Heavy quark diffusion in strongly coupledN=4Yang-Mills theory

Abstract

We express the heavy quark diffusion coefficient as the temporal variation of a Wilson line along the Schwinger-Keldysh contour. This generalizes the classical formula for diffusion as a force-force correlator to a non-Abelian theory. We use this formula to compute the diffusion coefficient in strongly coupled $\mathcal{N}=4$ Yang-Mills theory by studying the fluctuations of a string in ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}_{5}$. The string solution spans the full Kruskal plane and gives access to contour correlations. The diffusion coefficient is $D=2/\sqrt{\ensuremath{\lambda}}\ensuremath{\pi}T$ and is therefore parametrically smaller than momentum diffusion, $\ensuremath{\eta}/(e+p)=1/4\ensuremath{\pi}T$. The quark mass must be much greater than $T\sqrt{\ensuremath{\lambda}}$ in order to treat the quark as a heavy quasiparticle. The result is discussed in the context of the Relativistic Heavy Ion Collider (RHIC) experiments.