Viscous hydrodynamics relaxation time from AdS/CFT

TL;DR

The paper investigates the relaxation-time in second-order viscous hydrodynamics for a strongly coupled, expanding boost-invariant plasma using AdS/CFT for $\mathcal{N}=4$ SYM. By constructing dual geometries in Fefferman–Graham coordinates and enforcing the nonsingularity of the 5D spacetime, the authors extract the large-$\tau$ expansion of the boundary energy density $\varepsilon(\tau)$ and identify the relaxation time parameter $\tau_{\Pi}$. They find $\tau_{\Pi} = \frac{1 - \log 2}{6\pi T}$, i.e. about $1.6\times 10^{-2}/T$, which is roughly thirty times shorter than weak-coupling estimates, implying strong-coupling hydrodynamics behaves closer to first order. To cancel residual divergences in the gravity solution, a dilaton is turned on, producing a nonzero $\langle \mathrm{tr} F^2\rangle$ that scales as $\tau^{-10/3}$. These results enhance quantitative understanding of far-from-equilibrium dynamics in holographic plasmas and inform modeling of the quark-gluon plasma at strong coupling.

Abstract

We consider an expanding boost-invariant plasma at strong coupling using the AdS/CFT correspondence for N=4 SYM. We determine the relaxation time in second order viscous hydrodynamics and find that it is around thirty times shorter than weak coupling expectations. We find that the nonsingularity of the dual geometry in the string frame necessitates turning on the dilaton which leads to a nonvanishing expectation value for tr F^2 behaving like tau^(-10/3).