Drag Force in a Charged N=4 SYM Plasma

TL;DR

Using the AdS/CFT correspondence, the paper computes the drag force on a heavy external quark moving through a charged ${\cal N}=4$ SYM plasma by analyzing a stationary trailing string in the near-horizon geometry of rotating D3-branes. The key result is a drag force $F_x = -{r_0^2}/{(2\pi l_s^2 R^2)} \; {v}/{\sqrt{1-v^2}}$, with $r_0$ tied to the temperature $T$ and the charge density via a sixth-order equation in the dimensionless parameter $c = J/(2\pi N^2 T^3)$; in the small-$c$ limit, $r_0$ receives a correction $r_0 = \pi R^2 T [1 + {4 J^2}/{(\pi^2 N^4 T^6)} + \mathcal{O}(J^4)]$, leading to a drag correction $\frac{dp_x}{dt} = -\frac{\pi}{2} \sqrt{g_{YM}^2 N}\,T^2\,\frac{p_x}{m} [1 + {8 J^2}/{(\pi^2 N^4 T^6)} + \cdots]$. The main finding is a non-monotonic dependence of the drag on $c$, with a peak near $c\approx 0.199$ (enhancing the drag relative to the neutral case), and the results are related to jet-quenching analyses via the parameter $\hat{q}$ and discussed in the context of prior work. The study also compares ten-dimensional spinning D3 results with five-dimensional truncations, highlighting the role of the angular momentum in the dual gauge theory.

Abstract

Following recent developments, we employ the AdS/CFT correspondence to determine the drag force exerted on an external quark that moves through an N=4 super-Yang-Mills plasma with a non-zero R-charge density (or, equivalently, a non-zero chemical potential). We find that the drag force is larger than in the case where the plasma is neutral, but the dependence on the charge is non-monotonic.

Figures (1)

• Figure 1: Drag force as a function of the dimensionless charge parameter $c=J/ 2\pi N^2 T^3$.