The Shear Viscosity to Entropy Ratio: A Status Report

TL;DR

The paper surveys how the shear viscosity to entropy ratio η/s behaves in strongly coupled gauge theories via holography. It starts from the universal Einstein-gravity result η/s = 1/(4π) and analyzes how higher-derivative curvature corrections map to finite-λ and finite-N effects, which can violate the KSS bound, with violations tied to differences in central charges a and c. The discussion covers chemical potential effects, the holographic Weyl anomaly, and causality constraints, notably in Gauss-Bonnet gravity, which link possible bound violations to UV-consistency requirements. It concludes that while holographic models can exhibit bound violations, there may be theory-dependent lower and upper limits set by causality and energy positivity, and that η/s can exhibit temperature-driven flow in certain IR/UV decoupled setups.

Abstract

This review highlights some of the lessons that the holographic gauge/gravity duality has taught us regarding the behavior of the shear viscosity to entropy density in strongly coupled field theories. The viscosity to entropy ratio has been shown to take on a very simple universal value in all gauge theories with an Einstein gravity dual. Here we describe the origin of this universal ratio, and focus on how it is modified by generic higher derivative corrections corresponding to curvature corrections on the gravity side of the duality. In particular, certain curvature corrections are known to push the viscosity to entropy ratio below its universal value. This disproves a longstanding conjecture that such a universal value represents a strict lower bound for any fluid in nature. We discuss the main developments that have led to insight into the violation of this bound, and consider whether the consistency of the theory is responsible for setting a fundamental lower bound on the viscosity to entropy ratio.