The Wake of a Heavy Quark in Non-Abelian Plasmas : Comparing Kinetic Theory and the AdS/CFT Correspondence

TL;DR

This paper compares the stress tensor induced by a heavy quark in weakly coupled QCD plasma and strongly coupled N=4 SYM theory, highlighting differences in hydrodynamic behavior and the role of second order coefficients.

Contribution

It provides a detailed comparison between kinetic theory and AdS/CFT predictions for heavy quark dynamics in non-Abelian plasmas, emphasizing the significance of second order hydrodynamic effects.

Findings

Strongly coupled theory aligns better with hydrodynamics at sub-asymptotic distances.

Second order hydrodynamic coefficient τ_π is large in kinetic theory.

Differences in shear lengths influence the hydrodynamic description.

Abstract

We compute the non-equilibrium stress tensor induced by a heavy quark moving through weakly coupled QCD plasma at the speed of light and compare the result to N = 4 Super Yang Mills theory at strong coupling. The QCD Boltzmann equation is reformulated as a Fokker-Planck equation in a leading log approximation which is used to compute the induced stress. The transition from nonequilibrium at short distances to equilibrium at large distances is analyzed with first and second order hydrodynamics. Even after accounting for the obvious differences in shear lengths, the strongly coupled theory is significantly better described by hydrodynamics at sub-asymptotic distances. We argue that this difference between the kinetic and AdS/CFT theories is related to the second order hydrodynamic coefficient $\tau_\pi$. $\tau_\pi$ is numerically large in units of the shear length for theories based on the Boltzmann equation.