lambda }_{\mathrm{GB}}=0.245$. $c_g^2$ has a maximum $c_{g,\max }^2$ at $z_{\max }$. As ${\lambda }_{\mathrm{GB}}$ is increased from ${\lambda }_{\mathrm{GB}}=\frac{9}{100}$ to ${\lambda }_{\mathrm{GB}}=\frac{1}{4}$, $c_{g,\max }^2$ increases from 1 to 3. $c_g^2(z)$ also serves as the classical potential for the 1D system (17). The horizontal line indicates the trajectory of a classical particle. Right: $U(y)$ [defined in (25)] as a function of $y$ for ${\lambda }_{\mathrm{GB}}=0.245$.

Figure 2

$V(z)$ as a function of $z$ for ${\lambda }_{\mathrm{GB}}=0.2499$ and $\tilde{q}=500$.