Drag force in AdS/CFT

TL;DR

This paper computes the drag force on an external heavy quark moving through a thermal ${\cal N}=4$ SYM plasma by modeling the quark as a trailing string in the $AdS_5$-Schwarzschild background. Using the Nambu-Goto action and a late-time ansatz, it derives a constant worldsheet flux and obtains the drag force $\frac{dp_1}{dt} = -\frac{\pi}{2}\sqrt{g_{YM}^2 N}\, T^2 \frac{v}{\sqrt{1-v^2}}$, which translates into a relaxation time $t_0 = \frac{2}{\pi\sqrt{g_{YM}^2 N}} \frac{m}{T^2}$. Expressed in momentum terms, the decay is $p_1(t) = p_1(0) e^{-t/t_0}$, highlighting strong-coupling energy loss for heavy quarks. The results offer a holographic estimate of jet-quenching-like energy loss and provide qualitative insights for heavy-ion phenomenology, while recognizing limitations from the ${\cal N}=4$ setup and the idealization of infinitely massive external quarks.

Abstract

The AdS/CFT correspondence and a classical test string approximation are used to calculate the drag force on an external quark moving in a thermal plasma of N=4 super-Yang-Mills theory. This computation is motivated by the phenomenon of jet-quenching in relativistic heavy ion collisions.