Viscosity Bound and Causality Violation

TL;DR

This paper investigates the relationship between viscosity bounds and causality in conformal field theories with Gauss-Bonnet gravity duals, showing that violating the viscosity bound leads to causality violations and inconsistency.

Contribution

It demonstrates that tuning the shear viscosity to entropy density ratio below a certain threshold causes causality violations, linking viscosity bounds to theory consistency.

Findings

Violating the viscosity bound induces causality violation.

Lower bound on viscosity correlates with theory consistency.

Supports the idea of a universal viscosity bound 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, $\eta/s$, could violate the conjectured Kovtun-Starinets-Son viscosity bound, $\eta/s\geq1/4\pi$. 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.