Viscosity Bound and Causality Violation

Abstract

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 paper 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.

Comments: 5 pages, 2 figures; v2: a slight change in the title and minor revisions made, references updated