The universal viscosity to entropy density ratio from entanglement

Abstract

We present evidence that the universal Kovtun-Son-Starinets shear viscosity to entropy density ratio of 1/4\pi can be associated with a Rindler causal horizon in flat spacetime. Since there is no known holographic (gauge/gravity) duality for this spacetime, a natural microscopic explanation for this viscosity is in the peculiar properties of quantum entanglement. In particular, it is well-known that the Minkowski vacuum state is a thermal state and carries an area entanglement entropy density in the Rindler spacetime. Based on the fluctuation-dissipation theorem, we expect a similar notion of viscosity arising from vacuum fluctuations. Therefore, we propose a holographic Kubo formula in terms of a two-point function of the stress tensor of matter fields in the bulk. We calculate this viscosity assuming a minimally coupled scalar field theory and find that the ratio with respect to the entanglement entropy density is exactly 1/4\pi in four dimensions. The issues that arise in extending this result to non-minimally coupled scalar fields, higher spins, and higher dimensions provide interesting hints about the relationship between entanglement entropy and black hole entropy.