Proof of a universal lower bound on the shear viscosity to entropy density ratio

TL;DR

This paper proves a universal lower bound on the shear viscosity to entropy density ratio in certain gravity theories, confirming a conjecture based on gauge-gravity duality.

Contribution

It establishes the bound for ghost-free Einstein gravity extensions, showing the ratio's minimal value occurs at Einstein gravity, thus confirming the conjecture.

Findings

Bound holds for ghost-free Einstein gravity extensions

Shear viscosity is minimized at Einstein gravity

Entropy density can be calibrated to Einstein value

Abstract

It has been conjectured, on the basis of the gauge-gravity duality, that the ratio of the shear viscosity to the entropy density should be universally bounded from below by 1/ 4 pi in units of the Planck constant divided by the Boltzmann constant. Here, we prove the bound for any ghost-free extension of Einstein gravity and the field-theory dual thereof. Our proof is based on the fact that, for such an extension, any gravitational coupling can only increase from its Einstein value. Therefore, since the shear viscosity is a particular gravitational coupling, it is minimal for Einstein gravity. Meanwhile, we show that the entropy density can always be calibrated to its Einstein value. Our general principles are demonstrated for a pair of specific models, one with ghosts and one without.