The Energy of a Moving Quark-Antiquark Pair in an N=4 SYM Plasma

TL;DR

Using the AdS/CFT correspondence, the paper analyzes the energy of a moving quark–antiquark pair in a strongly coupled ${\mathcal N}=4$ SYM plasma. It shows that the dipole experiences no drag and computes the energy as a function of separation and velocity, revealing Coulombic behavior at small $L$ and velocity-dependent screening with a finite $L_*(v)$ beyond which binding is lost; the results also establish the relation between the pair-rest and plasma-rest frame energies and explore the $v\to 1$ limit in relation to lightlike Wilson loops and jet-quenching parameter definitions. The study finds a velocity-dependent maximum separation $L_{max}(v)$ and a screening-length scaling $L_*(v)$, notes a gap between bound and unbound states for high $v$, and discusses how timelike string worldsheets relate to, but do not smoothly reproduce, Liu's lightlike Wilson loop. The work further connects holographic Wilson-loop computations to jet-quenching phenomenology via a coefficient ${\mathcal K}$ that mirrors ${\hat q}$ in the appropriate limit, highlighting how strong-coupling dynamics encode energy loss signatures in a moving color-neutral probe.

Abstract

We make use of the AdS/CFT correspondence to determine the energy of an external quark-antiquark pair that moves through strongly-coupled thermal N=4 super-Yang-Mills plasma, both in the rest frame of the plasma and in the rest frame of the pair. It is found that the pair feels no drag force, has an energy that reproduces the expected 1/L (or gamma/L) behavior at small quark-antiquark separations, and becomes unbound beyond a certain screening length whose velocity-dependence we determine. We discuss the relation between the high-velocity limit of our results and the lightlike Wilson loop proposed recently as a definition of the jet-quenching parameter.

Figures (6)

• Figure 1: Sketch of the string dual to a moving quark-antiquark pair. The radial coordinate runs downward, so the horizon at $r=r_H$ is shown at the top and the boundary at $r\to\infty$ is represented by the plane at the bottom. The dash-dot line at $r=r_v$ marks a velocity-dependent radius beyond which the string cannot penetrate. As the string moves to the right, its endpoints (dual to the external quark and antiquark) trace out the dotted trajectories. Its shape codifies information on the configuration of the SYM color fields. (a) One might expect the string to lean backward as a result of the motion. This turns out to be possible only if the string has a nontrivial time-dependence. (b) The lowest-energy configuration for the moving string is in fact upright, similar to the one obtained in the static case. See text for further discussion.
• Figure 2: Quark-antiquark separation (in units of $1/2\pi T$) as a function of the applied external force (in units of $\pi \sqrt{g_{YM}^2 N}T^2/2$), for velocities $v=0,0.45,0.7,0.95$. Lower curves correspond to larger velocities.
• Figure 3: Quark-antiquark energy (in units of $T\sqrt{g_{YM}^2 N}/4$) as a function of separation (in units of $1/2\pi T$), for (a) $v=0$ (b) $v=0.45$. The solid (dashed) portion of each curve corresponds to stable (metastable) configurations.
• Figure 4: Quark-antiquark energy (in units of $T\sqrt{g_{YM}^2 N}/4$) as a function of separation (in units of $1/2\pi T$), for (a) $v=0.7$, (b) $v=0.95$. The solid (dashed) portion of each curve corresponds to stable (metastable) configurations.
• Figure 5: Maximum quark-antiquark distance $L_{max}$ and screening length $L_*$ as functions of the velocity. Both lengths are given in units of $1/2\pi T$.