Non-universal shear viscosity from Einstein gravity

Abstract

A very famous result of gauge/gravity duality is the universality of the ratio of shear viscosity to entropy density in every field theory holographically dual to classical, two-derivative (Einstein) gravity. We present a way to obtain deviation form this universality by breaking the rotational symmetry spontaneously. In anisotropic fluids additional shear modes exist and their corresponding shear viscosities may be non-universal. We confirm this by explicitly calculating the shear viscosities in a transversely isotropic background, a p-wave superfluid, and study its critical behavior. This is a first decisive step towards further applications of gauge/gravity duality to physical systems.

Figures (2)

• Figure 1: Ratio of shear viscosities $\eta_{yz}$ and $\eta_{xy}$ to entropy density $s$ over the reduced temperature $T/T_c$ for different values of the ratio of the gravitational coupling constant to the Yang-Mills coupling constant $\alpha$: The color coding is as follows: In yellow, $\eta_{yz}/s$ for all values of $\alpha$; while the curve for $\eta_{xy}/s$ is plotted in green for $\alpha=0.032$, red for $\alpha=0.224$ and blue for $\alpha=0.316$. The shear viscosities coincide and are universal in the normal phase $T\ge T_c$. However in the superfluid phase $T<T_c$, the shear viscosity $\eta_{yz}$ has the usual universal behavior while the shear viscosity $\eta_{xy}$ is non-universal.
• Figure 2: Ratio of shear viscosities $\eta_{yz}$ (blue) and $\eta_{xy}$ (red) to entropy density $s$ over the reduced temperature $T/T_c$ for $\alpha=0.447$, which is bigger than the critical value where the phase transition becomes first order: The shear viscosities coincide in the normal phase $T\ge T_c$ and are universal. In the superfluid phase $\eta_{xy}$ is non-universal. Close to the phase transition, it is multivalued as expected for a first order phase transition.