The viscosity bound in string theory

TL;DR

This paper investigates the robustness of the KSS bound on $η/s$ under quantum ($1/λ$) and finite-$N_c$ corrections in string-theory-inspired holographic models. Using a 5d effective action with higher-curvature corrections and, separately, fundamental matter via D7-branes, it shows that positive corrections in the absence of fundamental matter keep $η/s$ above $1/(4π)$, while theories with fundamental matter can violate the bound at subleading order due to $c-a>0$, with chemical potential further aggravating violations. It discusses extending AdS/CFT to RHIC/LHC phenomenology by calibrating holographic parameters $λ_1$ and $λ_3$ against lattice data and experiment to predict transport properties and relaxation times, while ensuring the higher-derivative expansion remains controlled. The results suggest there is no universal bound, but holographic methods offer a structured framework for connecting strongly coupled plasmas to QCD phenomenology.

Abstract

The ratio of shear viscosity to entropy density $η/s$ of any material in nature has been conjectured to have a lower bound of $1/4π$, the famous KSS bound. We examine string theory models for evidence in favour of and against this conjecture. We show that in a broad class of models quantum corrections yield values of $η/s$ just above the KSS bound. However, incorporating matter fields in the fundamental representation typically leads to violations of this bound. We also outline a program to extend AdS/CFT methods to RHIC phenomenology.