Stress-energy tensor of a quark moving through a strongly-coupled<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">N</mml:mi><mml:mo>=</mml:mo><mml:mn>4</mml:mn></mml:math>supersymmetric Yang-Mills plasma: Comparing hydrodynamics and AdS/CFT duality

Abstract

The stress-energy tensor of a quark moving through a strongly-coupled $\mathcal{N}=4$ supersymmetric Yang-Mills plasma, at large ${N}_{\mathrm{c}}$, is evaluated using gauge/string duality. The accuracy with which the resulting wake, in position space, is reproduced by hydrodynamics is examined. Remarkable agreement is found between hydrodynamics and the complete result down to distances less than $2/T$ away from the quark. In performing the gravitational analysis, we use a relatively simple formulation of the bulk to boundary problem in which the linearized Einstein field equations are fully decoupled. Our analysis easily generalizes to other sources in the bulk.