Heavy Quark Diffusion in Strongly Coupled $\mathbb{N}=4$ Yang Mills

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 $\mathbb{N}=4$ Yang-Mills by studying the fluctuations of a string in $Ad{S}_5\times S_5$. 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 quasi-particle. The result is discussed in the context of the RHIC experiments.

17 pages + 2 figures

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