Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics

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 $\hslash /4\pi k_B$ 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.

Figure 1

The dependence of the ratio $\eta /s$ on the ’t Hooft coupling $g^2{N}_c$ in $\mathcal{N}=4$ supersymmetric Yang-Mills theory. The ratio diverges in the limit $g^2{N}_c\to 0$ and approaches $\hslash /4\pi k_B$ from above as $g^2{N}_c\to \infty$. 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.”