Wake of color fields in charged ${\cal N}=4$ SYM plasmas

TL;DR

The authors extend holographic jet-quenching analyses to $R$-charged ${\cal N}=4$ SYM plasmas by computing the linear dilaton response to a moving test string in the rotating near-extremal D3-brane background. They formulate and solve the momentum-space dilaton equation, extract $\langle {\cal O}_{F^2} \rangle$ after subtracting near-field contributions, and demonstrate that wake-like, directionally peaked profiles persist for moderate rotation parameters $l$ (up to $l \lesssim h_1$). The numerical results reproduce known neutral-plasma behavior in the $l=0$ limit and show how recoil energy and opening angles depend on velocity $v$ and charge parameter $l$, indicating a robust wake picture in charged strongly coupled plasmas within a certain parameter range. Overall, the work supports the relevance of AdS/CFT-based wake analyses for jet-quenching-like phenomena in charged ${\cal N}=4$ SYM plasmas and delineates the regime of validity set by the rotation parameter.

Abstract

The dissipative dynamics of a heavy quark passing through charged thermal plasmas of strongly coupled ${\cal N}=4$ super Yang-Mills theory is studied using AdS/CFT. We compute the linear response of the dilaton field to a test string in the rotating near-extremal D3 brane background, finding the momentum space profile of $<\textrm{tr}F^{2}>$ numerically. Our results naively support the wake picture discussed in hep-th/0605292, provided the rotation parameter is not too large.

Figures (3)

• Figure 1: Distributions of equi-value lines of $\textrm{Re}B(K_1,K_\bot)$, $-\textrm{Im}B(K_1,K_\bot)$, $|B(K_1,K_\bot)|$, and $K_\bot|B(K_1,K_\bot)|$ in the momentum plane $(K_{1},K_{\bot})$, for angular momentum $l=0$, at speeds $v=0.75,0.90,0.95,0.99$. We have subtracted the near field contribution (\ref{['nearFieldContribution']}) from $B(K_{1},K_{\bot})$.
• Figure 2: Distributions of equi-value lines of $|B(K_1,K_\bot)|$ and $K_\bot|B(K_1,K_\bot)|$ in the plane $(K_{1},K_{\bot})$, for angular momentum $l=0.5$ and $1$, at speeds $v=0.75,0.90,0.95,0.99$. We have subtracted the near field contribution (\ref{['nearFieldContribution']}) from $B(K_{1},K_{\bot})$. The left eight ones are plots of $|B(K_1,K_\bot)|$ and $K_\bot|B(K_1,K_\bot)|$ for $l=0.5h_1$, and the right eight ones are the corresponding plots for $l=1.0h_1$.
• Figure 3: Distributions of equi-value lines of $|B(K_1,K_\bot)|$ and $K_\bot|B(K_1,K_\bot)|$ in the plane $(K_{1},K_{\bot})$, for $l=2$, at speeds $v=0.75,0.90,0.95,0.99$. The near field contribution (\ref{['nearFieldContribution']}) has been subtracted from $B(K_{1},K_{\bot})$. The left eight plots are computed using the boundary conditions (\ref{['bc']}), while the right eight ones are the corresponding plots with the new boundary conditions $W_{NH}|_{r=1.001h_1}=0$, $W_{NB}|_{r=800h_1}=0$ imposed.