Gravitation, Thermodynamics, and the Bound on Viscosity

Abstract

The anti-de Sitter/conformal field theory (AdS/CFT) correspondence implies that small perturbations of a black hole correspond to small deviations from thermodynamic equilibrium in a dual field theory. For gauge theories with an Einstein gravity dual, the AdS/CFT correspondence predicts a universal value for the ratio of the shear viscosity to the entropy density, $η/s=1/4π$. It was conjectured recently that all fluids conform to the lower bound $η/s \geq 1/4π$. This {\it conjectured} bound has been the focus of much recent attention. However, despite the flurry of research in this field we still lack a proof for the general validity of the bound. In this essay we show that this mysterious bound is actually a direct outcome of the interplay between gravity, quantum theory, and thermodynamics.

6 pages. This essay received the Third Award in the Annual Essay Competition of the Gravity Research Foundation for the year 2009