Hydrodynamic Long-Time tails From Anti de Sitter Space

TL;DR

This paper demonstrates that the long-time power-law decay of conserved current correlations in finite-temperature field theories can be derived from black hole horizon dynamics in Anti de Sitter space, confirming predictions of non-linear hydrodynamics.

Contribution

It provides a one-loop gravity computation showing the hydrodynamic long-time tails originate from black hole horizon dynamics, aligning with gauge-gravity duality.

Findings

Power-law decay of correlations is reproduced by black hole horizon dynamics.

The result confirms the gauge-gravity correspondence for hydrodynamic long-time tails.

Black hole horizons encode long-time hydrodynamic behavior.

Abstract

For generic field theories at finite temperature, a power-law falloff of correlation functions of conserved currents at long times is a prediction of non-linear hydrodynamics. We demonstrate, through a one-loop computation in Einstein gravity in Anti de Sitter space, that this effect is reproduced by the dynamics of black hole horizons. The result is in agreement with the gauge-gravity correspondence.