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 ${\mathrm{AdS}}_5\times S_5$. The string solution spans the full Kruskal plane and gives access to contour correlations. The diffusion coefficient is $D=2/\sqrt{\lambda }\pi T$ and is therefore parametrically smaller than momentum diffusion, $\eta /(e+p)=1/4\pi T$. The quark mass must be much greater than $T\sqrt{\lambda }$ 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.

• Received 20 June 2006

DOI:https://doi.org/10.1103/PhysRevD.74.085012