On the velocity and chemical-potential dependence of the heavy-quark interaction in N=4 SYM plasmas

TL;DR

This work analyzes the velocity and chemical-potential dependence of heavy-quark interactions in ${\cal N}=4$ SYM plasmas using the gravity dual of non-extremal rotating D3-branes. The authors derive a phenomenological law for the maximal quark-antiquark screening length ${L}_{\rm max}$ that captures leading velocity scaling and R-charge effects, with explicit forms in the quark-pair rest frame and in the plasma rest frame. They compute ${L}_{\rm max}$ for zero and nonzero R-charge cases, obtaining a universal high-velocity behavior ${L}_{\rm max}\sim \gamma^{-1/2}$ and revealing how R-charge density modifies the prefactors via functions ${\cal F}(v,\xi)$ and ${G(\xi)}$. The results provide a framework for phenomenological modeling of color screening in strongly coupled plasmas, including Lorentz-contraction and angular-averaging effects relevant to moving heavy quarkonia. The findings highlight that, despite intricate angular dependences, the leading velocity-driven screening remains governed by a small set of slowly varying functions, enabling practical extrapolation to QCD-like plasmas.

Abstract

We consider the interaction of a heavy quark-antiquark pair moving in N=4 SYM plasma in the presence of non-vanishing chemical potentials. Of particular importance is the maximal length beyond which the interaction is practically turned off. We propose a simple phenomenological law that takes into account the velocity dependence of this screening length beyond the leading order and in addition its dependence on the R-charge. Our proposal is based on studies using rotating D3-branes.

Figures (4)

• Figure 1: Wilson loop for the energy computation of a $q \bar{q}$ pair in a moving plasma (shaded rectangle).
• Figure 2: (a,b) Potential energy $\varepsilon$ plotted as a function of the separation $\ell$ for the values $v=0$, $0.5$, $0.7$, $0.9$ and $0.99$ (right to left) using the maximum and minimum subtraction prescriptions respectively. (c) Plots of various approximations to $\ell_{\rm max}(v)$, namely the result of numerical computation (solid), the approximation (\ref{['jhf9']}) (dashed) and its leading-order form (dotted).
• Figure 3: (a), (b) Plots of $\ell_{\rm max}(v)$ for the case of two angular momenta at $\theta={\pi \over 2}$ (with similar plots for $\theta=0$) with $\lambda=0.5$ and $\lambda=0.95$ respectively; The solid, dashed and dotted lines are as in Fig. 2(c). (c) Plot of the function $G(\xi)$ for the case of two angular momenta.
• Figure 4: (a), (b) Plots of $\ell_{\rm max}(v)$ for the case of one angular momentum at $\theta=0$ (with similar plots for $\theta={\pi\over 2}$) with $\lambda=0.7$ and $\lambda=1.4$ respectively; the solid, dashed and dotted lines are as in Fig. 2(c). (c) Plot of the function $G(\xi)$ for the case of one angular momentum.