Spacelike strings and jet quenching from a Wilson loop

TL;DR

This work analyzes stationary spacelike string solutions in an $AdS_5$ black hole background to study jet quenching in ${\\cal N}=4$ SYM at finite temperature via a Wilson-loop observable. By computing the lightlike limit of spacelike string worldsheets, the authors apply a non-perturbative definition of the jet-quenching parameter $\\hat{q}$ and find $\\hat{q}=0$ independent of the limiting path. The dominant minimum-action configuration exhibits a linear in $L$ dependence, rather than the perturbative quadratic $L^2$ form, suggesting that energy loss in this strongly coupled theory is governed by linear dissipation in this framework. The analysis reveals an infinite family of spacelike string branches and discusses limit-order and subtraction subtleties, indicating that, at large $N$ and strong coupling, the conventional $L^2$ jet-quenching signal may be absent within this holographic setup. These results have implications for understanding parton energy loss in strongly coupled plasmas and raise questions about the applicability of a non-perturbative $\\hat{q}$ definition in certain holographic models.

Abstract

We investigate stationary string solutions with spacelike worldsheet in a five-dimensional AdS black hole background, and find that there are many branches of such solutions. Using a non-perturbative definition of the jet quenching parameter proposed by Liu et. al., hep-ph/0605178, we take the lightlike limit of these solutions to evaluate the jet quenching parameter in an N=4 super Yang-Mills thermal bath. We show that this proposed definition gives zero jet quenching parameter, independent of how the lightlike limit is taken. In particular, the minimum-action solution giving the dominant contribution to the Wilson loop has a leading behavior that is linear, rather than quadratic, in the quark separation.

Figures (6)

• Figure 1: Both timelike and spacelike worldsheets can exist above the radius $r=\sqrt{\gamma} r_0$ (blue line) for $v<1$ and $v>1$, respectively. On the other hand, only spacelike worldsheets exist in the region between the blue line and the event horizon, given by $r_0<r<\sqrt{\gamma} r_0$.
• Figure 2: Spacelike string solutions with fixed $L/{\beta}=0.25$, ${\gamma}=20$ ($v\approx0.99875$), $z_7=2$, and with low values of $n$ (the number of turns at the horizon). The horizon is the solid line at $z=1$, and the minimum radius of the D7-brane is the dashed line at $z=2$.
• Figure 3: $L/{\beta}$ as a function of ${\alpha}$ for spacelike string configurations with perpendicular velocity, $z_7=2$ and ${\gamma}=4.2$, $7$, and $10$. Green curves correspond to the (a)--series, blue to (b)--series, and red to (c)--series. Only the series up to $n=20$ are shown; the rest would fill the empty wedge near the $L/{\beta}$ axis. Note that the scale of the ${\gamma}=4.2$ plot is half that of the other two.
• Figure 4: Spacelike string lengths $\ell$ in units of $\sqrt{\lambda}/{\beta}$ as a function of endpoint separation $L/{\beta}$ and $z_7=2$, for ${\gamma}=6,15$ and $100$. The gray line along the $L/{\beta}$ axis is the (subtracted) length of a pair of straight strings stretched between the D7-brane and the horizon. Note that the scale of the ${\gamma}=6$ plot is half that of the others.
• Figure 5: $Lv^8/{\beta}$ as a function of ${\alpha}/v$ for spacelike string configurations with perpendicular velocity, $z_7=2$, and $v=1.005$ (red), $1.05$ (green), and $1.2$ (blue).