Holographic Wilsonian renormalization of a heavy quark moving through a strongly coupled plasma

A heavy quark moving through a strongly coupled deconfined plasma has a holographic dual description as a string moving in a black brane geometry. We apply the holographic Wilsonian renormalization method to derive a holographic effective string action dual to the heavy quark. The effective action only depends on the geometry between the black brane horizon and a cutoff localized in the radial direction, corresponding to the IR of the dual theory. We derive RG flow equations for the coefficients in the effective action and show that the force acting on the heavy quark is independent of the position of the cutoff. All the information about the UV is hidden in integration constants of the RG flow equations. This type of approach could be used to improve semi-holographic models where the UV is described by perturbative QCD and the IR by a holographic model.