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, η/s, could violate the conjectured Kovtun-Starinets-Son viscosity bound, η/s≥1/4π. In this Letter we argue, in the context of the same model, that tuning η/s below (16/25)(1/4π) 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 η/s for all consistent theories.