Jets in strongly-coupled N = 4 super Yang-Mills theory

TL;DR

This work uses the AdS/CFT correspondence to model jets in strongly coupled ${\cal N}=4$ SYM by evolving open strings in AdS geometries at zero and finite temperature. The authors derive boundary baryon densities from bulk electromagnetic fields sourced by string endpoints, showing that endpoint motion rapidly becomes geodesic and that certain averaged jet observables depend only on asymptotic endpoint behavior. At zero temperature, the boundary baryon density concentrates into two forward cones with angular profiles fixed by the asymptotic velocity, while at finite temperature the jets exhibit a quasi-particle stage before thermal diffusion dominates, characterized by a diffusive relaxation with $D=1/(2\pi T)$. The results illuminate universal aspects of jet showering at strong coupling and offer insight into jet quenching and hydrodynamic transition in hot plasmas, illustrating how geometric optics and hydrodynamics emerge from string dynamics in AdS/CFT.

Abstract

We study jets of massless particles in N=4 super Yang-Mills using the AdS/CFT correspondence both at zero and finite temperature. We set up an initial state corresponding to a highly energetic quark/anti-quark pair and follow its time evolution into two jets. At finite temperature the jets stop after traveling a finite distance, whereas at zero temperature they travel and spread forever. We map out the corresponding baryon number charge density and identify the generic late time behavior of the jets as well as features that depend crucially on the initial conditions.

Figures (13)

• Figure 1: A plot of a falling string at zero temperature. The string is created at radial coordinate $u=u_0$ and expands as it falls. The endpoint trajectories, shown in the figure as solid green and orange lines, asymptotically approach light-light geodesics which are shown in the figure as dotted blue lines.
• Figure 2: A cartoon of the bulk to boundary problem at finite temperature. The endpoints of strings are charged under a $U(1)$ gauge field $\mathcal{A}_M$. The boundary of the geometry, located at radial coordinate $u = 0$, behaves like a perfect conductor and consequently, the presence of the string endpoints induces a mirror current density $j^\mu$ on the boundary. Via the AdS/CFT correspondence, the induced current density has the interpretation of the baryon current of a jet. Similarly, the presence of the string induces a perturbation $h_{MN}$ in the metric of the bulk geometry. The behavior of the metric perturbation near the boundary encodes the information contained in the perturbation in the SYM stress tensor due to the presence of the jet.
• Figure 3: A falling string at zero temperature. The solid blue curve represents the string at three successive times $t_1 = 15u_0, \, t_2 = 30u_0,$ and $t_3 = 45u_0$. The dashed red curve represents the null string approximation $\ell = t$ at the same three times. The orange and green solid curves represent the trajectories of the string endpoints while the dotted blue lines represent the geodesic fit the the endpoint trajectories. The numerical string was generated with the initial conditions in Eq. (\ref{['zeroTsymIC']}) at the large blue dot near the top of the plot. As time progresses, the difference between the null string and the numeric string becomes small compared to the overall size of the string.
• Figure 4: An asymmetric string at zero temperature generated from the initial conditions Eq. (\ref{['zeroTsymIC']}). The solid blue curve represents the string at three successive times $t_1 = 7u_0, \, t_2 = 14u_0,$ and $t_3 = 21u_0$. The dashed red curve represents the null string approximation $\ell = t$ at the same three times. The orange and green solid curves represent the trajectories of the string endpoints while the dotted blue lines represent the geodesic fit to the endpoint trajectories. As time progresses, the perturbations in the string profile inflate and become long wavelength. Correspondingly, the difference between the null string and the numeric string becomes small compared to the overall size of the string.
• Figure 5: A plot of the deviation $(\ell(t,\varphi)-t) \, t$ of the string shown in Fig. \ref{['zeroTasymSeq']} from the null string. According to the asymptotic expansion given in Eq. (\ref{['Rexpansion']}), for constant values of $\varphi$, $(\ell(t,\varphi)-t) \, t$ should be a linear function of $t$ at late times. The linearity of the plots at late times reinforces the form of the expansion in Eq. (\ref{['Rexpansion']}).