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Dressed spectral densities for heavy quark diffusion in holographic plasmas

We analyze the large frequency behavior of the spectral densities that govern the generalized Langevin diffusion process for a heavy quark in the context of the gauge/gravity duality. The bare Langevin correlators obtained from the trailing string solution have a singular short-distance behavior. We argue that the proper dressed spectral functions are obtained by subtracting the zero-temperature correlators. The dressed spectral functions have a sufficiently fast fall-off at large frequency so that the Langevin process is well defined and the dispersion relations are satisfied. We identify the cases in which the subtraction does not modify the associated low-frequency transport coefficients. These include conformal theories and the non-conformal, non-confining models. We provide several analytic and numerical examples in conformal and non-conformal holographic backgrounds.