Acceleration, Energy Loss and Screening in Strongly-Coupled Gauge Theories

TL;DR

This work uses the AdS/CFT correspondence to analyze heavy-quark dynamics in strongly coupled gauge plasmas, focusing on energy loss, dispersion relations, and screening in both vacuum and finite-temperature settings. Building on Mikhailov’s analytic zero-temperature construction, it extends to finite quark mass and finite temperature, revealing how external forcing, mass, and the plasma modify dispersion relations and energy dissipation through worldsheet horizons. It also investigates quark–antiquark evolution, distinguishing singlet and adjoint configurations, and studies how screening lengths interplay with the transition to asymptotic, constant-drag regimes, including the velocity dependence of screening. The findings illuminate non-equilibrium real-time dynamics in a strongly coupled medium, offering insights relevant to quark energy loss and quarkonium suppression in quark-gluon plasma phenomenology, and bridge the gap between transient and stationary dissipative behavior.

Abstract

We explore various aspects of the motion of heavy quarks in strongly-coupled gauge theories, employing the AdS/CFT correspondence. Building on earlier work by Mikhailov, we study the dispersion relation and energy loss of an accelerating finite-mass quark in N=4 super-Yang-Mills, both in vacuum and in the presence of a thermal plasma. In the former case, we notice that the application of an external force modifies the dispersion relation. In the latter case, we find in particular that when a static heavy quark is accelerated by an external force, its rate of energy loss is initially insensitive to the plasma, and there is a delay before this rate approaches the value derived previously from the analysis of stationary or late-time configurations. Following up on work by Herzog et al., we also consider the evolution of a quark and antiquark as they separate from one another after formation, learning how the AdS/CFT setup distinguishes between the singlet and adjoint configurations, and locating the transition to the stage where the deceleration of each particle is properly accounted for by a constant friction coefficient. Additionally, we examine the way in which the energy of a quark-antiquark pair moving jointly through the plasma scales with the quark mass. We find that the velocity-dependence of the screening length is drastically modified in the ultra-relativistic region, and is comparable with that of the transition distance mentioned above.

Figures (17)

• Figure 1: Schematic illustration of the string worldsheet (shaded in gray), in the static gauge $\tau=t$, $\sigma=z$, showing the upward null Mikhailov (fixed $t_{\hbox{\scriptsize tret}}$) lines $z_{\hbox{\scriptsize grab}}$ and $z_{\hbox{\scriptsize release}}$ (solid green), the stationary limit curve $z_{\hbox{\scriptsize ergo}}$ (dotted blue), and the event horizon $z_{\hbox{\scriptsize BH}}$ (thick dotted red) above which lies the worldsheet black hole (shaded light red). See text for discussion.
• Figure 2: Quark velocity as a function of time from our numerical integration (in red) compared against (\ref{['vhkkkynr']}) with the value of $\mu$ deduced in hkkky (in black), and (\ref{['vhkkkynr']}) with $\mu$ chosen to fit the data (in light blue), for a) $z_m/z_h=0.2$ and b) $z_m/z_h=0.4$. See text for discussion,
• Figure 3: a) Accumulated energy loss (in units of $\sqrt{\lambda}T/2$) as a function of time (in units of $1/\pi T$) for a) $z_m=0.2$ (red) and $z_m=0.4$ (blue) with $v_{\hbox{\scriptsize release}}=0.051$, and b) $z_m=0.2$ (red) and $z_m=0.3$ (blue) with $v_{\hbox{\scriptsize release}}=0.073$. For comparison, the dashed curves of the same colors give the energy loss that would follow from the stationary rate (\ref{['EPlossgubser']}) obtained in hkkkygubser. The green lines represent the rate (\ref{['EPlossgubser']}) evaluated with $v=v_{\hbox{\scriptsize release}}$, which can be contrasted against the slope of the numerical curves, shown in black.
• Figure 4: a) Accumulated energy loss (in units of $\sqrt{\lambda}T/2$) as a function of time (in units of $1/\pi T$) for a) $z_m=0.2$ with $v=0.056$ (red) and $v=0.111$ (blue) and b) $z_m=0.3$ with $v=0.036$ (red) and $v=0.073$ (blue). The dashed curves of the same colors give the energy loss obtained with the stationary rate (\ref{['EPlossgubser']}). The green lines represent this rate evaluated at $t=t_{\hbox{\scriptsize release}}$ with velocity $v$, which is to be contrasted against the slope of the numerical curves, shown in black.
• Figure 5: Rate of energy loss (points, in units of $\sqrt{\lambda}\pi T^2/2$) as a function of velocity for a) $z_m=0.2$ and b) $z_m=0.3$, together with the corresponding quadratic fits $(\partial_t E_q)_n(0.2,v)=0.31v^2$ and $(\partial_t E_q)_n(0.3,v)=0.41v^2$.