Viscosity bound violation in holographic solids and the viscoelastic response

TL;DR

The paper shows that the universal holographic viscosity bound ${\eta}/{s}=1/(4\pi)$ can be violated in solids by introducing a nonzero shear modulus $G$ through massive gravity with $V(X,Z)$ potentials. Using both numerical solutions and analytic zero-frequency expansions of the tensor mode in a 3+1D AdS black brane, the authors demonstrate that ${\eta}/{s}$ decreases below the KSS value when the solid-type mass term is active, and they establish a direct link between viscoelasticity (nonzero $G$) and bound violation. They derive explicit expressions for the elasticity ${G}$ and for the viscosity correction ${\eta}/{s}$, showing agreement between analytic and numerical results, and they discuss a possible generalized bound that also involves the ratio ${G}/{p}$. The findings imply that the KSS bound is not universal across all strongly coupled media and hint at real-world realizations in strongly correlated solids, including graphene, where viscoelastic effects could permit smaller ${\eta}/{s}$ values and motivate a broadened framework for transport bounds in solids.

Abstract

We argue that the Kovtun--Son--Starinets (KSS) lower bound on the viscosity to entropy density ratio holds in fluid systems but is violated in solid materials with a non-zero shear elastic modulus. We construct explicit examples of this by applying the standard gauge/gravity duality methods to massive gravity and show that the KSS bound is clearly violated in black brane solutions whenever the massive gravity theories are of solid type. We argue that the physical reason for the bound violation relies on the viscoelastic nature of the mechanical response in these materials. We speculate on whether any real-world materials can violate the bound and discuss a possible generalization of the bound that involves the ratio of the shear elastic modulus to the pressure.

Figures (4)

• Figure 1: Backreacted model $V(X)=X^n$ for $r_h=1$ and zero charge $\mu=0$ for different $n=\frac{4+\nu}{2}$, $\nu=-3,-2,0,2$. Left: Elasticity; Right:$\eta/s$ ratio, the horizontal dashed line shows the value $\eta/s=1/(4\pi)$.
• Figure 2: Comparison between the numerical results (solid lines) in the backreacted model $V(X)=X$ (with $\nu=-2$) and the probe limit results (dashed lines) for $r_h=1$ and zero chemical potential $\mu=0$. Left: the real part of the Green's function; Right:$\eta/s$ ratio.
• Figure 3: Comparison between the numerical results for the Schwarzschild--AdS case and analytic results as a function of the dimensionless graviton mass parameter $m$ for the mass function with $\nu=-2$. Solid and dashed lines are the numerical and analytic results respectively. Left: Real part of the retarded Green's function for $r_h=0.6$. Right:$\eta/s$ ratio for $r_h=1$.
• Figure 4: Viscosity--elasticity diagram for the $V(X)=X$ backreacted model at fixed chemical potential $\mu=1$ and different values of $r_h$. The value of the graviton mass and the temperature are changing along the solid lines, with $m=0$ at the point where $\eta/s=1/4\pi\approx 0.08$. Similar plots are obtained by keeping $m$ constant and varying $T$ only.