Viscosity Bound and Causality Violation

TL;DR

It is argued, 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, supporting the idea of a possible universal lower bound on eta-s for all consistent theories.

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, $η/s$, could violate the conjectured Kovtun-Starinets-Son viscosity bound, $η/s\geq1/4π$. In this paper 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.

Figures (2)

• Figure 1: Left: $c_g^2 (z)$ as a function of $z$ for ${\lambda}_{GB} = 0.245$. $c_g^2$ has a maximum $c_{g,{\rm max}}^2$ at $z_{\rm max}$. As ${\lambda}_{GB}$ is increased from ${\lambda}_{GB}={9 \over 100}$ to ${\lambda}_{GB} = {1 \over 4}$, $c_{g,{\rm max}}^2$ increases from $1$ to $3$. $c_g^2 (z)$ also serves as the classical potential for the 1D system (\ref{['geoE']}). The horizontal line indicates the trajectory of a classical particle. Right: $U(y)$ [defined in (\ref{['Upro']})] as a function of $y$ for ${\lambda}_{GB} =0.245$.
• Figure 2: $V(z)$ as a function of $z$ for ${\lambda}_{GB} =0.2499$ and $\tilde{q} =500$.