Transverse Momentum Broadening of a Fast Quark in a $\N=4$ Yang Mills Plasma

Abstract

We compute the momentum broadening of a heavy fundamental charge propagating through a $\mathcal{N}=4$ Yang Mills plasma at large t' Hooft coupling. We do this by expressing the medium modification of the probe's density matrix in terms of a Wilson loop averaged over the plasma. We then use the AdS/CFT correspondence to evaluate this loop, by identifying the dual semi-classical string solution. The calculation introduces the type ``1'' and type ``2'' fields of the thermal field theory and associates the corresponding sources with the two boundaries of the AdS space containing a black hole. The transverse fluctuations of the endpoints of the string determine $\kappa_T = \sqrt{\gamma \lambda} T^3 \pi$ -- the mean squared momentum transfer per unit time. ($\gamma$ is the Lorentz gamma factor of the quark.) The result reproduces previous results for the diffusion coefficient of a heavy quark. We compare our results with previous AdS/CFT calculations of $\hat{q}$.