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On the energy deposited by a quark moving in an N=4 SYM plasma

Amos Yarom

TL;DR

The work addresses how energy is deposited by a heavy quark moving through a strongly coupled quark-gluon plasma modeled by $\mathcal{N}=4$ SYM, using the AdS/CFT correspondence. It employs a trailing string in AdS-Schwarzschild to source linearized metric fluctuations and computes the dissipative near-field contribution ⟨T⟩|_d to the stress tensor by holographic renormalization, subtracting both the zero-temperature quark piece and the ambient plasma. The study finds velocity-dependent, directionally structured features in the near-field energy density ⟨T_{tt}⟩|_d, including lobes emerging for certain $v^2$ ranges, while the Mach cone appears in the far field for $v^2>1/3$; at higher velocities a behind-the-quark energy deficit reminiscent of LPM-like effects can dominate. These results provide non-perturbative insights into energy loss and jet quenching in strongly coupled plasmas and illustrate the utility of AdS/CFT for resolving near-field, dissipative dynamics that are inaccessible to perturbation theory. The near-quark tensor is encapsulated in eq. (E:main1), linking the holographic coefficients to a real-space stress-energy distribution.

Abstract

We evaluate the energy momentum tensor of a massive quark as it moves through an N=4 SYM quark gluon plasma at constant velocity. We find that in the near-quark region, where the dynamics is expected to be dominated by dissipative behavior, the energy density may be quantitatively characterized by a transient at velocities above the speed of sound of the plasma.

On the energy deposited by a quark moving in an N=4 SYM plasma

TL;DR

The work addresses how energy is deposited by a heavy quark moving through a strongly coupled quark-gluon plasma modeled by SYM, using the AdS/CFT correspondence. It employs a trailing string in AdS-Schwarzschild to source linearized metric fluctuations and computes the dissipative near-field contribution ⟨T⟩|_d to the stress tensor by holographic renormalization, subtracting both the zero-temperature quark piece and the ambient plasma. The study finds velocity-dependent, directionally structured features in the near-field energy density ⟨T_{tt}⟩|_d, including lobes emerging for certain ranges, while the Mach cone appears in the far field for ; at higher velocities a behind-the-quark energy deficit reminiscent of LPM-like effects can dominate. These results provide non-perturbative insights into energy loss and jet quenching in strongly coupled plasmas and illustrate the utility of AdS/CFT for resolving near-field, dissipative dynamics that are inaccessible to perturbation theory. The near-quark tensor is encapsulated in eq. (E:main1), linking the holographic coefficients to a real-space stress-energy distribution.

Abstract

We evaluate the energy momentum tensor of a massive quark as it moves through an N=4 SYM quark gluon plasma at constant velocity. We find that in the near-quark region, where the dynamics is expected to be dominated by dissipative behavior, the energy density may be quantitatively characterized by a transient at velocities above the speed of sound of the plasma.

Paper Structure

This paper contains 5 sections, 39 equations, 1 figure.

Table of Contents

  1. Introduction and summary
  2. Evaluation of $\langle T_{\mu\nu} \rangle$.
  3. Acknowledgements
  4. The equations of motion for the energy momentum tensor
  5. WKB approximation

Figures (1)

  • Figure 1: Contour plots of the leading dissipative contribution to the energy density $\frac{1}{\sqrt{\lambda}T^4}\langle T_{tt}(x_-,r) \rangle |_{d}$ due to the motion of a quark moving at constant velocity $v$. The horizontal axis corresponds to the comoving coordinate of the quark, $x_- = x-vt$, while the vertical one corresponds to the direction transverse to the quark motion, $r$. Large positive values are shaded in red and marked with an 'H' while lower values correspond to blue shading and are marked 'L'. See emanimation for an animation.