The Wake of a Quark Moving through Hot QCD Plasmas vs. N = 4 SYM Plasmas

TL;DR

This paper compares the energy density and flux of a moving heavy quark in hot QCD and N=4 SYM plasmas, using kinetic theory and AdS/CFT, revealing insights into hydrodynamic behavior and second order coefficients.

Contribution

It introduces a detailed comparison of energy-momentum distributions in QCD and N=4 SYM plasmas using kinetic theory and holography, highlighting the role of second order hydrodynamic coefficients.

Findings

Hydrodynamics describes energy-momentum tensor well after kinetic theory corrections.

Differences between kinetic theory and AdS/CFT are linked to the second order coefficient τ_π.

Energy and flux distributions show transition to ideal hydrodynamics.

Abstract

We present the energy density and flux distribution of a heavy quark moving through high temperature QCD plasmas and compare them with those in the strongly coupled N = 4 SYM plasma. The Boltzmann equation is reformulated as a Fokker-Planck equation at the leading log approximation and is solved numerically with nontrivial boundary conditions in momentum space. We use kinetic theory and perform a Fourier transform to calculate the energy and momentum density in position space. The angular distributions exhibit the transition to the ideal hydrodynamics and are analyzed with the first and second order hydrodynamic source. The AdS/CFT correspondence allows the same calculation at strong coupling. Compared to the kinetic theory results, the energy-momentum tensor is better described by hydrodynamics even after accounting for the differences in the shear viscosities. We argue that the difference between the Boltzmann equation and the AdS/CFT correspondence comes from the second order hydrodynamic coefficient $\tau_\pi$ which is generically large compared to the shear length in a theory based on the Boltzmann equation.