In this section, I will take the bulk point of view originally discussed in [297, 268], with a related fluctuation analysis in . The goal is to highlight the power of the techniques developed in Sections 4 and 5 rather than being self-contained. For a more thorough discussion, the reader should check the review on this particular topic .
The thermal medium is holographically described in terms of the AdS5-Schwarzschild black hole,. Notice is the location of the conformal boundary and is the radius of AdS5.
If one is interested in describing the dragging effect suffered by the quark due to the interactions with the thermal medium, one considers a non-static quark, whose trajectory in the boundary satisfies , assuming motion takes place only in the direction. One can parameterise the bulk trajectory as where it was concluded that the relevant physical solution is given by
To compute the rate at which quark momentum is being transferred to the bath, one can simply integrate the conserved current over a line-segment and given the stready-state nature of the trailing string configuration, one infers [272, 137]. The latter also includes a discussion of the same physical effect for a finite, but large, quark mass, and the possible implications of these results and techniques for quantum chromodynamics (QCD).
More recently, it was argued in  that one can compute the energy loss by radiation of an infinitely-massive half-BPS charged particle to all orders in using a similar construction to the one mentioned at the end of Section 6.1. This involved the use of classical D5-brane and D3-brane world volume reaching the AdS5 boundary to describe particles transforming in the antisymmetric and symmetric representations of the gauge group, respectively.
Living Rev. Relativity 15, (2012), 3
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