Holography and hydrodynamics: diffusion on stretched horizons

TL;DR

The authors show that the infrared dynamics of theories with black-brane gravity duals at finite temperature are governed by hydrodynamics, exhibiting diffusive and shear modes with dispersion relations of the form ω = -i D q^2 and ω = -i 𝒟 q^2. They derive metric-based expressions for the diffusion constant D and the shear viscosity η, which map to kinetic coefficients in the dual field theory; for near-extremal Dp, M2, and M5 branes these match previously known AdS/CFT results. A striking outcome is the universal value η/s = 1/(4π) (in natural units), observed across a wide class of backgrounds and conjectured as a lower bound, with some supporting results from Buchel–Liu analyses. The paper provides a robust, holography-agnostic framework showing that horizon fluctuations consistently reproduce hydrodynamic behavior in the dual theories and offers directions for exploring sound modes and non-linear effects.

Abstract

We show that long-time, long-distance fluctuations of plane-symmetric horizons exhibit universal hydrodynamic behavior. By considering classical fluctuations around black-brane backgrounds, we find both diffusive and shear modes. The diffusion constant and the shear viscosity are given by simple formulas, in terms of metric components. For a given metric, the answers can be interpreted as corresponding kinetic coefficients in the holographically dual theory. For the near-extremal Dp, M2 and M5 branes, the computed kinetic coefficients coincide with the results of independent AdS/CFT calculations. In all the examples, the ratio of shear viscosity to entropy density is equal to \hbar/(4πk_B), suggesting a special meaning of this value.