Causal hydrodynamics of gauge theory plasmas from AdS/CFT duality

TL;DR

The paper uses AdS/CFT to study causal hydrodynamics in strongly coupled gauge theory plasmas, computing relaxation times $\tau_J$ and $\tau_\pi$ from diffusive, shear, and sound-mode analyses across several supersymmetric theories including ${\cal N}=4$ SYM. It solves perturbations in Schwarzschild-AdS backgrounds to extract higher-order transport coefficients, confirming $\eta/s=1/(4\pi)$ and obtaining distinct values of $\tau_\pi$ from different hydrodynamic channels. A key finding is a mismatch between the shear-mode and sound-mode extractions of $\tau_\pi$, implying that the Israel-Stewart second-order framework may not adequately describe gauge theory plasmas and suggesting the need for alternative causal formulations. Across the studied theories, $\tau_\pi$ lies in a similar range, but no universal pattern emerges, highlighting limitations in extrapolating AdS/CFT results to QCD-like plasmas and motivating further theoretical development.

Abstract

We study causal hydrodynamics (Israel-Stewart theory) of gauge theory plasmas from the AdS/CFT duality. Causal hydrodynamics requires new transport coefficients (relaxation times) and we compute them for a number of supersymmetric gauge theories including the N=4 SYM. However, the relaxation times obtained from the "shear mode" do not agree with the ones from the "sound mode," which implies that the Israel-Stewart theory is not a sufficient framework to describe the gauge theory plasmas.