Langevin diffusion of heavy quarks in non-conformal holographic backgrounds

The Langevin diffusion process of a relativistic heavy quark in a non-conformal holographic setup is analyzed. The bulk geometry is a general, five-dimensional asymptotically AdS black hole. The heavy quark is described by a trailing string attached to a flavor brane, moving at constant velocity. From the equations describing linearized fluctuations of the string world-sheet, the correlation functions defining a generalized Langevin process are constructed via the AdS/CFT prescription. In the local limit, analytic expressions for the Langevin diffusion and friction coefficients are obtained in terms of the bulk string metric. Modified Einstein relations between these quantities are also derived. The spectral densities associated to the Langevin correlators are analyzed, and simple analytic expressions are obtained in the small and large frequency limits. Finally, a numerical analysis of the jet-quenching parameter, and a comparison to RHIC phenomenology are performed in the case of Improved Holographic QCD. It is shown that the jet-quenching parameter is not enough to describe energy loss of very energetic charm quarks and the full Langevin correlators are needed.