Dressed spectral densities for heavy quark diffusion in holographic plasmas

TL;DR

This paper studies the high-frequency behavior of spectral densities related to heavy quark diffusion in holographic plasmas, proposing a subtraction method to obtain well-defined dressed spectral functions consistent with physical constraints.

Contribution

It introduces a subtraction scheme to obtain dressed spectral functions from bare correlators, ensuring proper high-frequency fall-off and consistency with dispersion relations in holographic models.

Findings

Dressed spectral functions decay sufficiently fast at large frequencies.

Subtraction of zero-temperature correlators preserves low-frequency transport coefficients.

Analytic and numerical examples confirm the method's validity in various holographic backgrounds.

Abstract

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.