Gluon energy loss in the gauge-string duality

TL;DR

This work develops a holographic framework to quantify gluon energy loss in a strongly coupled plasma by modeling a high-energy off-shell gluon as a doubled string rising from the ${\rm AdS}_5$-Schwarzschild horizon. By examining both spacetime and worldsheet geodesics, the authors derive a stopping-length scaling $\\Delta x \\sim \\hat{E}^{1/3}$ in the large-energy limit, provide analytic and numerical estimates for $\\Delta \hat{x}$, and translate these into rough ${\\hat{q}}$ values under two QCD-matching schemes. A null-string limit is developed to yield a tractable description of the stress tensor as an ensemble of massless-particle trajectories, offering a controlled corner of the calculation for $\\langle T_{mn}\\rangle$. While the approach involves significant conceptual differences from perturbative BDMPS and relies on idealizations including large-$N$ and no fluctuations, the results suggest faster energy dissipation for gluons than perturbative expectations and illuminate how strong coupling dynamics could shape hard probe phenomenology in the quark-gluon plasma.

Abstract

We estimate the stopping length of an energetic gluon in a thermal plasma of strongly coupled N=4 super-Yang-Mills theory by representing the gluon as a doubled string rising up out of the horizon.

Figures (8)

• Figure 1: If a string starts at $t=0$ in a straight up-and-down configuration, it doesn't hold its shape as time evolves forward. At a later time, indicated as $t=1$ in the figure, one must solve difficult classical equations of motion to find the shape of the string. But because of the infinite redshift characteristic of black hole horizons, the point where the string comes out of the horizon cannot move at all. At times $t>1$, the string continues to fall down toward the horizon. Although it takes an infinite time to fall all the way in, it only propagates a finite distance $\Delta x$ forward.
• Figure 2: A string starts at $t=0$ in the shape of a falling string that extends up to a finite minimum depth, $y=y_{\rm UV}$. (Recall that $y=z/z_H$.) If the string extended up to the boundary, as shown with a dashed curve, its endpoint would move at a speed $v$. The lightly shaded region, below the trajectory labeled POND, retains the shape of the trailing string. At times $t>0$ (for instance at the time denoted $t=1$ in the figure), the string probably projects somewhat beyond the POND trajectory into the narrow region between it and the null spacetime geodesic. The POND trajectory and the spacetime geodesic are mutually tangent at the point $t=0$, $y=y_{\rm UV}$.
• Figure 3: Typical orbits for a massless particle in $AdS_5$-Schwarzschild, all leading into the horizon (the dashed black line) at $x^1=0$. An open orbit is shown in red; the critical orbit is shown in green; and a closed orbit is shown in blue.
• Figure 4: Evaluations of the maximum penetration depth $\Delta \hat{x}_A(\hat{E})$ with a variety of assumptions. The solid blue curve shows the analytic approximation \ref{['LargeEWorldsheet']} to the blue circles, and the solid black curve shows the analytic approximation \ref{['LargeESpacetime']} to the black diamonds.
• Figure 5: The penetration length $\Delta \hat{x}$ as a function of $\gamma$ for fixed $\hat{E}$. The blue curves represent the penetration length for a spacetime geodesic, while the black curve represent the same quantity for the point of no disturbance (POND), which is explained in section \ref{['WORLDSHEET']}. For all curves, the energy was computed at fixed $x^1$ using \ref{['Efixedx1']}. The red points mark the maxima of each curve and correspond to data points in figure \ref{['CombinedPlot']}.