Momentum fluctuations of heavy quarks in the gauge-string duality

TL;DR

Using gauge-string duality, the paper computes two-point functions of the force on a heavy quark moving through a thermal N=4 SYM plasma. It develops a trailing-string description to derive real-time Green's functions for force fluctuations, connects them to momentum diffusion and jet-quenching concepts, and shows a strong γ-dependence of fluctuations that challenges simple Langevin pictures. The results yield κ_T, κ_L, hat_q_T, and hat_q_L with nontrivial velocity dependences and reveal violations of the Einstein relation at high v. The discussion cautions about mapping to QCD and outlines regimes where the trailing-string predictions could impact heavy-quark phenomenology in heavy-ion collisions.

Abstract

Using the gauge-string duality, I compute two-point functions of the force acting on an external quark moving through a finite temperature bath of N=4 super-Yang-Mills theory. I comment on the possible relevance of the string theory calculations to heavy quarks propagating through a quark-gluon plasma.

Figures (2)

• Figure 1: The thick red lines come from numerical evaluations of $g_T(w)$ and the most accurate form of $g_T(\ell)$ I was able to obtain. The thin black lines are the analytic approximations $g^{\rm approx}_T(w)$ and $g^{\rm approx}_T(\ell)$. The thin dash-dot line in the $g_T(\ell)$ plot is the residual, $g_T(\ell)-g^{\rm approx}_T(\ell)$. The thick dashed line is an approximation to $g_T(\ell)$ obtained by subtracting off only the leading $|w|^3$ behavior from $g_T(w)$ and numerically Fourier transforming the remainder out to $W=20$.
• Figure 2: (A) The Penrose diagram for $AdS_5$-Schwarzschild with conventions on the phase of $t$ specified. Increasing the real part of $t$ corresponds to moving upward on the R boundary and downward on the L boundary. Increasing $y$ means moving to the left in R and to the right in L. (B) The odd-numbered regions are narrow slices of the Penrose diagram corresponding to series expansions around $y=0$, $y_S$, and $1$. The even-numbered regions fill in between these series expansions. Note that $3$ and $\tilde{3}$ are disjoint, but $5$ is a subset of $\tilde{5}$. The corresponding regions $-1$ to $-6$ are the reflections of $1$ to $6$ through the point $U=V=0$.