Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics

Abstract

The ratio of shear viscosity to volume density of entropy can be used to characterize how close a given fluid is to being perfect. Using string theory methods, we show that this ratio is equal to a universal value of $\hbar/4πk_B$ for a large class of strongly interacting quantum field theories whose dual description involves black holes in anti--de Sitter space. We provide evidence that this value may serve as a lower bound for a wide class of systems, thus suggesting that black hole horizons are dual to the most ideal fluids.

Figures (2)

• Figure 1: The dependence of the ratio $\eta/s$ on the 't Hooft coupling $g^2N_c$ in ${\cal N}=4$ supersymmetric Yang--Mills theory. The ratio diverges in the limit $g^2 N_c\to0$ and approaches $\hbar/{4 \pi k_B}$ from above as $g^2N_c\to\infty$. The ratio is unknown in the regime of intermediate 't Hooft coupling.
• Figure 2: The viscosity-entropy ratio for some common substances: helium, nitrogen and water. The ratio is always substantially larger than its value in theories with gravity duals, represented by the horizontal line marked "viscosity bound."