Relaxation time of a CFT plasma at finite coupling

TL;DR

The authors compute finite coupling corrections to key second-order hydrodynamic coefficients in a strongly coupled conformal plasma by incorporating ${\alpha'}^3$ (C^4) corrections in the gravity dual of ${\cal N}=4$ SYM. They derive a γ-corrected effective action for metric perturbations, solve for the ingoing mode, and extract the retarded stress-energy correlator via holographic renormalization to obtain $\tau_\Pi$ and $\kappa$, with $\tau_\Pi T = \frac{2-\ln 2}{2\pi} + \frac{375}{4\pi}\gamma + O(\gamma^2)$ and $\kappa = \frac{\eta}{\pi T}(1-145\gamma+O(\gamma^2))$. Complementarily, a sound-mode analysis to ${\cal O}(q^3)$ yields a dispersion relation whose γ-dependent terms agree with the Kubo result and fixes a numerical constant $z_{1,0}^{(2)} \approx 264.76$, reinforcing the consistency between the two approaches. Overall, the work provides universal finite-coupling corrections to second-order transport in 4D conformal plasmas and informs hydrodynamic modeling of strongly coupled systems such as the sQGP.

Abstract

Following recent formulation of second order relativistic viscous hydrodynamics for conformal fluids, we compute finite coupling corrections to the relaxation time of N=4 supersymmetric Yang-Mills plasma. The result is expected to be universal for any strongly coupled conformal gauge theory plasma in four dimensions.