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Quenching parameter in a holographic thermal QCD

We have calculated the quenching parameter, $\hat{q}$ in a model-independent way using the gauge-gravity duality. In earlier calculations, the geometry in the gravity side at finite temperature was usually taken as the pure AdS blackhole metric for which the dual gauge theory becomes conformally invariant unlike QCD. Therefore we use a metric which incorporates the fundamental quarks by embedding the coincident D7 branes in the Klebanov-Tseytlin background and a finite temperature is switched on by inserting a black hole into the background, known as OKS-BH metric. Further inclusion of an additional UV cap to the metric prepares the dual gauge theory to run similar to thermal QCD. Moreover $\hat{q}$ is usually defined in the literature from the Glauber-model perturbative QCD evaluation of the Wilson loop, which has no reasons to hold if the coupling is large and is thus against the main idea of gauge-gravity duality. Thus we use an appropriate definition of $\hat{q}$: $\hat{q} L^- = 1/L^2$, where $L$ is the separation for which the Wilson loop is equal to some specific value. The above two refinements cause $\hat{q}$ to vary with the temperature as $T^4$ always and to depend linearly on the light-cone time $L^-$ with an additional ($1/L^-$) correction term in the short-distance limit whereas in the long-distance limit, it depends only linearly on $L^-$ with no correction term. These observations agree with other holographic calculations directly or indirectly.