Stochastic String Motion Above and Below the World Sheet Horizon

We study the stochastic motion of a relativistic trailing string in black hole AdS_5. The classical string solution develops a world-sheet horizon and we determine the associated Hawking radiation spectrum. The emitted radiation causes fluctuations on the string both above and below the world-sheet horizon. In contrast to standard black hole physics, the fluctuations below the horizon are causally connected with the boundary of AdS. We derive a bulk stochastic equation of motion for the dual string and use the AdS/CFT correspondence to determine the evolution a fast heavy quark in the strongly coupled $\N=4$ plasma. We find that the kinetic mass of the quark decreases by $\Delta M=-\sqrt{\gamma \lambda}T/2$ while the correlation time of world sheet fluctuations increases by $\sqrt{\gamma}$.