- either from the bulk perspective, where the thermal medium gets replaced by a black hole and energy flows down the string towards its horizon,
- or from the gauge-theory perspective, where energy and momentum emanate from the quark and eventually thermalise.

In this section, I will take the bulk point of view originally discussed in [297, 268], with a related fluctuation analysis in [138]. 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 [272].

The thermal medium is holographically described in terms of the AdS_{5}-Schwarzschild black hole,

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 satisfies as . To determine , one must solve the classical equations of motion of the bosonic worldsheet action (16) in the background (435). These reduce to a set of conserved equations of the form is the worldsheet momentum current conjugate to the position . Plugging the ansatz (436) into Eq. (437), one finds where is an integration constant. A priori, there are several allowed possibilities compatible with the reality of the trailing function . These were analysed in [272] where it was concluded that the relevant physical solution is given by where is a rescaled depth variable .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]

This allows us to define the drag force as For a much more detailed discussion on the physics of this system see [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 [212] 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 AdS_{5} boundary to describe particles transforming in the antisymmetric and symmetric
representations of the gauge group, respectively.

Living Rev. Relativity 15, (2012), 3
http://www.livingreviews.org/lrr-2012-3 |
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