Universality of the diffusion wake in the gauge-string duality

TL;DR

The paper analyzes how energy lost by a heavy quark moving through a strongly coupled plasma, modeled via gauge-string duality, partitions into diffusion wake and sound modes. Using a trailing string in general $AdS_5$ backgrounds with scalars, and performing linearized, axial-gauge fluctuations, the authors show the diffusion wake contribution is universally strong relative to the total drag, with $P^{\rm d} = - P^{\rm t} / v^2$, and they decompose the stress-tensor response into sound and diffusion parts that obey a universal ratio $P^{\rm s} : P^{\rm d} : P^{\rm t} = 1+v^2 : -1 : v^2$. They connect these gravity results to linearized hydrodynamics, discuss subleading corrections, and explore implications for di-hadron correlations and jet-splitting in heavy-ion collisions, highlighting potential tensions with data and the need for more realistic, expanding-hadronization modeling. The work provides a robust, universal fingerprint of diffusion wakes in holographic plasmas and informs the interpretation of away-side jet observables in experiments.

Abstract

As a particle moves through a fluid, it may generate a laminar wake behind it. In the gauge-string duality, we show that such a diffusion wake is created by a heavy quark moving through a thermal plasma and that it has a universal strength when compared to the total drag force exerted on the quark by the plasma. The universality extends over all asymptotically anti-de Sitter supergravity constructions with arbitrary scalar matter. We discuss how these results relate to the linearized hydrodynamic approximation and how they bear on our understanding of di-hadron correlators in heavy ion collisions.

Figures (3)

• Figure 1: Top: A cartoon of the diffusion wake and the sonic boom. The Mach cone and the diffusion wake experience comparable viscosity broadening, controlled by the parameter $\Gamma_s = 4\eta/3Ts$. Bottom: The Poynting vector $\vec{S}$ produced by a heavy quark propagating through a thermal plasma of ${\cal N}=4$ super-Yang-Mills theory, from Gubser:2007ga. The arrows indicate the direction of $\vec{S}$, and the color indicates its magnitude, with red meaning large $|\vec{S}|$. The dashed green line marks the Mach angle, and the gray line marks the curve where the far field asymptotics of the wake falls to half its maximal value.
• Figure 2: The diffusion wake and the integration surface $\Delta$ used in equation (\ref{['DiffusionPower']}). The inviscid limit of the diffusion wake is an infinitesmially narrow, forward directed stream of energy, as shown in lighter blue. After viscosity broadening, the diffusion wake thickens to a parabolic shape.
• Figure 3: A cartoon of a hard process in a heavy ion collision. The blue and green crescents are the parts of the nuclei that didn't interact. The gold region is the thermalizing medium. The red dot is the vertex of a hard process that occurs early in the collision, producing two partons with back-to-back momenta in the azimuthal direction. For simplicity we show all particles in the $x$-$y$ plane meaning at mid-rapidity. If particles $1$ and $2$ escape to form hadrons, it would correspond to $\Delta\phi \approx \pi$. If instead particle $2$ stops in the medium but emits a high-angle secondary which is then observed as $3$, then $\Delta\phi$ is significantly different from $\pi$.